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School District of Clayton Mathematics

Program Review

Interim update report to the Board of Education December 15, 2010

DRAFT FOR COMMITTEE REVIEW Prepared by Dottie Barbeau & Heidi Shepard

December 10th Draft to be sent to BOE on Friday December 14th Second Committee Discussion prior to Dec 15th BOE meeting December 15th BOE meeting

The following report is an interim summary of the internal processes of the K-12 math program review conducted by the Assistant Superintendent of Teaching and Learning and the Director of Assessment and Mathematics, in collaboration with the K-12 Mathematics Committee. A final report with recommendations will be submitted to the Board of Education in April 2011.

Mathematics Committee Members 2008-2011

Parents: Adam Ackerburg Parent Paula Brandenburg Parent Dave Curry Parent Trish Lopata Parent Ruth Wall Parent Administrators: MaryAnn Goldberg Principal, Wydown Middle School Annette Isselhard Principal, Meramec Elementary School Teachers: Trisha Brennan Captain Elementary School Terry Bladt Captain Elementary School Tyler Harger Captain Elementary School Carri McDougal Meramec Elementary School Geta Jackoway Meramec Elementary School Karen Finder Meramec Elementary School Susan Carter Glenridge Elementary School Gina McNamara Glenridge Elementary School Jessica Johnston Wydown Middle School Suellen Slais Wydown Middle School Melanie Surgener Wydown Middle School Jane Glenn Clayton High School Mike Rust Clayton High School Heidi Shepard Director of Assessment and Mathematics Dottie Barbeau Assistant Superintendent of Teaching and Learning

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Table of Contents

School District of Clayton Overview Mission Statement ...................................................................................................................... 5 Guiding Principles ...................................................................................................................... 5 Kid Check Statement ................................................................................................................. 5 Five-Year Long Range Planning Goals ...................................................................................... 6

School District of Clayton Mathematics Program

Philosophy .................................................................................................................................. 7 Enduring Understandings ........................................................................................................... 8

Introduction to Math Review ....................................................................................................... 9

Program Goals

Study Questions ....................................................................................................................... 10 Program Evaluation Design and Components ......................................................................... 11

Findings ........................................................................................................................................ 15

Recommendations ....................................................................................................................... 21

Timeline: Next Steps (December 15 – April 19, 2011) ............................................................. 25

Section I: Literature Review ...................................................................................................... 27

History: Debate over curriculum – Math Wars ........................................................................ 27 Need for International Level of Mathematics Preparedness .................................................... 31 What Have We Learned? .......................................................................................................... 42 Common Core State Standards ................................................................................................ 44

Section II: Student Achievement Data ...................................................................................... 50

Section III: Survey of Teachers, Parents and Students ........................................................... 52

Section IV: Guiding Principles and Program Specifications .................................................. 57

Appendix A: Student Achievement Data .................................................................................. 58

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Appendix B: Comparative Schools Studies .............................................................................. 99

Appendix C: Mathematic Benchmarks Comparisons ........................................................... 121

Appendix D: Math Survey Overview ...................................................................................... 150

Appendix E: Annotated Bibliography..................................................................................... 206

Appendix F: PISA Data ............................................................................................................ 227

Appendix G: TIMSS Data on High Achieving Countries Grades 4 & 8.............................. 228

Appendix H: Memo to Board of Education – Core Plus ....................................................... 236

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THE SCHOOL DISTRICT OF CLAYTON

District Mission The School District of Clayton will strive to develop in all its children the strength of character, the skills, the knowledge, and the wisdom necessary to build creative, productive lives and to contribute to a global society.

Guiding Principles

As a public school system dedicated to the education of all children who come to our schools, the School District of Clayton makes decisions using the following guiding principles: • The primary responsibility of our schools is teaching and learning. • Every member of the school community is both a learner and a teacher. • The individuality of every learner is recognized and welcomed. • The school culture nurtures both the joy of learning and the satisfaction of achievement. • Decisions are based on the best interests of students, balancing individual and group needs. • We value all members of our learning organization and demonstrate honesty, respect, and trust in all of our relationships. • Our schools promote equitable access to educational opportunities. • We encourage effective partnership with parents and the broader community. • We allocate our resources in a prudent manner consistent with our principles and goals. • Our shared vision of education empowers us to explore, experiment, and grow. • Effective assessment informs our decisions. • Learners accept responsibility for their learning and feel confident in their ability to create a positive future for themselves. • We provide a solid academic foundation, a broad choice of programs, and maintain high standards for all learners. • We are committed to diversity in our school population because it enriches our lives, mirrors our world, and reflects our future. • We strive to develop thoughtful citizens who contribute responsibly to their global community.

District Kid Check Statement

“We are responsible for student learning by knowing students well, by valuing every child by placing students at the center of every decision.”

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The School District of Clayton Five-Year Long Range Planning Goals

2008 – 2013 The identified program questions support and extend the 2008 School District Of Clayton’s five-year Comprehensive School Improve Goals:

By 2013 the written, instructed, and tested curriculum will reflect vertical and horizontal alignment of expected learner outcomes across all disciplines, courses, schools, and support programs.

By 2013 the District will have developed and implemented a district-wide professional

development plan that directly addresses expectations for teachers’ learning relative to established professional practice for each discipline and that provides adequate time, differentiated learning opportunities, and a common district wide focus in order to improve teaching practice and student achievement.

By 2013 interventions, structures and programs that are reflective of and responsive to

students’ strengths, abilities, learning styles, and career interests will be established at all levels in order to increase students’ self knowledge and achievement.

By 2013 high quality technology will be accessible to all students and staff and usage of that technology by both students and staff will meet the level of expertise established by state and national standards.

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The School District of Clayton Mathematics Program

Philosophy

We live in a world in which it is important for all students to have an understanding of mathematics. Students must realize the power of mathematics and its interrelationship with other disciplines, as well as the relationships among different strands of mathematics. Students are engaged in experiences that enable them to see the power of mathematics in modeling and predicting real world phenomena. Students realize the importance of mathematical communication as they express ideas in written and verbal form, and as they work together to solve problems and generalize results. The curriculum is developed to ensure that mathematics is taught to all depths of understanding. Students should be offered opportunities to learn mathematics in ways that make sense for them. The mathematics curriculum is delivered through teacher instruction that is supported by professional development, collaboration, and focused, sustained learning experiences. Assessment in mathematics should be aligned with instruction and tap into all aspects of mathematical knowledge. Student assessment serves as an opportunity for student growth toward high expectations. Multiple methods and sources of information strengthen the assessment process. The use of technology is embedded throughout the curriculum to increase mathematical opportunities and prepare students for the workplace of the future. Technology is used to enhance understanding and facilitate learning of mathematical concepts. The mathematics curriculum is a well-balanced program that values skills development through a variety of media, including multiple technologies. Families function as partners with the schools, encouraging their children to value a strong mathematics education. Home learning environments can enhance mathematics studies in school. As all partners understand the changing goals and priorities of school mathematics, student learning is supported. Those who understand and can do mathematics will have opportunities that others do not. Students have different needs, abilities, and interests, yet everyone must be able to use mathematics in his/her personal life, in the workplace, and in further study. The mathematics curriculum challenges students at all levels and prepares students for these future experiences. The curriculum provides graduates of the School District of Clayton with an excellent base of mathematical understanding that empowers them to be strong users of mathematics in their daily lives.

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MATHEMATICS

ENDURING UNDERSTANDINGS

Mathematics is a language of patterns and relationships.

Physical situations can be modeled mathematically.

Mathematical understanding is built through problem solving and reasoning.

Problems can be approached from multiple perspectives.

Mathematical ideas are communicated through a variety of representations.

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Introduction to the Math Review In April, 2009, the School District of Clayton launched a scheduled Mathematics Curriculum Review, a comprehensive, transparent, and position-neutral review into best practices in the teaching and learning of K-12 mathematics. In an effort to ensure that the math review was transparent and neutral, several additional community members were invited to join the existing math committee. The math review committee has functioned as a learning community and up to this point has met regularly over an 18-month period. The charge to the committee has included study in mathematical, cognitive, educational, cultural, political, and psychological issues, representing a very complex undertaking. The combined expertise and experience of the committee members, in addition to research, helped inform decisions, findings, and recommendations. Curriculum reviews occur on a regularly scheduled rotation, assuring a scheduled in depth study of content area challenges and advancements. However, this rotation of mathematics review occurs amidst a global inquiry into “world class” curriculum and “international benchmarking,” concepts designed to explain, measure, and promote curriculum and instruction to prepare students for the Global Age in which we now live. So, as we review the research on best practice in teaching and learning mathematics, we also will learn what it means to be “globally competitive,” and determine action steps to assure that the mathematics curriculum in Clayton meets or exceeds performance in countries around the world that have demonstrated through international assessments a high level of global proficiency. In this interim report we will cover the following sections:

• Findings and (interim) Recommendations • Literature Review • Student Achievement Data • Surveys of Teachers, Parents, Students, and Alumni

Students everywhere deserve the opportunity to succeed in the global economy and contribute as global citizens. Knowing what knowledge and skills they need to seize that opportunity, and designing schools that help to attain them, are essential for students to succeed in the interconnected world of the twenty-first century. Tony Jackson Vice President, Education Asia Society, 2010 A major lesson learned and a recurring theme of the discussions (is) that the strategies employed to move a system from bad to adequate (are) not the same and indeed might be antithetical to the strategies needed to move from good to great.

Council of Chief State School Officers International Perspectives on U.S. Education Policy and Practice: What Can We Learn from High-Performing Nations? 2010

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Program Goals The School District of Clayton has set forth one primary question to lead the mathematics program review:

What is the best mathematics curriculum design and program today, determined from a world class perspective?

In order to answer this question with clarity and evidence, we also are led by supporting questions in order to break the study into meaningful components.

1. What are the “best practices” for implementing curriculum to ensure mathematical growth for all students?

Literature Review Curriculum, program, and standards reviews Comparison schools studies

2. What evidence does the District have regarding the effectiveness of the current K-12 math program? Student achievement data Surveys Personal interviews and focus groups Comparison schools studies

3. How can the district effectively communicate information that will help parents support their

child’s mathematical growth?

Surveys Personal interviews and focus groups Comparison schools studies

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PROGRAM EVALUATION DESIGN For this program report, sources of information and data collection tools included, but are not limited to, the following:

Student achievement data Comparison schools studies Curriculum, program, and standards reviews Surveys Personal interviews and focus groups Literature Review

Student Achievement Data (Appendix A) The following data were internally collected and reviewed:

• Average Scale Scores for Algebra I End of Course Exam (2009, 2010) • Percent Scoring Proficient or Advanced on Algebra I End of Course Exam (2009, 2010) • National Percentiles on the PLAN Mathematics 2006-2009 • EXPLORE to PLAN and PLAN to ACT Growth, Class of 2009, 2010, 2011 • EXPLORE, PLAN and ACT Mathematics Performance by Math Sequences, Class of 2009

through Class of 2014 • Percent of Students Meeting ACT College Readiness Benchmark Scores by Race/Ethnicity:

MATHEMATICS (2009) • Percent of Students Ready for College-Level Coursework (2009) • SAT Math Scores for the top ten highest achieving school districts in the State of Massachusetts,

2006-2007 as reported on Massachusetts State Department of Education website, including data on Percentage of students taking Advanced Placement Calculus, AP Calculus AB, and AP Calculus BC

• Cohort Mathematics Data Over Time – this report looks at the total population of students as well as the cohort of African-American students and Caucasian students over time with regards to their performance on the MAP-Mathematics Assessment grades 3, 4, 5, 6, 7 and 8.

• Longitudinal Grade-Level Expectation Analysis Data – this report looks at each Grade-Level Expectation for grades 3, 4, 5, 6, 7 and 8 and the questions asked for the past 5 years on the MAP-Mathematics Assessment.

• Item Analysis of 6th Grade Placement Tests – this report looks at the mean and median of the Orleans-Hanna Algebra Readiness Test and the mean, median and item analysis of the District Computation Test.

• Grades 3-8 MAP Student Achievement 2006 – 2010 Percent Advanced/Proficient for White and African American Students

• Assessment Report presented by Heidi Shepard, Director of Assessment on December 1, 2010 to the Board of Education. Can be found on the math curriculum website - http://www.clayton.k12.mo.us/40372063214152777/site/default.asp?403610321114854303Nav=|&NodeID=350&40372063214152777Nav=|2478|&NodeID=2478

• Need to put in all the AA graphs completed for VICC

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Comparative Schools Studies (Appendix B)

• SAT Math Scores for the top ten highest achieving school districts in the State of Massachusetts, 2006-2007 as reported on Massachusetts State Department of Education website, including data on Percentage of students taking Advanced Placement Calculus, AP Calculus AB, and AP Calculus BC

• Comparison School Study Massachusetts and School District of Clayton as measured by ACT scores 2009

• Comparison of Instructional resources utilized by highest-performing school districts nationally in terms of Math ACT scores, 2009 (Project Blueprint Consortium, Ladue Consortium, ACT schools)

• Comparison of College Prep Study Achievement Data as measured by ACT Quartile Scores • Comparison of Neighboring Districts’ MAP Math Scores Grades 3-Algebra I

Mathematic Benchmarks Comparisons

• Elementary, Middle, High School benchmarks comparisons (Appendix C) • Massachusetts Common Core Plus recommendations October 2010 (Appendix C)

Surveys Administered and Reviewed (Appendix D) In order to inform decisions regarding the mathematics study and review, four data collection surveys were administered to primary stakeholders. In order to assure open and transparent collection of data, the School District of Clayton hired an outside consultant, Unicom ARC, to oversee the administration of surveys, collect all data, analyze all data, and report on the survey results directly to the Board of Education. The coordination of the survey with Unicom ARC was conducted through the District’s Communications Office under the direction of Mr. Chris Tennill, Chief Communication Officer. All survey questions were preapproved by the math review committee and Board of Education members prior to the launch of the surveys to assure confidence in survey results and responses of various stakeholders.

• School District of Clayton parent survey, including parents of elementary, middle school, and high school students, 2010

• School District of Clayton teacher survey, including elementary, middle school, and high school teachers, 2010

• School District of Clayton current students - elementary, middle, and high school, 2010 • School District of Clayton alumni survey, 2010

Personal interviews and focus groups

• Elementary, Middle School, and High School Teacher focus groups (2009) • Community member interviews (2009)

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Literature Review The mathematics committee read literally hundreds of articles related to teaching and learning math. Appendix E includes an annotated bibliography of main articles read to assure a deep understanding on the broad range of topics related to a quality mathematics review. Below is a brief list of key research articles relevant to understanding the complex issues under consideration by the math committee.

• The Math Wars, Alan H. Schoenfeld.

This article was submitted to us by community member, Marty Rochester, and is a very thorough and well written history of the math wars. Schoenfeld’s work is referenced in a great many of the articles we have read in the review. The author explains the complexity of the debate between traditional and reform mathematics and makes a case for “the middle ground.” This was one of the first articles read and discussed by the entire committee.

• What the United States Can Learn From Singapore’s World-Class mathematics System (and what Singapore can learn from the United States), American Institutes for Research

The full article (192 pages) can be found at http://www.eric.ed.gov/PDFS/ED491632.pdf. This article was selected because Singapore is one of the leading countries on the Trends in International Mathematics and Science Study (TIMSS) 2007 assessment. As a result, there has been significant comparison between U. S. and Singapore math programs. Although other countries also have demonstrated high achievement on the TIMSS, Singapore is most often selected for comparison because English is their academic language, and information from Singapore does not get lost in translation.

• Measuring Up: How the highest performing state (Massachusetts) compares to the highest performing country (Hong King) in grade 3 mathematics, American Institutes for Research

The full article (88 pages) can be found at http://www.air.org/files/AIR_Measuring_Up_Report_0427091.pdf. This article was reviewed because it focused on the top performing state in the U. S. and compared it to a top performing TIMSS 2007 country.

• The Report of the National Mathematics Advisory Panel. U. S. Department of Education

The full article can be found at http://www2.ed.gov/about/bdscomm/list/mathpanel/reports.html. No review of mathematics curriculum could be conducted without looking at the recent work of the Advisory Panel.

• Helping Children Learn Mathematics, Jeremy Kilpatrick and Jane Swafford, Editors, Center for

Education, National Research Council (NRC)

This article was selected because it was written by NRC to provide parents and community members a deeper understanding of mathematics curriculum. This article is a summary of the book Adding it Up.

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• Beyond Singapore’s Mathematics Textbooks, Patsy Wang-Iverson, Perla Myers, and Edmund Lim

W.K.

This was provided to show the breadth of the Singapore math program beyond the textbook series. The Singapore program depends on extensive teacher preparation and Lesson Study and cannot be implemented with just the purchase of the textbook and still expect equal success.

• Reaching for Common Ground in K-12 Mathematics Education, Deborah Loewenberg Ball, Joan Ferrini-Mundy, Jeremy Kilpatrick, R. James Milgram, Wilfried Schmid, Richard Schaar

This article was written by experts in mathematics education and the field of mathematics on what they both agree to be necessary components of a K-12 mathematics program.

• World-Class High Quality Mathematics Education for All K-12 American Students, Om P. Ahuja

This paper seeks to discuss issues in an international context related to the goal of creating world-class high quality mathematics education for all K-12 American students. In particular, the author also shares his reflections and depicts lessons from Singapore’s success story in mathematics education. Includes information on Singapore’s spiral approach without unnecessary repetition.

• Problem Solving in Mathematics Education in Finland, Erkki Pehkonen.

This article was selected because Finland is a top performing TIMSS country located in Europe, unlike the other two articles provided that were based on Asian countries. The Math Committee wanted to see what similarities exist between top performing Asian and European countries in mathematics.

• Six Principles for School Mathematics and the Standards for Pre-K-12 Mathematics, National Council of Teachers of Mathematics

This article is an overview of the principles and standards of mathematics that have been a driving force in mathematics curricula for the past twenty years.

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Findings THESE ARE INTERIM FINDINGS to be sent as a draft to math committee for review. FINAL REPORT IN APRIL 2011 Over the time period of approximately one year, the math review committee read and synthesized literally hundreds of research articles on the history of and best practice in the teaching and learning of mathematics, including international comparisons. In addition, comprehensive student achievement data sets were analyzed, and extensive surveys were conducted to gather input from the District’s stakeholders. The primary outcomes of this comprehensive review are reported below in key findings. Two outcomes, however, were overwhelmingly supported by research and are reported below as Primary Findings 1 and 2. PRIMARY FINDING 1. Mathematics instruction should promote mathematical proficiency: conceptual understanding, computational fluency, strategic competence, productive disposition, and problem solving; these proficiencies reinforce one another. (Source: National Research Council, “Adding It Up”) This finding was supported by the National Mathematics Advisory Panel. Across the nation, as well as in the Clayton community, debates have persisted for years over the best way to teach mathematics, traditional vs. reform efforts, basically placing the interests of mathematicians and mathematics educators in opposition. (See Literature Review section, Math Wars, page 27) The math committee found the research to be very clear that both conceptual knowledge and procedural knowledge in mathematics are critical and develop simultaneously, and that a quality mathematics program should be well balanced, ensuring adequate attention is given to both the development of basic skills and conceptual understanding. (See Literature Review section, On Common Ground, page 29) In a key research article, Helping Children Learn Mathematics, from the National Research Council (2002), neither extreme position of the “math wars” is correct because both are too narrow.

“When people advocate only one strand of proficiency, they lose sight of the overall goal. Such a narrow treatment of math may well be one reason for the poor performance of U.S. students in national and international assessments. Math instruction cannot be effective if it is based on extreme positions. Students become more proficient when they understand the underlying concepts of math, and they understand the concepts more easily if they are skilled at computational procedures.”

PRIMARY FINDING 2. Preliminary and ongoing professional development in math content and pedagogy was found to be a key contributor to success in all international programs studied. The District should align goals, policies, and resources to result in highly prepared teachers – prepared in the content of math and techniques of teaching math. As the math committee researched math programs nationally and internationally, we found the commitment to the teaching profession and in-depth focus of teacher professional development to be the most important component for success on international assessments. Singapore is recognized as a top world performer in the area of mathematics and most often used for comparison to the United States to identify areas for improvement. From selecting only top graduates from high school, two years of intense content training, mentorships, and regular half-day release from teaching for professional development, Singapore has made a tremendous commitment to adequately preparing its teachers for high quality math

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instruction. We found similar commitment to teacher training across other top international countries such as Hong Kong, Finland, and England. As the State of Missouri and School District of Clayton adopt and assess the Common Core State Standards (CCSS), we will experience earlier exposure to the mathematics strands of Number & Operations, and Algebraic Thinking across grades 3-8. However, as stated in International Perspectives on U.S. Education Policy and Practice (2010), “standards are not self implementing. Attracting, maintaining, and supporting high-quality teachers and school leaders is critical to enabling students to reach high standards and for driving schools forward.” As we implement the new CCSS, the need will increase for all elementary school teachers to have a solid understanding of and ability to teach mathematics through concepts of Algebra 1. “Lesson Study” as practiced in Asian countries is fast becoming of interest to school districts across the United States. The laser-focused attention to teaching strategies for each lesson taught enables teachers to plan for and implement high quality lessons for all students. The research clearly indicates that high performing nations do not have the discrepancy in scores for subgroups as found in our country. A strong, national curriculum, with focused and coherent content standards and pedagological structures provide for the needs of all students, including those in demographic and ethnic subgroups. In order to practice purposeful lesson study in mathematics, teachers need significant release time to meet with teams and collaborate intensively over the lessons to be implemented. The research is clear that significant and sustained teacher professional development is a foundation for success internationally. For example, a simple adoption of the Elementary or Secondary Syllabus of Singapore Math will not alone enable schools to attain the superior results found in Singapore schools. In order to develop international levels of math competency, teacher preparation and development will need to be supported and cannot be addressed without a substantial investment in math content-based professional development. Clear guidelines for content expectations and a plan for structuring the necessary professional development will need to be developed. FINDING 3. The District’s mathematics curriculum should be realigned and articulated to result in earlier learning of core concepts of algebra and geometry with a continuous and progressively increasing depth of knowledge so that by the end of 8th grade the majority of students will have completed Algebra 1 and be well prepared to master mathematics at the high school level. The adoption of the Common Core State Standards and the Massachusetts Core Plus Standards will support a realignment of the current curriculum to introduce concepts in fractions and algebra at least one year earlier at the elementary level. In addition, during the research to gather comparison data on like districts, most high achieving districts surveyed in Massachusetts reported that all but a small set of their 8th graders take the equivalent of high school level Algebra I. In Clayton, the Challenge Algebra students meet this benchmark, but this represents only approximately 38% of our 8th grade population. Currently, the “regular” 8th grade Algebra students, while learning algebra, do not cover all the concepts in an Algebra I course. The realignment of elementary and middle school curriculum will help Clayton to establish a more rigorous elementary and middle school math curriculum and provide opportunities for more 8th grade students to take Calculus during their senior year. It is acknowledged that not all students will (or even should be expected to) progress to attain Calculus as a senior, but the 8th grade algebra course will not be a “gatekeeper” preventing students from attaining Calculus as a senior.

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FINDING 4. The district’s mathematics program should assure a challenging, coherent, and focused preK-12 curriculum for ALL students. “All students can and should be proficient in mathematics.” (Helping Children Learn Mathematics, 2002). Although there is an appeal to making curriculum based decisions at the school level, when taken as a whole, this practice creates a lack of coherence. Fidelity to the curriculum, whatever that curriculum may be, is important to assure guaranteed teaching and learning experiences across and within the grade spans. Monitoring of the time dedicated to math instruction, fidelity to the math curriculum, and analysis of common assessments are key to assuring a guaranteed and viable written, taught, and tested curriculum. We are charged with meeting the needs of all students, from those who struggle the most to our most gifted individuals. A key finding in the literature when studying international mathematics programs is that our world competitors do not have the diversity-based discrepancies in student achievement found in the United States (and Clayton.) Models such as Lesson Study, as practiced in Asian countries, contribute to development of a universal, proactive curriculum with appropriately challenging learning experiences for all students. FINDING 5. Meta-analyses of research show that once the effects of student, teacher, and school factors are controlled for, there is little effect on learning attributed to the textbooks selected. Primary factors contributing to student learning are 1) a strong, aligned, standards-based curriculum, 2) high quality teachers and teacher development, 3) equitable education so that indicators such as socio-economic status, education of the parents, and available academic resources do not effect student achievement, and 4) quality internal and external assessments. Textbooks do not have a significant impact to high student achievement. Though textbooks are not as important as other areas the committee does believe a textbook serves as an important resource for both students and parents in students’ learning and parents’ understanding of the math being taught. FINDING 6. The surveys indicate that most teachers, parents and students offer a positive assessment of the mathematics instruction provided by the district. Total surveys received: 676 parent surveys, 74 teachers, 439 elementary students, 479 middle school students, 616 high school students, 295 alumni In general, teachers approve of the district curriculum, especially at the high school level. Overall students approve of and feel challenged by their mathematics instruction. Likewise, parents generally approve of the mathematics instruction and think it is adequately challenging for their children. Although a majority of our parents offered a positive assessment of our math instruction, 25.6% of the parent respondents are very/somewhat dissatisfied with our math program, and that number of dissatisfied parents is too high.

Two formal presentations on the surveys were given to the Board of Education, one in June and one in September, 2010. In order for the math review committee to further analyze the surveys for strengths and needed areas of improvement, we extracted responses that were reported by a “significant” population. To define “significant” we set a cut score of 30%+ dissatisfied/somewhat dissatisfied (with a 2% margin for error) and, 70%+ (with a 2% margin for error) satisfied/somewhat satisfied.

• Of the parent responses, 8 were found to have 30%+ dissatisfied/somewhat dissatisfied, and 10 were found to have 70%+ satisfied/somewhat satisfied.

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• Of the teachers, 4 were found to have 30%+ dissatisfied/somewhat dissatisfied and 15 were found to have 70%+ satisfied/somewhat satisfied.

• Of the students, 4 were found to have 30%+ dissatisfied/somewhat dissatisfied and 11 were found to have 70%+ satisfied/somewhat satisfied (See UNICOM.ARC Survey Highlights on math curriculum website.)

Three areas in the parent surveys were noted with high dissatisfaction responses (40%+), skill mastery before moving on at the elementary level (43.7), communication from teachers at the high school (45.5), and receiving enough information from the District to be able to help children with homework at the middle (40.6) and high school (53.8) levels. The parent, teacher, and student surveys all provided information we can use to help us make the most of our strengths and improve weaknesses. See Finding 7 below. FINDING 7. The parent surveys uncovered concern with communication, homework related issues, and concerns about their children not mastering skills before moving on to the next math concept. A significant number of parents were concerned about their ability to communicate with teachers about their children’s progress in math, as well as concerned about having adequate information to assist with math homework. Conclusions from the analysis of the elementary mathematics program in the area of strengths are that overall parents are satisfied with the teacher and feel that their child is prepared for math. Both parents and children were positive about mathematics. Areas that need attention according to the survey are better communication with parents regarding their child’s progress, making sure a child has mastered a skill before moving on and feeling adequately challenged in the area of mathematics. Conclusions from the analysis of the middle school mathematics program in the area of strengths are that overall, parents are satisfied with the teacher, with the amount of help that their child receives outside of class and feel that their child is prepared for math. Areas that need attention according to the survey are better communication with parents regarding their child’s progress, making sure a child has mastered a skill before moving on and that providing information to parents so they can assist their child with homework. Conclusions from the analysis of the high school mathematics program in the area of strengths are that overall the parents are satisfied with their child’s teacher and feel that their child is prepared for their current math class. Students felt that they were adequately challenged and that their teachers understand the math concepts that they teach. Areas that need attention according to the parent surveys are communication on their child’s progress in mathematics, information to assist with their child’s math homework, their child’s computation skills, their teacher’s ability to teach the class, and satisfaction with the math program. Both parents and students stated that a mutual area of concern is ensuring that a skill has been mastered before moving on.

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FINDING 8. Both parent and student surveys refuted a commonly held community belief that the majority of parents across the District seek paid, outside math tutoring for their children and do so because of a perceived gap in the District curriculum. 16.8% of elementary parent respondents reported to currently receiving tutoring for their child. Of those, 47.7% stated “I think there are gaps in the math curriculum, and additional tutoring makes up for these gaps” as the reason. 11.1% of elementary student respondents reported receiving paid assistance (tutoring). Of those, about half (55.3%) receive tutoring in math only. Of the students who responded positively to tutoring, 62.2% stated “I want to be better at math” as the reason.

24% of middle school parent respondents reported to currently receiving tutoring for their child. Of those, 21.5% stated “I think there are gaps in the math curriculum, and additional tutoring makes up for these gaps” as the reason. 10.5% of middle school student respondents reported receiving paid assistance (tutoring). Of those, 62.2% receive in math. Of the students who responded positively to tutoring, 57.6% stated “I mostly understand the concepts but need a little additional help with some of the work in my math class” as their reason.

17.4% of high school parent respondents reported to currently receiving tutoring for their child. Of those, 28.3% stated “I think there are gaps in the math curriculum, and additional tutoring makes up for these gaps” as the reason. 37.8% of high school student respondents reported they receive outside professional tutoring (22.7% for math only), and 71.8% of the students who received outside tutoring indicated they received tutoring for ACT/SAT prep and for test taking strategies.

73% of the alumni respondents who received tutoring (N=86) indicated they received tutoring for ACT/SAT prep.

74.6% of the alumni respondents who received tutoring for ACT/SAT prep (N=63) indicated they received tutoring for test taking strategies. FINDING 9. The teacher surveys uncovered a concern expressed by elementary teachers that the current Everyday Math assessments do not give adequate opportunities for students to demonstrate their understanding of all the goals for a unit. See Survey Highlights and analysis, page 52. FINDING 10. Student achievement item analysis of elementary and middle school MAP scores identified a concern at the middle school level in the area of algebraic relationships. High school student achievement data indicates concerns in subgroups of gender, ethnicity, and non-honors mathematics students. Elementary: When looking at the data from the Missouri Assessment Program assessments and 6th grade placement tests, the Mathematics Committee found no one learning strand to be of issue and only one grade-level expectation for grade 3 and grade 4 to be an area of concern. This leads to the conclusion there isn’t one deficient area or areas for the student population in the area of mathematics. The data does show an increase in student performance over the past 5 years regarding the number of students that are proficient or advanced as a total population. However, there is still concern with the subgroup of African-American students and students who receive Free/Reduced Lunch.

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Middle School: When looking at the data from the Missouri Assessment Program assessments and the EXPLORE test, the Mathematics Committee found concerns in the mathematics strands of Algebra, Geometric and Spatial Relationships, and Measurement. All three of these strands saw a decrease in proficiency as students progressed through middle school. When looking at the grade-level expectations there were both areas of strengths and weaknesses and an identification of misalignment to the currently implemented mathematics curriculum. The data does show a strong performance among our Caucasian students though there is reason for concern among our African-American students and our students who receive Free/Reduced Lunch. When looking at the data for our high achieving students in the area of mathematics we see a strong performance in the number of students scoring advanced on the MAP, scoring proficient or advanced on the Algebra 1 End-of-Course exam, and meeting the benchmark on the EXPLORE test. However, for students not in Challenge Algebra in 8th grade, there is concern in the number of students not meeting the benchmark on the EXPLORE test. High School: When looking at the data from the PLAN and ACT test the Mathematics Committee found the data to show strength in the overall performance of the PLAN and ACT. When looking at the ACT profile from the 2010 school, the upper quartile, median and lower quartile were at or above the ACT benchmark in the area of mathematics. There is concern with the difference between male and female performance on the PLAN and ACT in the area of mathematics, with males outperforming females. There is also concern with performance of African-American students and the percent of students in the non-honors sequence meeting the benchmark on the PLAN, given during a student’s sophomore year. FINDING 11. Overall, the student achievement data confirm known district strengths, such as ACT and Advanced Placement performance, and known problems, such as the percentage of students in non-honors classes meeting the benchmarks for the EXPLORE and the PLAN, and the achievement gap experienced by demographic and ethnic categories.

The achievement gap is predictable according to race and socioeconomic status, which should not be an acceptable outcome for students in the School District of Clayton.

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Recommendations DRAFT FOR THE MATH COMMITTEE TO REVIEW

This section contains the recommendations relevant to the findings.

To significantly improve teachers’ mathematical knowledge for teaching mathematics in the School District of Clayton, the District should: 1/2. Provide regular, ongoing professional development for teachers to ensure that teachers have a solid

content knowledge, are able to communicate and teach for conceptual understanding of mathematics, and use effective pedagogy.

a. Establish the goal that Clayton math teachers, grades 1-5, will have a minimum content proficiency equal to that of an Algebra 1 course.

b. Establish the goal that Clayton math teachers, grades 6-8, will have a minimum content proficiency in Geometry and Algebra II.

3. A significant mathematics professional development commitment needs to be made for all preK-12 math teachers. The professional development should include significant amounts of time for teacher collaboration, and Lesson Study, as supported throughout our research of the literature on high academic achievement of international leaders in mathematics. Teachers need to be able to learn from each other, analyze achievement data, plan for instruction, meet needs of diverse learners, and ensure both horizontal and vertical alignment of the curriculum.

The challenge of implementing Recommendations 1-3 is complex, partly due to current elementary teachers’ requirements for the elementary generalist license (does not require proficiency to Algebra 1), but also because of the impact on budgeting and scheduling of professional development. It may be necessary for the District to implement Recommendations 1-3 in stages, first focusing on grades 3-5 and middle school teachers where the greatest change in curriculum is occurring, then turning to the content knowledge development of teachers in the remaining elementary grades. Professional development needs will be assessed and a plan to address these needs will be developed.

To significantly improve the rigor of the current District mathematics curriculum, the District should:

4. Adopt the Common Core State Standards and additions provided by the Massachusetts Core Plus Standards (2010) for the PreK-12 mathematics curriculum. At grades 3-5 the Fractions and Algebraic Thinking standards will be introduced one grade earlier than provided in our current curriculum, which in turn allows for earlier development of algebraic ideas as students progress into middle school and on to high school.

5. Align the middle school mathematics curriculum to the Common Core State Standards Accelerated Traditional Pathway and the Massachusetts Core Plus Standards, placing the standards for grades 6, 7, and 8 into the 6th and 7th grade curriculum. This, together with the increased rigor at the elementary level with the adoption of the CCSS should provide a challenging, coherent, and focused preK-12 mathematics curriculum. The realigned curriculum should result in earlier development and learning of core concepts of algebra and geometry with a continuous and progressively increasing depth of knowledge so that by the end of 8th grade the majority of the students will have mastered the

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equivalent of an Algebra 1 course and be well prepared for college-prep or honors mathematics at the high school level.

6. At minimum, align the high school curriculum to the Common Core State Standards and the Massachusetts Core Plus Standards.

7. Adopt mathematics curriculum materials/resources that address mathematical fluency specified in the National Research Council’s report Adding It Up, addressed in the Common Core State Standards and part of Clayton Mathematics Guiding Principles and Program Specifications: conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), adaptive reasoning, and strategic competence.

8. Set clearly defined benchmarks aligning with the Common Core State Standards and the Massachusetts Core Plus Standards with examples for each grade level and course K-12.

9. The Assistant Superintendent, Superintendent and Director of Assessment and Mathematics recommended to the Board of Education to not bring forward the Core Plus Math series for adoption in our new curriculum review cycle. Clayton High School is experiencing challenges due to offering multiple sequences at the College Prep level. The current College Prep track at Clayton High School consists of two sequences of study – traditional and integrated math. Multiple sequences cause challenges across the board, from administrators to teachers, students and parents.

• Having multiple sequences reduces the number of sections for any one course making it more

difficult to do scheduling for students. • Having multiple sequences causes an excessive number of courses within one department, which

in turn creates a large number of singletons. • Singletons do not allow for collaborative study among math teachers. Lesson Study, as we well

know from our research on math instruction in Japan, has been proven to improve instruction, thus student achievement.

• Moving to one sequence for the college prep students will provide more flexibility for students in their schedules.

• Multiple tracks at the college prep level often cause angst for freshman parents who are making placement decisions.

• A significant portion of our community, through our parent survey, indicated they were not in support of our integrated math sequence.

10. Instruction at all grade levels should be well balanced and focus on the integration of conceptual and procedural knowledge. The balanced curriculum should provide for problem solving, reasoning, procedural fluency and development of basic skills.

11. A value added analysis should be purchased as part of our District’s Assessment Framework and reporting protocol. This value added assessment will monitor students’ progress with regard to the benchmarks for their particular grade level and occur three times during the school year. Implementation of this assessment will be launched Fall 2011. The Superintendent has recommended and supports this purchase.

12. Along with value added assessment, other formative assessments will be used to identify students who are below grade level for targeted intense intervention. These programs will be monitored for success

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and the effectiveness of the intervention being used by math specialists, subject area manager or department chair, with results being shared with the Director of Assessment and Mathematics.

13. Along with value added assessments, other formative assessments should be used to determine student mastery of concepts before moving on during the school year. This ongoing formative assessment information needs to be clearly explained and communicated to parents in an ongoing manner. Student achievement levels should be routinely monitored for progress, by the school level math specialist, subject area manager, or department chair, with results shared with the Director of Assessment and Mathematics at the end of each semester and/or more frequently if the results dictate a need.

14. The District should investigate the causes of the problem currently experienced at the middle school in the strands of algebraic relationships and implement research based remedies.

15. The District should research/investigate successful middle school programs and factors influencing their success (adopted curriculum materials, implementation of curriculum, time of instruction, number of sequences offered per grade level, etc.).

16. Parents should be provided opportunities to learn about District mathematics instruction to be able to assist and reinforce homework and student learning at home. Throughout our research on parent involvement we encountered recommendations to offer parent support in understanding the mathematics being taught to their children.

17. Survey data indicated an increased need for communication between the teacher and parent regarding student achievement. Increased communication should be monitored by the Director of Assessment and Mathematics until follow up surveys indicate the problem has been addressed.

18. The District should address the academic achievement gap between subgroups of students.

It is recognized that there has been a dedicated effort across the District for many years designed to remedy the inequities experienced by our African American students, however, according to our latest data, there has been little improvement over time. All children in our district deserve for us to figure this out. Academic achievement is predictable in our district according to race and socioeconomic status, with a clear progression of achievement from our African American students who qualify for Free and Reduced Lunch, who experience the least success, to our resident white children, who experience the most success with the curriculum. Academic achievement should not be dependent upon race and/or poverty.

19. Since it has been ten years since new textbooks were reviewed by the math faculty and math committee, it is recommended that all levels - elementary, middle, and high school – review current texts, including digital text options, to determine if new materials are available that better meet District standards, student achievement needs, and math review recommendations than those currently in use.

Curriculum is multifaceted, including the standards to which we align, the instructional practices used by teachers, the assessments we use to measure student performance against the standards, and the materials, textbooks, and resources teachers and students use as tools and supports during the teaching and learning process.

Stakeholders throughout the District should be invited to provide input to the math committee. Any change from the current curriculum materials should be grounded in solid research, proven favorable

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and sustained outcomes by other high achieving districts or high achieving pilot districts, and be at minimum aligned to the Common Core State Standards. Textbooks should be reviewed and decided upon against best alignment to agreed-upon standards (CCSS, for example) as well as balanced approach (conceptual and procedural) to teaching and learning math as proposed by the National Math Advisory Panel. Consideration of materials should include digital learning materials, resources, and/or texts.

Given the abundant research on the primary impacts on student learning, the District should recognize that math textbooks are not the “silver bullet” for increasing student performance but are tools and resources utilized in the teaching and learning of mathematics. The charge to the math committee was to conduct a program review, not just a textbook review.

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School District of Clayton Mathematics Curriculum Review Timeline

(Revised) November 19, 2010 Primary Research Question: What is the best mathematics curriculum design and program available today, determined from a world class perspective? October 15, 2010 Friday Memo

Student achievement data: K-8 • MAP item analysis longitudinal data • MAP cohort longitudinal data • Grade 5 Middle school placement data

October 29, 2010 Friday memo Student achievement data: 9-12

• PLAN data • ACT data • Explore-PLAN, PLAN-ACT growth data

November 19, 2010 Friday Memo Frameworks/standards comparisons Clayton, Massachusetts, Common Core Standards International comparisons Hong Kong, Singapore, Clayton template/matrix comparison

December 15, 2010 Board of Education Update Analysis of mathematics literature review, student achievement data, survey indicators, and Common Core Standards

December 2010 PISA (Programme for International Student Achievement) data Release of data is scheduled for sometime in December

January 11, 2011 Parent Evening – 7:00 – 9:00 PM Clayton High School Auditorium PISA results will be shared with the community, placing the results in the context of international benchmarking and the Common Core Standards

January 19, 2011 Board of Education Meeting Update on Textbook Selection Process and Timeline

January24-28, 2011 Phase 1: Initial review of available texts Math Committee and Faculty will conduct an initial review of all available texts to select elementary, middle, and high school materials to move forward to Phase 2. Selections from the Common Core State Standards, Massachusetts Plus Standards, and National Math Panel Recommendations will be used as minimum criteria to advance texts to Phase 2.

February 2011 Phase 2: Curriculum materials and texts review Evaluate Phase 2 materials and texts. Vendors will schedule evening presentations during this month for Math Committee, faculty, and community members. Dates will be determined as soon as Phase 1 is completed. All interested stakeholders are invited to attend vendor presentations and review the Phase 2 instructional materials/resources to provide input on selections. All instructional materials under consideration will be available at a text review location at the Administration Building for open review and feedback by stakeholders.

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For each Phase 2 selection, the math faculty will compare two strands, Numbers and Operations, and Algebra, using the Common Core State Standards, Massachusetts Plus Standards, and National Math Panel Recommendations Pilot Options – Selected lessons to be piloted. Site Visits – If necessary, faculty will visit schools currently using materials under consideration.

March 2011 Phase 3: Final Selection of Math Materials and Resources Math Committee reviews feedback and makes final selections for recommendation to Board of Education.

April 13, 2011 Board of Education Meeting Review and Recommendations – The Math Curriculum Committee will present a recommendation to the Board of Education in April.

Summer 2011 PD begins and continues for full implementation as recommended by math review

Professional Development – The Math and Professional Development Departments will organize summer professional development for those teachers launching new materials in the Fall of 2011. Professional development will be a necessary component during the implementation year and following years as layers of recommendations go into effect.

Fall 2011 Implementation of recommendations. Parent Communication – Schools and members of the Mathematics Curriculum Committee will hold Parent Nights to help the parents become familiar with changes that have occurred within the math program. The committee will also be looking to other methods of communication that can be sustainable over time.

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Section 1: Literature review

History: Debate over curriculum – Math Wars Need for International Level of Mathematics Preparedness International Leaders in Rigorous Mathematics What Have We Learned? Common Core State Standards

History: Debate over curriculum: The Math Wars In our review of the “Math Wars” the math committee came across literally dozens of articles and sources on the topic, covering everything from far extremes on the sides of traditionalists and reformers to finding common ground. The following recap of the history of the Math Wars comes from two of the most influential and comprehensive articles, each presenting historical perspectives and facts in a professional and understandable manner, and each proposing a viable solution to the controversy over the “best” way to teach mathematics. The two articles are:

• The Math Wars, (2004) Alan Schoenfeld • Reaching for Common Ground in K-12 Mathematics Education, (2005) Deborah Loewenberg

Ball, Joan Ferrini-Mundy, Jeremy Kilpatrick, R. James Milgram, Wilfried Schmid, Richard Schaar

Traditionalists fear that reform-oriented, “standards-based” curricula are superficial and undermine classical mathematical values; reformers claim that such curricula reflect a deeper, richer view of mathematics than the traditional curriculum.

Schoenfeld (2004)

What, exactly, is a “math war?” For more than ten years the “math war” battle has raged over the teaching of mathematics, and that battle rages over mostly opposing perspectives of traditionalists and reformers, mathematicians vs. mathematics educators. As in any war, there are underlying conditions that lead to disagreement, and those disagreements can build until eventually reaching a tipping point. That tipping point was the onset of what we know as the math wars. Although there is evidence of debate over mathematics starting in the early 1900’s, generally, it is agreed that the beginning of the math wars we know today began in 1957 when the Soviet Union launched Sputnik. Our country was in the midst of the cold war and Khrushchev was threatening world domination. With the launch of Sputnik the United States was caught off guard, and so came a cry for the U.S. to take action to clearly claim superiority in mathematics and science. In response, the National Science Foundation (NSF) developed what came to be called “the new math,” essentially modern content added to the existing math and science curriculum. According to Schoenfeld, the new math quickly became a social issue and a lesson to be learned by reformers. Teachers did not have the necessary background and preparation to teach the new math and parents did not feel competent to help their children with the new math. Without the support of the stakeholders, by the early 1970’s the new math was on the way out, and in its place came a call to go

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“back to basics.” Math curriculum went back to what had been in place before, focusing primarily on skills and procedures. For the next ten years, with the “back to basics” curriculum in place, student performance showed no improvement in basic skills, and also showed poor performance at problem solving. In 1980, the National Council of Teachers of Mathematics (NCTM) published An Agenda for Action, calling for mathematics curriculum to replace “back to basics” with a focus on developing students’ problem solving skills. Textbook publishers inserted problem solving editions, but generally the changes were minor, and math curriculum was for the most part unchanged. The influential report, A Nation at Risk, was published in 1981 highlighting the serious vulnerability the United States faced with rising influence and innovation taking place around the world. In addition, in the early 1980’s, the Second International Mathematics Study (SIMS) was performed and clearly showed the poor performance of U.S. students when compared to international peers. Both of these key indicators highlighted the crises in mathematics and were seen as a rally for change, but gave no clear direction to what the changes should be, and because of political problems faced at the time by the NSF, there was no clear leadership to step in. But, it was clear that mathematics instruction needed to both teach the math content and teach students how to think mathematically. In 1989, the National Research Council (NRC) published Everybody Counts which highlighted some of the problems surrounding traditional curriculum, called for “mathematics for all,” and influenced the release of the Standards, also in 1989, by NCTM to help outline a revision of school mathematics. Materials began to be developed to support the Standards, but because they were vague, some materials were good but some were “considered pretty flaky,” for which NCTM and the Standards were blamed. The Standards, however, did usher in an age of standards and standards based curriculum. In 1992, California published its Mathematics Frameworks and “took the Standards somewhat further along the lines of reform.” New textbooks that supported the Standards and California Frameworks were quite different from the traditional texts. The seriousness, sequence of instruction and practice problems that parents and teachers were used to were replaced with colorful pages, fun names, sidebars, etc. and set off the same problems that occurred in the new math days. Now, with the introduction of the standards aligned curriculum, the name “new-new math” came to be. In addition, the standards aligned curriculum was harder to teach and called for teachers to support students in different ways as students explored, made sense of the math, and became productive. This process was “alien” to those who were raised with traditional math instruction. According to Schoenfeld,

“…advocates of reform committed some mistakes that were the public relations equivalent of handing the traditionalists a gun and saying “shoot me.” For example, the California Learning Assessment System released a sample mathematics test item in 1994 in which students were asked to arrive at an answer and then write a memo justifying it. The sample response from a student who got the right answer but failed to write a coherent memo was given a low score, whereas a sample student response that contained a computation error but a coherent explanation was given a high score. Editorial comments raked the California Learning Assessment System (and reform in general) over the coals, saying that in the new, “fuzzy” math, being able to write baloney counted more than getting the right answer.”

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In the late 1990’s, for the first time full cohorts of students had worked through an entire sequence of reform mathematics. According to Schoenfeld, “The evidence at this point is unambiguously in favor of reform (see, e.g., ARC Center, 2003;p Senk & Thompson, 2003). But such data turn out to be largely irrelevant to the story of the math wars. When things turn political, data really do not matter…..Conclusion: we cannot and must not inhibit the extensive field testing of well-designed reform curricula, but we must at the same time be vigilant.” (Schoenfeld, 1994, pp. 73-74) By 1998, the math wars were raging on a national scale. Then Secretary of Education, Richard Riley, “pleaded for civility.” But the antireform networks were well organized and were able to launch large scale efforts against districts implementing reform math. According to Schoenfeld, antireform tactics can become “rather nasty…. strong similarity between the tactics used by some antireformers and the antirevolution tactics used by ‘creation scientists’…. Generally speaking, those on the reform side of the wars have been slow to develop effective techniques to counter the most extreme attacks of the antireformers.” Interestingly, as time passes and our national agenda focuses on high mathematics learning for all students, we are being directed to a common ground. There are still “vocal extremes, partly by screaming for attention and partly by claiming the middle ground (“it’s the other camp that is extreme”), that have exerted far more influence than their numbers should dictate.” (Schoenfeld, pg 281) According to Schoenfeld,

The democratic language of the Standards and its successor, Principles and Standards for School Mathematics, clearly situates core reform efforts under the umbrella of education for democratic equality (schools should serve the needs of democracy by promoting equality and providing training for citizenship) and education for social mobility (schools should serve the needs of individuals by providing the means of gaining advantage in competitions for social mobility). In contrast, the traditional curriculum, with its filtering mechanisms and high drop-out and failure rates (especially for certain minority groups) has had the effect of putting and keeping certain groups “in their place.” Thus the traditionalist agenda can (at least by its likely impact) be seen as situated under the umbrella of education for social efficiency (schools should serve the needs of the social and economic order by training students to occupy different positions in society and the economy). In a zero-sum game, those who hold privilege are best served by the perpetuation of the status quo.(pg 281) Resolution is essential because the math wars, like all wars, involve casualties to innocent parties. When extremists battle, the “collateral damage” to those in the middle (in this case, America’s children, who should be well served by mathematics education) can be significant. (Schoenfeld, pg 254)

Finding Common Ground: In December 2004, a small group of nationally prominent and influential mathematicians and mathematics educators came together to discuss the foundations of the ongoing math debate. Their hypothesis was “that there might be common ground in K–12 mathematics education that would begin the process of changing the focus toward student outcomes instead of controversy.” (Schaar, 2005). Their work focused on finding topics and positions upon which both sides could agree, resulting in common ground on “key perspectives on K-12 mathematics education.” After only two sessions, they were able to come to agreement around very specific principles, evidence that there is common ground between mathematicians and mathematics educators and that we can work together to improve mathematics

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education in our country. Although the two sessions mainly focused on K-8 topics and issues, they committed to continued conversations and sessions to find common ground K-12. The areas in which the researchers were able to come to agreement and find common ground include the topics shown below. The notes below have been shortened representing highlights, however the full report can be found at http://smu.edu/education/teachereducation/graduate/Milgram_rdg_comm-schmid.pdf. Fundamental Premises All students must have a solid grounding in mathematics to function effectively in today’s world. The need to improve the learning of traditionally underserved groups of students is widely recognized; efforts to do so must continue. Students in the top quartile are underserved in different ways; attention to improving the quality of their learning opportunities is equally important. Expectations for all groups of students must be raised. By the time they leave high school, a majority of students should have studied calculus.

1. Basic skills with numbers continue to be vitally important for a variety of everyday uses. 2. Mathematics requires careful reasoning about precisely defined objects and concepts. 3. Students must be able to formulate and solve problems.

Areas of Agreement Discussions of the following items are often riddled with difficulties in communication, making it sometimes confusing to determine whether and how much disagreement exists. Issues also arise from a confounding of a mathematical idea with its implementation in the classroom. For example, the fact that algorithms have often been taught badly does not imply that algorithms themselves are bad.

A. Automatic recall of basic facts: Certain procedures and algorithms in mathematics are so basic and have such wide application that they should be practiced to the point of automaticity.

B. Calculators: Calculators can have a useful role even in the lower grades, but they must be used carefully so as not to impede the acquisition of fluency with basic facts and computational procedures.

C. Learning algorithms: Students should be able to use the basic algorithms of whole number arithmetic fluently, and they should understand how and why the algorithms work.

D. Fractions: Understanding the number meaning of fractions is critical. Ratios, proportions, and percentages cannot be properly understood without fractions.

E. Teaching mathematics in “real-world” contexts: It can be helpful to motivate and introduce mathematical ideas through applied problems.

F. Instructional methods G. Teacher knowledge

Researchers contributing to Reaching for Common Ground in K-12 Mathematics Education: Deborah Loewenberg Ball, Joan Ferrini-Mundy, Jeremy Kilpatrick, R. James Milgram, Wilfried Schmid, and Richard Schaar

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Need for International Level of Mathematics Preparedness and International Benchmarking

Countries around the world, including the United States, are paying increasing attention to international comparisons as they seek to improve their own educational systems. The three most well known and comprehensive of the international benchmarks are: the Organization of Economic Cooperation and Development (OECD), an organization of 30 member countries; Programme for International Student Assessment (PISA); and the Trends in International Mathematics and Science Study (TIMSS). (See “A Brief History of International Assessments” below, on page 41) The following data outlines the challenges that lie ahead of the U.S. as we work toward world leadership in mathematics: According to the Asia Society’s article, International Benchmarking (2010), by authors Andreas Schleicher and Vivien Stewart:

In the second half of the 20th century, the US set the world standard of excellence. It was the first country to pursue and achieve mass secondary education and mass higher education. As a result it has the largest supply of highly qualified people in its adult labor force of any country in the world. This stock of human capital has helped the US become the dominant economy in the world and take advantage of the globalization and expansion of markets. However, what was once the gold standard – high school graduation – has now become the norm in most industrialized countries. …. The US has fallen from 1st to 10th…. Not because the US high school graduation rates dropped but because graduation rates rose so much faster elsewhere….. The US ranks only 18th among the 24 OECD countries…. South Korea illustrates the pace of progress that is possible. Two generations ago, the country had the economic output of Afghanistan today and ranked 24th in education output among the 30 OECD countries. Today, South Korea is the world’s top performer in secondary school graduation rates, with 93 percent of an age cohort obtaining a high school degree, compared with 77 percent in the US.

According to the 2006 PISA assessment: Science: The US ranked 21st out of the 30 OECD countries Math: The US ranked 25th out of the 30 OECD countries

Reading: The US ranked 15th of 29 OECD (a printing error invalidated the 2006 PISA in reading) So, what can we learn from high-performing nations that achieve more with less?

o Strong performance and improvement are always possible. Countries such as Japan, Korea, Finland, and Canada display strong overall performance and equally important show that a disadvantaged socioeconomic background does not necessarily result in poor performance in school.

o Performance is not simply a matter of money, because only Luxembourg, Switzerland, and

Norway spend more per student that the US.

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Key Features that play a substantial role in preparing countries to meet the world’s new definition of excellence:

1. High Universal Standards. By setting national standards, countries seek to raise aspirations and define educational excellence, make educational objectives transparent to students, and provide a framework for teachers while avoiding the risks of narrowing the curriculum and teaching to the test.

2. Accountability and Autonomy. ….in most of the countries that performed well in PISA,

schools now have substantial autonomy with regard to adapting and implementing education content and allocating and managing resources. The strongest effects on outcomes seem to be where schools have substantial control over two key areas – budgeting and hiring.

3. Strengthened Teacher Professionalism. High performing countries recruit strong teacher

candidates, promote sound subject-matter preparation, offer induction programs that support new teachers during their first few years of teaching, and offer ongoing professional development. …..Singapore is an excellent example of best practices. Singapore recruits teachers from the top 30% of each high school class, provides financial support for their initial training, gives teachers 100 hours per year of professional development, and offers a choice of three career paths – master teacher, content specialist, or principals.

4. Personalized Learning. In all school systems, there is a correlation between student

socioeconomic status and performance, but systems vary enormously in the extent to which socio economic status predicts such performance…..In Sweden, for example, school funding formulas link additional resources to the magnitude of the challenges that schools face; in Finland, schools organizes more than one-fifth of student learning time outside formal classroom settings. …..some countries also show that excellence can become a consistent and predictable education outcome: In Finland, the country with the strongest overall results in PISA, the performance variation among schools amounts to only 5% of students’ overall performance variation. Parents can rely on high and consistent performance standards in whatever school they choose to enroll their children.

So, What Does It Mean?

….No nation has a patent on excellence. All are striving to modernize their education systems to meet the demands of the global knowledge economy and produce a new global skill set.

…..The US has much to offer….from its research on child development, to its institutional and instructional innovations, to its more “creative” culture. It also has much to learn from other countries in which educational excellence is more systemic. Success will go to those countries that are swift to adapt, slow to complain, and open to change.

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The Building Blocks of World-Class Education (Barber, 2010, Excellence in Education Summit) The following chart synthesizes the literature and international assessment analyses on what constitutes a “world-class education” as determined by the most successful countries on international assessments such as the TIMSS and the PISA.

Standards and Accountability

Human Capital &

Collective Capacity

Structure and Organization

Globally benchmarked standards

Recruit great people & train them well

Effective, enabling, central departments and agencies

Good, transparent data & accountability

Continuous improvement of pedagogical skills and knowledge

Capacity to manage change and engage communities at every level

Every child is on the agenda. Always in order to challenge inequality.

Great leadership at the school level

Operational responsibility and budgets significantly devolved to the school level

According to Barber (2010), the journey to “world-class” performance has four steps as shown below. The key is to hold to accountability, but give educational leaders and teachers space to make decisions and innovate.

Poor to Fair

Fair to Good

Good to Great

Sustaining Great

According to Barber, from recent years of study of international benchmarking results, the above items represent the “knowns” for attaining a world class education system. However, we are not yet as certain of the “unknowns” listed below:

• 21st century curriculum With the rapid increase of technology and digital learning opportunities, we don’t yet know what will become the ideal 21st century curriculum. That is developing right now and being piloted and tested in progressive countries all around the world.

• The human capital model The current classroom/seat time model is outdated. • School & out of school The latest technologies that provide high quality high school course

access to students is rapidly expanding to all children and all grade levels, and will include out of school and hybrid models.

• Knowledge management technology

Achieving the basics of literacy and numeracy

Getting the foundations in place

Shaping the professional

Improving through peers and innovation

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International Leaders in Rigorous Mathematics: The Search for High and Equitable Achievement

From the Council of Chief State School Officers (CCSSO) article: International Perspectives on US Education Policy and Practice: What Can We Learn from High-Performing Nations? 2010) …the US is widely viewed as a leader in educational innovation but a failure in taking successful practice to scale. …According to CCSSO, … participating countries discussed the key drivers of their school reform. Excerpts from the study are shown below: Detailed information on key high achieving international countries: Australia: Australia, a federal system of six states and two territories, is a relatively high-performing country on international assessments, but concerned about growing competition from other countries that are improving faster and its relative lack of equity, Australia has recently (2008) undertaken a major program of reform. This includes the development of a national curriculum in all major subjects (English, mathematics, science, history, geography, world languages, and the arts), the first federal system to do so; new assessments in literacy and numeracy and sample assessments in other subjects; significant new financial resources; and a school reporting service (MySchool.com), which includes private as well as public schools.5 Finland: Schools have played an important role in transforming Finland from a traditional industrial-agrarian nation into a modern innovation-based knowledge economy. In the 1980s, Finland had a tracked and low-achieving education system that was well below the level of other European countries. Today, Finland is the highest achieving country on PISA international tests of student achievement, has very equitable outcomes (less than 5% variation in performance between schools), and a graduation rate of 96%, all achieved with moderate overall spending. The Finnish approach is quite distinct. Although the curriculum framework is set at the national level, the design of the curriculum is left to teachers. The Finnish system places enormous emphasis on and trust in high-quality teachers. Teaching is a highly admired profession by young Finns because of the autonomy and responsibility it entails. Only one in ten applicants is accepted into teaching. This emphasis on high-quality teachers is combined with a systematic early intervention system whenever a child falls behind, individualized learning plans, a philosophy of “teach less, test less, learn more,” and high quality vocational as well as academic paths in upper secondary school. While many other countries are trying to improve their achievement through focusing on one or two subjects, standardization, and test-based accountability, the “Finnish way” has only light national direction, a broad and individualized curriculum that emphasizes creativity and a global outlook, and gives trust-based responsibility to excellent teachers. (International Benchmarking, Asia Society, 2010) Singapore: In 1965, Singapore became independent and was a poverty stricken island with no natural resources, low education levels and conflicting ethnic groups. Now it has world-class math, science, and technical education, and has attracted high tech industries, global banks, petrochemical, and pharmaceutical industries by closely linking its economic development strategy and its education system. The American Institute for Research published in 2005 an extensive, in-depth review of Singapore’s math system. A (lengthy) synopsis of the article follows:

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“What the United States Can Learn From Singapore’s World-Class Mathematics System (and what Singapore can learn from the United States): An Exploratory Study (January 28, 2005) Prepared for: U.S. Department of Education Policy and Program Studies Service Prepared by: American Institutes for Research [Alan Ginsburg-US Ed; Steven Leinwand-AIR; Terry Anstrom-AIR; Elizabeth Pollock-AIR] [Principal Editor – Elizabeth Witt] Notes from the article:

-‐ Singapore has a world-class mathematics system with quality components aligned to produce students who learn mathematics to mastery

-‐ Components include: o Highly logical national mathematics framework o Mathematically rich problem-based textbooks o Challenging mathematics assessments o Highly qualified mathematics teachers whose pedagogy centers on teaching to mastery

-‐ Singapore provides its mathematically slower students with an alternative framework and special assistance from an expert teacher

-‐ The study showed that it takes more than using the Singapore math textbooks to replicate the success of Singapore. Professional development improved the odds of success, as did serving a stable population.

-‐ QUOTE: “The U.S. mathematics system has some features that are an improvement on Singapore’s system, notably an emphasis on 21st century thinking skills, such as reasoning and communications, and a focus on applied mathematics. However, if U.S. students are to become successful in these areas, they must begin with a strong foundation in core mathematics concepts and skills, which, by the international standards, they presently lack.” Preferred Features Of The Singapore Mathematics System Frameworks

-‐ A mathematically logical, uniform national framework that develops in-depth at each grade guides Singapore’s mathematics system. The U.S. system, in contrast, has no official national framework. State frameworks differ greatly; some resemble Singapore’s, whereas others lack Singapore’s content focus.

o Balanced set of mathematical priorities centered on problem solving o Emphasis on computational skills along with more conceptual and strategic thinking

processes o Covers a relatively small number of topics in-depth o Topics are carefully sequenced grade-by-grade o Follows a spiral organization in which topics presented at one grade are covered in later

grades, but only at a more advanced level o Students are expected to have mastered prior content, not repeat it

-‐ Singapore recognizes that some students may have more difficulty in mathematics and provides them with an alternative framework; the U.S. frameworks make so such provisions

o Alternative framework for lower performing students covers all the math topics in the regular framework, but as a slower pace and with greater repetition

o Slower students are provided with extra help from well-trained teachers

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Textbooks -‐ Singapore’s textbooks build deep understanding of mathematical concepts through multistep

problems and concrete illustrations that demonstrate how abstract mathematical concepts are used to solve problems from different perspectives. Traditional U.S. textbooks rarely get beyond definitions and formulas, developing only students’ mechanical ability to apply mathematical concepts

o Clear difference in how mathematical concepts are developed o Singapore texts are rich with problem-based development o U.S. textbooks the illustrations make virtually no contribution to helping students

understand how to use the mathematics to solve real-world problems o Singapore illustrations feature a concrete to pictorial to abstract approach o Singapore illustrations demonstrate how to graphically decompose, represent, and solve

complicated multistep problems o U.S. texts’ lack focus o Singapore students are expected to complete about one thorough lesson focused on a single

topic per week, while U.S. students are expected to complete about one lesson on a narrowly focused topic each day

o Both Singaporean and U.S. textbooks “spiral” mathematical content – returning in successive years to the same concepts.

o The U.S. textbooks spiral includes significant repetition and reteaching of the same content in two or three consecutive grades

o Singapore textbooks do not repeat earlier-taught content, because students are taught to mastery the first time around

Assessments

-‐ The questions on Singapore’s high-stakes grade 6 Primary School Leaving Examination are more challenging than the released items on the U.S. grade 8 National Assessment of Education Progress and the items on the grade 8 state assessments

o Singapore’s grade 6 assessment contains almost double the percentage of constructed-response items. This is an important difference because constructed-response questions generally are more suitable for demonstrating students’ higher-level cognitive process in mathematics.

o Singapore uses a value-added contribution to student achievement Teachers

-‐ Singaporean elementary school teachers are required to demonstrate mathematics skills superior to those of their U.S. counterparts before they begin teacher training. At every phase of pre- and post-service training, they receive better instruction both in mathematics content and in mathematics pedagogy.

o Singapore teachers continue to improve their knowledge and skills through 100 hours of required annual professional training

Areas Of Strengths In The U.S. Mathematics System Compared With Singapore’s System

-‐ The U.S. frameworks give greater emphasis than Singapore’s framework does to developing important 21st century mathematical skills such as representation, reasoning, making connections, and communication.

-‐ The U.S. places a greater emphasis on applied mathematics, including statistics, probability, and real-world problem analysis.

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QUOTE: “Even though Singapore’s textbooks would benefit from more real-world applications, their emphasis on conceptual development of mathematics and problem-based learning make them superior to U.S. textbooks overall.” Conclusion on Mathematics Frameworks

-‐ Singapore’s framework offers a highly logical mathematical approach to setting mathematical priorities and content across the primary grades

-‐ The approach balances conceptual, computational, and strategic problem-solving skills. -‐ Mathematical topics and outcomes are precisely specified, and content is sequenced across grades

with a spiral approach that limits topic repetition -‐ Develop a strong foundation in numbers while also developing basic geometric and statistical

concepts. -‐ Singapore’s unique emphasis on multistep word problems, in particular, is consistent with its

emphasis on promoting conceptual understanding through solving thoughtful problems -‐ The separate measurement strand and the emphasis on data analyses and statistics in the NCTM

and state standards, which stress important mathematical skills that students need to develop in a digital world, elevate the importance of applied mathematics.

-‐ Recommendations: o Consider strengthening overarching process priorities like reasoning and making

connections across mathematical topics. o Consider adding an additional process standard for addressing “computational fluency” o Organize content grade by grade instead of by grade bands o Tightening up their standards, eliminate content that is inappropriate to a grade as well as

excessive repetition of content across grades o Retain their emphasis on data analysis and probability o Adopt mathematical frameworks and supporting policies for slower students with

additional class time in which to learn core introductory math content

Conclusion on textbooks -‐ Singapore textbooks are tightly aligned with the topics and outcomes in the Singapore framework. -‐ Students’ conceptual understanding is developed through lessons that explain concepts through

problem-based learning exercises that illustrate how concepts are applied from different perspectives in both routine and non routine ways.

-‐ Concrete and pictorial illustrations in the texts use visual explanations to help student understand abstract mathematical concepts

-‐ Extensive and challenging problem sets reinforce strong conceptual understanding and support procedural fluency

-‐ U.S. nontraditional text poses interesting real-world problems and uses illustrations that demonstrate the practical application of math topics, the Singapore texts do not do

Recommendations

-‐ Align text with state frameworks and develop rubrics that identify which chapters and lessons line up with which items in the state standards

-‐ Influence textbook publishers to publish books that contain fewer topics that are developed through extended lesson that use problem-based learning

-‐ Textbook should focus on limited number of topics at each grade, that use rich problem-based learning to promote mathematical understanding, and that have extensive and challenging problem sets

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-‐ Textbooks should expose students to the multistep non routine problems found in Singapore textbooks

-‐ U.S. text books should: o Increase the number, variety, and overall use of pictorial representations directly tied to

concepts in textbooks o Increase the use of mathematical connections, particularly between and among

mathematical concepts o Increase the number of multistep and non routine problem to enhance the ability to develop

stronger conceptual understanding and problem-solving capabilities Conclusion on Assessments

-‐ Singapore assessments are more likely to o Require preparing constructed responses o Solving for intermediate unknowns o Develop non routine solutions

-‐ U.S. needs to make their tests more rigorous if it is to match Singapore’s impressive performance on international assessments

-‐ Include more items that measure advanced levels of mathematics proficiency Conclusion on Teachers of Mathematics

-‐ School systems should consider reviewing their current professional development policies and practices for supporting highly qualified teachers to determine whether they provide ongoing and sustained professional development opportunities tied to content delivery

-‐ School systems should consider having teachers specialize in mathematics and other content areas from the earliest grades, a practice that is the norm in the Chinese education system, a system that produces teachers with in-depth understanding of mathematics

Conclusion of U.S. Singapore Pilot Sites

-‐ Singapore math textbooks produced uneven improvements in the pilot sites -‐ Smaller sites with stable enrollments and those that enrolled gifted students made remarkable

progress -‐ Singapore textbooks should be introduced with considerable care. [ because the curriculum is not

repeated in the Singapore textbooks in the same way it is in U.S. textbooks, teachers of students in upper elementary grades, students transferring into a school from a non-Singapore textbook school, and students who may be weaker in math face special challenges in using the Singapore textbooks]

-‐ Participation in professional development tailored to implementing the content of the Singapore curriculum and text is essential.

If you plan to introduce Singapore math textbooks: -‐ Districts should be prepared to provide teachers with extensive professional development

opportunities to help them use Singapore math textbooks effectively. Professional training requires a commitment of time, and teachers need to be encouraged and recognized for their in service efforts.

-‐ The ideal time for districts to begin using Singapore books is in kindergarten and first grade because the textbooks are built around a spiral curriculum that builds new content on top of previously taught mathematics.

-‐ Districts should offer weaker students more time and extra help in mathematics. They should identify weaker students beginning in grade 1 and provide them with extra mathematics.

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-‐ Districts should make sure that any misalignment between the Singapore textbook and state math frameworks and assessments is addressed in advance. Before adopting the Singapore math text, districts should conduct a curriculum alignment analysis and identify supplementary math material, preferably from other Singaporean text, to fill any gaps.

-‐ Districts should use the current U.S. edition of the Singapore text. Teachers in the pilot sites noted that the older edition contain terms and examples unfamiliar to U.S. students.

Hong Kong: A review of a key article comparing Massachusetts and Hong Kong in mathematics follows: “Measuring Up: How the highest performing state (Massachusetts) compares to the highest performing country (Hong Kong) in grade 3 mathematics” (April 2009) American Institutes for Research

-‐ Steven Leinwand (American Institutes for Research) -‐ Alan Ginsburg (U.S. Department of Education)

QUOTE: “The higher cognitive difficulty level of the items on the Hong Kong assessment, especially in the core areas of numbers and measurement, is a distinguishing feature of the comparison with the Massachusetts assessment. It is important that assessment problems establish expectations for students’ deep conceptual understanding and students’ ability to develop strategies for applying conceptual learning even in the very early years of mathematics learning.” Hong Kong assessments are:

-‐ Hong Kong and Massachusetts have about the same percentage of number strand items but Hong Kong is more mathematically demanding

-‐ Involves larger numbers -‐ More complicated arithmetic -‐ Higher cognitive complexity in the number strand items -‐ More likely to involve multiple steps, multiple representations, examining concepts from different

perspectives and occasionally handling novel situations -‐ Hong Kong places more emphasis on measurement -‐ Measurement items are more likely to test the application of concepts -‐ Measurement problems require students to apply, adapt, or integrate knowledge of measurement

concepts, tools, and principles -‐ Multistep problems in the measurement strand -‐ Both Hong Kong and Massachusetts include challenging geometric problems that involve

construction and manipulation of figures that require students to apply what they know -‐ Massachusetts includes the Algebra strand, Hong Kong does not. Though many of their algebra

problems would also fall in the number strand and the pattern problems are straightforward

Comparison -‐ Hong Kong’s grade 3 assessment items emphasize the number and measurement strands (75% of

the items), which form the core of a strong foundation in early mathematics understanding. -‐ Hong Kong items are more likely to require students to construct a response (86%) than are

Massachusetts items (29%) -‐ The Hong Kong assessment contains a somewhat higher percentage (71%) of items with graphical

content than the Massachusetts assessment, at 57%. -‐ The Hong Kong assessment has 37% of its items requiring more than simple computational

difficulty, compared with only 3% for the Massachusetts assessment.

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-‐ The percentage of Hong Kong items with middle or high cognitive complexity was 55%, or two thirds more than the 34% of middle or high cognitive demand items on the Massachusetts assessment.

An examination of the items rated as more cognitively demanding, most from the Hong Kong assessment, shows that the following features increase mathematical rigor:

-‐ Developing multistep solutions that require students to carry out a series of mathematical procedures rather than a solution with single calculation or one-step mathematical analysis

-‐ Solving problems in non routine situations that require students to adapt what they have learned from familiar situations

-‐ Satisfying multiple problem conditions simultaneously -‐ Correctly differentiating among multiple representations of the same concept -‐ Translating different representations to a common representation before completing solution -‐ Finding the most efficient solution strategy among alternative solution strategies -‐ Having to manipulate problem elements to obtain the solution -‐ Selecting the appropriate information from a set that includes extraneous information

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A Brief History of International Assessments: Throughout the duration of the Math Wars, the “fires have been stoked” between traditionalists and reformers with each release of international assessments showing the United States students scoring well behind international competitors. With each international report of the United States’ comparatively low levels of achievement, there has been somewhat of a “your way hasn’t worked” response, with a follow up movement to either go “back to basics” or reform the way we “do math.” From the early 1960’s to current day, the United States has participated in numerous international assessments, and yet still remains woefully behind our international competitors in the area of mathematics. Finding common ground is now more important than ever so that everyone is working together to solve our nation’s math achievement problems, and that we are all collaboratively learning from both sets of experts on how to assure globally competitive mathematics for our nation’s children. In the late 1950’s, about the time of the Sputnik launch and the United States being caught off guard in math and science achievement, the International Association for the Evaluation of Educational Achievement (IEA) was founded to develop a way to measure and compare educational variables across countries. At the time the IEA was founded, the role that formal education played in economical development was becoming more apparent, but at the same time a way to measure educational productivity was lacking. In 1965, the IEA conducted its first successful large-scale quantitative international study in mathematics, the FIMS (First International Mathematics Study). Participants included Australia, Belgium, England, Finland, France, Germany, Israel, Japan, Netherlands, Scotland, Sweden, and the United States. Over the years, IEA has continued to conduct international studies in school subjects of math, reading, science, and other subjects. Typically, in an IEA study, data are collected in 3rd or 4th grade, and also in 7th or 8th grade. The following timeline is reported by the IEA on their “Brief History of IEA” website: http://www.iea.nl/brief_history_of_iea.html.

• First International Mathematics Study (FIMS), conducted in the 1960s, involved 13-year-old students from 10 countries and students in their last year of secondary school from 10 countries.

• The Second International Mathematics Study (SIMS), performed in the early 1980s, involved 13-year-old students from 18 countries and students in their last year of secondary school from 13 countries.

• The First International Assessment of Educational Progress, carried out in 1988, involved 13-year-olds from six countries.

• The Third International Mathematics and Science Study (TIMSS) was conducted in 1995. Forty-five countries participated in TIMSS, with more than half a million students encompassing five grades tested. The overall aims of the study were to measure the mathematics and science achievement in the various target populations and to identify the major in- and out-of-school determinants of the educational outcomes. IEA also carried out a special sub-study of mathematics and science curricula in these countries.

• The subsequent data collection for TIMSS (at present known as Trends in Mathematics and Science Study) took place in 1999, 2003 and 2007. The next TIMSS is scheduled for spring 2011.

In January 1990, President Bush established a specific goal for mathematics and science education—two subject areas critical to successful competition among international math leaders: "By the year 2000, U.S. students will be first in the world in science and mathematics achievement." To measure progress toward that objective, there was an increasing interest in the periodic international assessments of student performance in mathematics and science and as such, the United continued to participate in TIMSS, and in 2000 also looked to the PISA for data on U.S. student achievement.

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• The Programme for International Student Assessment (PISA) is a recognized and influential

international assessment that informs global math achievement levels for high school students. PISA is the only international education survey to measure the knowledge and skills of 15-year-olds, an age at which students in most countries are nearing the end of their compulsory time in school.

• PISA was officially launched in 1997, with the first survey taking place in 2000, the second in

2003, the third in 2006, and the fourth in 2009. Future surveys are planned in 2012, 2015 and beyond. The School District of Clayton participated in the 2009 PISA with results expected in December 2010. Add PISA data info here when we get it. Appendix F.

Ten years following President Bush’s proclamation of our goal to be First in the World in mathematics, we still are scoring well below that of international countries such as Singapore, Hong Kong, England, and Finland. Insert here the TIMSS comparison work from the math committee from Dec 14th Appendix G (country comparison chart that Heidi created goes in appendix) What Have We Learned? Several of the most influential studies in the area of mathematics have in fact been in response to international assessment results, such as the Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics, A quest for Coherence (2006, following the 2004 TIMSS), and the Final Report of the National Mathematics Advisory Panel (2008, following the 2004 and 2007 TIMSS). Report of the National Mathematics Advisory Panel 2008 Core Principles Of Math Instruction

• The areas to be studied in mathematics from pre-kindergarten through eighth grade should be streamlined and a well-defined set of the most important topics should be emphasized in the early grades. Any approach that revisits topics year after year without bringing them to closure should be avoided.

• Proficiency with whole numbers, fractions, and certain aspects of geometry and measurement are the foundations for algebra. Of these, knowledge of fractions is the most important foundational skill not developed among American students.

• Conceptual understanding, computational and procedural fluency, and problem solving skills are equally important and mutually reinforce each other. Debates regarding the relative importance of each of these components of mathematics are misguided.

• Students should develop immediate recall of arithmetic facts to free the “working memory” for solving more complex problems.

• The benchmarks set forth by the Panel should help to guide classroom curricula, mathematics instruction, textbook development, and state assessments.

• More students should be prepared for and offered an authentic algebra course at Grade 8. • Algebra should be consistently understood in terms of the “Major Topics of School Algebra,” as

defined by the National Math Panel. • The Major Topics of School Algebra include Symbols and Expressions; linear equations;

quadratic equations; functions; algebra of polynomials; and combinatorics and finite probability.

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Student Effort is Important Much of the public’s “resignation” about mathematics education is based on the erroneous idea that success comes from inherent talent or ability in mathematics, not effort. A focus on the importance of effort in mathematics learning will improve outcomes. If children believe that their efforts to learn make them “smarter,” they show greater persistence in mathematics learning. Importance of Knowledgeable Teachers

• Teachers’ mathematical knowledge is important for students’ achievement. The preparation of elementary and middle school teachers in mathematics should be strengthened. Teachers cannot be expected to teach what they do not know.

• The use of teachers who have specialized in elementary mathematics teaching could be an alternative to increasing all elementary teachers’ mathematics content knowledge by focusing the need for expertise on fewer teachers.

Effective Instruction Matters • Teachers’ regular use of formative assessments can improve student learning in mathematics. • Instructional practice should be informed by high-quality research, when available, and by the best

professional judgment and experience of accomplished classroom teachers. • The belief that children of particular ages cannot learn certain content because they are “too

young” or “not ready” has consistently been show to be false. • Explicit instruction for students who struggle with math is effective in increasing student learning.

Teachers should understand how to provide clear models for solving a problem type using an array of examples, offer opportunities for extensive practice, encourage students to “think aloud,” and give specific feedback.

• Mathematically gifted students should be allowed to accelerate their learning. • Publishers should produce shorter, more focus and mathematically accurate mathematics

textbooks. The excessive length of some U.S. mathematics textbooks is not necessary for high achievement.

Effective Assessment The National Assessment of Education Progress (NAEP) and state assessments in mathematics should be improved in quality and should emphasize the most critical knowledge and skills leading to Algebra. Importance Of Research The nation must continue to build the capacity for more rigorous research in mathematics education to inform policy and practice more effectively.

NCTM (National Council of Teachers of Mathematics) 2008 • A coherent curriculum effectively organizes and integrates important mathematical ideas so that

students can see how the ideas build on or connect with other ideas. • Problem solving, reasoning, connections, communication, and conceptual understand are all

developed simultaneously along with procedural fluency. • Students should have frequent opportunities to formulate, grapple with, and solve complex

problems that require a significant amount of effort. They should then be encouraged to reflect on their thinking. Problem solving is an integral part of all mathematics learning.

• Being able to reason is essential to understanding mathematics. By developing ideas, exploring phenomena, justifying results, and using mathematical conjectures in all content areas and at all grade levels, student should recognize and expect that mathematics makes sense.

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• Students must demonstrate understanding of numbers and relationships among numbers with a focus on the place-value system. Students must develop understanding of number operations and how they relate to one another.

• Students should become proficient at using mental math shortcuts, performing basic computations mentally, and generating reasonable estimates for situations involving size, distance, and magnitude.

• Algebraic concepts and skills should be a focus across the pre-K-12 curriculum. • Geometry is a natural place for the development of students’ reasoning and justification skills. • Students should have experience in formulating questions, designing simple surveys and

experiments, gathering and representing data, and analyzing and interpreting these data in a variety of ways.

• Basic ideas of probability form the underpinnings of statistical inference. • Alignment and coherence of curriculum, standards, and assessments are critically important

foundations of mathematics education. Common Core State Standards Mr. Mike Cohen, President of Achieve, sent on June 22, 2010 a memo to the Achieve Board of Directors explaining the Common Core State Standards (CCSS), including specific references to the CCSS in Mathematics. This memo clearly addresses the background of the standards and related questions pertaining to mathematics – excerpts of Mr. Cohen’s memo follow: The CCSS in mathematics build on and make a number of significant advances over most existing state standards. The K-5 standards provide students with a solid foundation in whole numbers, addition, subtraction, multiplication, division, fractions and decimals—which help young students build the foundation to successfully apply more demanding math concepts and procedures, and move into applications. They also provide detailed guidance to teachers on how to navigate their way through knotty topics such as fractions, negative numbers, and geometry, and do so by maintaining a continuous progression from grade to grade. Having built a strong foundation in K-5, students can do hands on learning in geometry, algebra and probability and statistics in the middle grades to gain a rich preparation for high school mathematics. Students who have completed 7th grade and mastered the content and skills through the 7th grade will be well prepared for algebra in grade 8. The high school standards call on students to practice applying mathematical ways of thinking to real world issues and challenges; they prepare students to think and reason mathematically across the major strands of mathematics, including number, algebra, geometry, probability and statistics. Note that the CCSS promote rigor not simply by including advanced mathematical content, but by requiring a deep understanding of the content at each grade level, and providing sufficient focus to make that possible. Will the CCSS in mathematics prepare high school graduates for college and careers? We compared the CCSS with the ADP Benchmarks in mathematics and found that they are as rigorous as, and in some cases extend beyond, the ADP Benchmarks in defining the knowledge and skills demanded of all students. Both the ADP Benchmarks and the CCSS identify a college- and career-ready set of standards as a subset of the high school standards, and also include standards that define more advanced content beyond that bar. In both cases the intent is that all students would be required to take a high school curriculum aligned with those standards. All students, particularly those who plan to pursue advanced study in math or prepare for STEM careers, are expected to take the more advanced math as well. (Note: ADP = American Diploma Project benchmarks)

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The college- and career-ready standards defined in the CCSS are slightly more rigorous than the ADP Benchmarks, as they contain several additional advanced topics. To learn the material incorporated in the college- and career-ready standards, a student would have to take a course sequence of Algebra I, Geometry, and Algebra II (or a 3-year sequence of integrated math that covers the same material), the same course sequence Achieve has recommended for high school graduation requirements in the ADP Network. The CCSS are more rigorous than the ADP benchmarks in another respect. Beyond the college- and career- ready bar, the CCSS contain content for a fourth year of additional math, intended to prepare students for college-level calculus or college-level statistics. The ADP Benchmarks were not as ambitious. How do the CCSS in mathematics compare with the expectations of high performing countries? When compared to the standards of high performing countries, the CCSS are equally rigorous. Furthermore, the CCSS tend to be similar in terms of focus and coherence, and sometimes even more demanding. The secondary level standards compare favorably with those in high performing countries such as Singapore and Japan; for example the CCSS college- and career-ready standards are comparable in rigor to the “O” levels in Singapore and other Commonwealth countries (which opens the door to postsecondary technical training) and the more advanced math standards in the CCSS are as rigorous as the “A” levels through Pre-calculus content, which set the standard for university admissions. Students who meet the CCSS when they complete high school will be internationally competitive, as well as ready for postsecondary education and training. The elementary grades standards provide unprecedented focus and coherence for U.S. standards, in contrast to the mile wide and inch deep character of the current U.S. elementary math curriculum. Like standards in high performing countries, the CCSS are highly focused in the early grades on a handful of topics, allowing the time for in-depth teaching and learning so that students can develop the conceptual understanding, procedural fluency and mathematical reasoning that provide a solid foundation for learning more advanced mathematics in middle and secondary school. The elementary grade standards draw heavily on the standards from Japan, Hong Kong and South Korea, which provide a strong focus on teaching numbers and the properties of operations as the foundation for learning algebra and more advanced math. In contrast, most U.S. state standards (drawing heavily on the work of the National Council of Teachers of Mathematics) introduce algebra through the creation, description and extension of number patterns. While number patterns have some value in preparation for algebra, they are usually overemphasized to the detriment of instruction on number and properties of operations leaving students ill prepared for algebra. Because of this different focus, some states that adopt the standards will experience some disruption in the early grades, as topics will be introduced at different grade levels than at present. Similarly, comparisons with standards in different high performing countries (e.g., Singapore) will also show that some topics are introduced in later grades in the CCSS than in some high performing countries. Such grade-by-grade differences do not speak to the rigor of the CCSS. Rather, they reflect a choice about the better approach to providing a solid foundation for preparing students for algebra in 8th grade, and as such are relatively unimportant.

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How do the CCSS in mathematics compare with the Massachusetts and California standards? Both Massachusetts and California have highly regarded, rigorous mathematics standards; Achieve has used both for years as benchmarks against which to compare other state standards. The Massachusetts standards are widely credited as the foundation for the state’s steady improvement and internationally competitive performance. Because leaders in both states have appropriately made clear that they will not adopt the CCSS if they are less rigorous then current state standards, the rigor of the math standards is a topic of considerable interest and debate in each. Our analysis indicates that overall the three sets of standards are similarly rigorous, and describe substantially similar bodies of knowledge, though there are some noteworthy differences between the CCSS and the particular state standards. Algebra is the gateway for high school mathematics and preparation for postsecondary education. California requires all students to take Algebra I in 8th grade, while Massachusetts does not. The 8th grade CCSS include a significant amount of Algebra I content, but the full coverage of Algebra I is treated as a high school level course. However, the CCSS are explicitly designed with California in mind; students who meet the standards at the end of 7th grade should be prepared for Algebra I, and the Algebra I course standards can be “moved down” to 8th grade if necessary. We believe that the CCSS do a better job-preparing students for algebra in 8th grade than either the California or Massachusetts standards. As noted above, the CCSS have incorporated the approach taken by Japan, Hong Kong and South Korea, particularly in the K-4 standards, whereas neither Massachusetts nor California use that approach. Further, the CCSS provide a precise definition of the core concepts and skills students must master in grades 5-7 to be well prepared for algebra (key aspects of rational numbers and geometry), and a very clear grade-by-grade progression of topics in each area. In contrast the California standards in particular are significantly less precise, and neither Massachusetts nor California nor provide a sufficiently clear progression across the grades. Therefore, students in each state must make a more abrupt transition from the concrete skills learned through 4th grade to the more abstract reasoning required for algebra, rendering them less well prepared than students who participate in the CCSS would be. One by-product of the approach taken in the CCSS is that most data, probability and statistics content is not introduced until 6th grade, while Massachusetts and California begin this work in 2nd grade. However, the strong foundation in number sense provided by the CCSS will allow students to progress quickly in middle and high school through data, probability and statistics, culminating in content that is generally more rigorous than that found in many states. Overall the content of the secondary level math standards is quite similar. There are relatively minor differences among the three sets of standards when comparing the content of particular courses; the biggest differences arise because the California math standards include math through Calculus (although Calculus is not required of students), while the Massachusetts and CCSS include content through Pre-calculus. Additionally, the CCSS pay greater attention to creating and using mathematical models based on real-world contexts than do either Massachusetts or California. Comparisons about the rigor of the secondary level standards are quite tricky. The CCSS specifically define the knowledge and skills necessary for success in entry-level credit –bearing courses and 21st century careers. Neither Massachusetts nor California similarly identifies college- and career-ready standards. While the CCSS Initiative appropriately steered clear of defining course-taking requirements for high school graduation, to meet the college and career ready standards all students would have to

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take 3 years of math through Algebra II, or the equivalent. ADP has urged states to require all students to complete a curriculum aligned with the college and career ready standards, including math through Algebra II. Twenty-one states now require students to complete such a course of study. In contrast, California requires students to take only 2 years of math including Algebra I. Massachusetts delegates decisions about course taking requirements to local school districts. Both states have rigorous graduation exams – but neither exam requires students to demonstrate knowledge and skills at the college and career ready level in order to pass. In short, while the California and Massachusetts standards may be similarly rigorous to the CCSS, or even more so in some limited ways, they are aspirational while the CCSS is intended to be required for all students. While symbolically and politically quite important, the debate in each state about the relative rigor of the high school standards seems to miss the larger educational point – very rigorous standards that students are neither required to meet nor have the opportunity to learn are not nearly as valuable as required standards that prepare all students for postsecondary success. In addition to mathematics content standards the CCSS provides overarching mathematical practices that every course or grade level should contain. The Standards for Mathematical Practice are listed below. Taken from: http://www.corestandards.org/the-standards/mathematics/introduction/standards-for-mathematical-practice/ The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy). 1. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

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2. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. 3. Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. 4. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. 5. Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and

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compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. 6. Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. 7. Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. 8. Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x2 + x + 1), and (x – 1)(x3 + x2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. Connecting the Standards for Mathematical Practice to the Standards for Mathematical Content The Standards for Mathematical Practice describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle and high school years. Designers of curricula, assessments, and professional development should all attend to the need to connect the mathematical practices to mathematical content in mathematics instruction. The Standards for Mathematical Content are a balanced combination of procedure and understanding. Expectations that begin with the word “understand” are often especially good opportunities to connect the practices to the content. Students who lack understanding of a topic may rely on procedures too heavily. Without a flexible base from which to work, they may be less likely to consider analogous problems, represent problems coherently, justify conclusions, apply the mathematics to practical

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situations, use technology mindfully to work with the mathematics, explain the mathematics accurately to other students, step back for an overview, or deviate from a known procedure to find a shortcut. In short, a lack of understanding effectively prevents a student from engaging in the mathematical practices. In this respect, those content standards which set an expectation of understanding are potential “points of intersection” between the Standards for Mathematical Content and the Standards for Mathematical Practice. These points of intersection are intended to be weighted toward central and generative concepts in the school mathematics curriculum that most merit the time, resources, innovative energies, and focus necessary to qualitatively improve the curriculum, instruction, assessment, professional development, and student achievement in mathematics. Section II: Analysis of Student Achievement (See Appendix A for data)

Elementary Student Achievement Data Middle School Achievement Data High School Achievement Data Outside Comparisons International Achievement Data - PISA

Student Achievement: Heidi Shepard’s group • The group did not spend time on the Algebra 1 EOC data because of the different times that the test is

given to the different population of math students and do not believe that there is much reliance put behind data from this test.

• EXPLORE/PLAN/ACT data o Concerned about the discrepancies between extension and non extension students and honors

and college-prep sequence students o The group wondered how students who are considered proficient in math did on the

EXPLORE/PLAN/ACT tests (remove the struggling students from the data) • Group discussed the need to evaluate readiness in transition from WMS to CHS with revised plan for

single topic math instruction at CHS. • Things for the Math Committee to consider as a result of the data

o Look at test prep for standardized testing o Look at curriculum alignment to the EXPLORE/PLAN/ACT o Consider setting a high benchmark for Clayton (State colleges in Missouri set a cut score of 24

for the composite on the ACT). o Continue support for content specific learning center math, staffed by teachers from the math

department Tyler Harger’s group • Algebra 1 EOC data tells us that 8th grade students are outscoring CHS students (8th grade honors

students are scoring on average 230 out of 250 and the CHS is around 200). • Algebra 1 EOC data tell us that 8th grade students are more proficient and advanced than CHS

students (nearly 100% of WMS honors/extensions are at proficient or advanced where CHS students are about 60-70% on proficient or advanced)

• EXPLORE/PLAN data tells us we need higher expectations for all students because students in regular Algebra 8 have the capability to meet the EXPLORE and PLAN benchmark (there are lower scores in Algebra 8 than Challenge Algebra, only 40-50% of Algebra 8 students are making the 17 on the test – this is the lowest benchmark)

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• ACT data tells us that the gap between honors and all other tracks is shrinking (60% of college prep students are making the benchmark of 22)

Dottie Barbeau’s group • Honors track at WMS for EOC is working – evidence nearly 100% of the students were proficient on

EOC test. The Algebra II students, the differentiation appears to be working based on fact that 80% are proficient or advanced on EOC.

• Clearly 140 Algebra 8 kids are not getting algebra skills consistently. Challenge Algebra kids are doing OK. Is it the programming, or curriculum, or instruction?

• Integrated Math II, when you looked at pool of students in Algebra II started out as a weaker. • On the EOC for Algebra 1, the PLAN test, the ACT test, the regular track outscores the Integrated

track. Integrated Math may not teach the skills that are tested on the PLAN and Algebra EOC and ACT.

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Section III: Survey of Teachers, Parents, and Students Copies of the full surveys are available at the office of Mr. Chris Tennill, Chief Communications Officer for the School District of Clayton. Additionally, a compilation of the surveys assembled by UNICOM ARC, an outside firm hired to conduct the surveys, can be found at Appendix D. In order for the committee to analyze the survey to develop findings and recommendations, all questions on the surveys were reviewed to find items of significant importance by stakeholders – important for identifying strengths as well as important for identifying areas for needed improvement. The following two-column chart demonstrates the “significantly important” responses from stakeholders that fall in the range of 30%+ voicing dissatisfied/somewhat dissatisfied as well as “significantly important” responses that indicated a 70%+ satisfied/somewhat satisfied response. An analysis of the survey highlights was developed by the math review committee and is included on the following chart.

UNICOM ARC Survey Highlights

Overview of Parents Survey (N = 676) STRENGTHS CONCERNS • “Your child’s teacher” satisfied/somewhat

satisfied o 91.9% elementary parents o 88.6% middle school parents o 87.3% high school parents

• “The math program in which my child is currently enrolled” satisfied/somewhat satisfied

o 69.5% middle school parents • “My child’s math teacher’s ability to teach the

math curriculum in a way so that my child can understand” satisfied/somewhat satisfied

o 78.6% elementary parents o 76% middle school parents

• “My child enjoys learning mathematics” satisfied/somewhat satisfied

o 90% elementary parents o 80.2% middle school parents o 72.9% high school parents

• “My child has a positive attitude towards math” satisfied/somewhat satisfied

o 87.15% elementary parents o 77.8% middle school parents o 69.8% high school parents

• “I am satisfied with the mount of help teachers are willing to give my child outside of math class” satisfied/somewhat satisfied

o 80.2% middle school parents • “My child was prepared to take his/her current

math class” satisfied/somewhat satisfied o 86.4% elementary parents o 81.3% middle school parents o 78% high school parents

• “My child is adequately challenged in math”

• “The math program in which my child is currently enrolled” dissatisfied/somewhat dissatisfied

o 32.9% high school parents • “My child’s math teacher’s ability to teach the

math curriculum in a way so that my child can understand” dissatisfied/somewhat dissatisfied

o 33.8% high school parents • “I am satisfied with the mount of help teachers

are willing to give my child outside of math class” dissatisfied/somewhat dissatisfied

o 28.7% high school parents • “I do not feel my child always has mastered a

skill before the teacher moves on to another math concept” dissatisfied/somewhat dissatisfied


• “My child is adequately challenged in math” dissatisfied/somewhat dissatisfied

o 30.6% elementary parents • “There is adequate communication from my

child’s teacher about his/her progress in math” dissatisfied/somewhat dissatisfied


• “I am satisfied with my child’s computation skills” dissatisfied/somewhat dissatisfied

o 30.8% high school parents • “I have enough information from the District to

assist my child with math homework” dissatisfied/somewhat dissatisfied

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satisfied/somewhat satisfied o 73.7% middle school parents o 73.8% high school parents

• “I am satisfied with my child’s computation skills” satisfied/somewhat satisfied

o 75.3% elementary parents o 69.1% middle school parents

• “I have enough information from the District to assist my child with math homework” satisfied/somewhat satisfied

o 68.6% elementary parents

o 40.6% middle school parents o 53.8% high school parents

Overview of Elementary Teacher Survey (N = 50) STRENGTHS CONCERNS • 70% indicated that they were very satisfied with

their overall educational experience teaching in the School District of Clayton

• 83.7% indicated that they agree with the statement “I enjoy teaching math”

• 69.4% indicated that they agree with the statement “There is adequate communication between teachers and parents regarding how students are progressing in math classes.”

• 73.5% indicated that they disagree/somewhat disagree with the statement “I would prefer the District use a textbook other than Everyday Math”

• 68.8% indicated that they agree with the statement “I use the current Everyday Math assessments to inform instruction”

• 30.6% indicated that they disagree/somewhat disagree with the statement “I feel the current Everyday Math assessments give adequate opportunities for students to demonstrate their understanding of all the goals for a unit”

Overview of Middle School Teacher Survey (N = 9) STRENGTHS CONCERNS • 88.9% indicated that they were very satisfied with their overall

educational experience teaching in the School District of Clayton • 77.8% indicated that they were very satisfied with the math

program as a whole at Wydown • 77.8% indicated that they were very satisfied with their overall

experience teaching the current math program in their grade level • 100% agree with the statement “The current math program provides

opportunities to adequately challenge all of the students in my class.”

• 77.8% agree with the statement “There is adequate communication between teachers and parents regarding how students are progressing in math class.”

• 88.9% agree with the statement “Decisions that I make regarding placement concerns are supported by District leadership.”

Overview of High School Teacher Survey (N = 15) STRENGTHS CONCERNS • 73.3% indicated that they were very satisfied

with their overall experience teaching the current math program in their grade level.

• 86.7% indicated that they were very satisfied with the textbook used to teach the curriculum.

• 40% indicated that they disagree/somewhat disagree with the statement “There is adequate communication between teachers and administration regarding the math curriculum.”

• 46.7% indicated that they disagree/somewhat

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• 93.3% indicated that they agreed with the statement “The curriculum adequately challenges all of the students in my class.”

• 92.3% indicated that they agreed with the statement “The majority of students in my class do not require a tutor to be successful.”

disagree with the statement “I often have to adjust the curriculum to help students learn key concepts.”

• 46.7% estimated that 0-25% of their students received extra help specifically in math from someone other than themselves or a family member.

Overview of Elementary Student survey (N = 439) STRENGTHS CONCERNS • 76.8% indicated that “I like my school” most of

the time • 72.3% indicated that “I understand what the

teacher is teaching in math” most of the time. • 76.1% indicated that “For me, math is just

right” • 70.7% indicated that “For me, math homework

is just right.” • 71.4% indicated that “For me, the amount of

math homework is just right.”

• 76.8% answered yes to the question “Do you ever have help with your math homework outside of school.”

• 83.7% when asked “Who helps you with math?” chose family

Overview of Middle School Student survey (N = 479) STRENGTHS CONCERNS • 74.3% indicated that “The math class you are

taking this year is good” • 78.1% indicated that “Your overall experience

with your math teacher this year is good” • 89.9% agreed with the statement “My teacher

really understands the math concepts he/she is teaching.”

Overview of High School Student survey (N = 616) STRENGTHS CONCERNS • 70.8% indicated that they agree with the

statement “My teacher really understands the math concepts he/she is teaching the class.”

• 75.2% of those receiving help from a professional tutor indicated that they used a “paid private tutor”

• 71.8% of the students responding that they received help from a professional tutor indicated that they used the tutor for ACT/SAT prep.

• 28.5% indicated that they disagree/somewhat agree with the statement “I do feel that I usually understand the math concepts before my teacher moves on to another concept.”

• 28.5% indicated that they disagree/somewhat disagree with the statement “I understand the class work in my math class and do not need a tutor to understand the basic concepts.”

Overview of Alumni survey (N = 295) STRENGTHS CONCERNS • 73.3% of the students who received tutoring

(N=86) indicated they received tutoring for ACT/SAT prep.

• 74.6% of the students who received tutoring for ACT/SAT prep (N=63) indicated they received tutoring for test taking strategies.

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Comments from math committee analysis on November 23, 2010: We received substantial feedback to help improve our program. Four clear areas for improvement were provided as evidenced by multiple responses from committee groups - communication with parents, mastery of secure goals and concepts before moving on, better assessments at elementary level, and parents receiving enough information to assist with homework. See Findings, page 15 Notes from Survey: three groups Heidi Shepard’s group • Communication came up as a concern from parents, consider having sample problems be part of the

book so that parents can give assistance • Continue to look at communication with parents • Continued professional development at all levels • Teacher’s ability will be addressed with the guiding principle regarding Basic Algebra understanding

for all elementary teachers • Need to look at mastering of math concepts, setting benchmarks for the different grade levels and

evaluate benchmarks • Help communicate to parents the purpose of the formative assessments given in elementary school,

that these topics are extensions of a unit and informs how a child is doing with the extension • Looking at the elementary program, continue with the model and continue with differentiation of

materials • Strength from parents at elementary level • Concern was elementary assessments

o take a look at different assessment tools o look at test writing at the district level, incorporate outside testing o overhaul elementary testing

• CHS teacher perception of tutoring is off base, tutoring might be alleviated with single topic sequence • Group was curious what percentage take 4 years of math, should Clayton consider this 4 years a must

for the district • Recommendation to talk with students regarding tutoring at CHS, question – “do students get tutored

to avoid parent/student conflict?” • CHS students need to understand concept before moving on Tyler Harger’s group • Strength – parents in this district are satisfied with the child’s math teacher. • Strength – over 80% of elementary teachers love teaching math and don’t want a new textbook. • Concerns from the survey was that 1/3 of the parents aren’t satisfied with communication about how

their child’s progress in math. • Concern- nearly ½ of the elementary parents feel that their child has not mastered a skill before the

teacher has moved on to another concept • Concern - 1/3 of elementary teachers feel the EDM assessments do not give adequate opportunities for

students to demonstrate their understanding • Concern – ½ of the elementary parents feel that their child isn’t challenged • Concern – 40 to 50% of the middle and high school parents feel they can’t assist their child with

homework • Concern – 1/3 of high school parents are dissatisfied with their child’s computation skills. • Concern - 40% of high school teachers and administrators aren’t communicating with each other. • Concern - 50% of high school teachers estimate that up to ¼ of their students receive tutoring • Concern - 30% of high school students don’t feel that they understand a concept before they move on.

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• Concern – 1/3 of the high school parents feel their child’s teachers don’t teach the curriculum in a way their child understands and the amount of help that is offered to their child outside of the classroom setting.

Dottie Barbeau’s group • 86% of parents feel our students are prepared to take the next math class. But in the process parents

are not sure that we are adequately preparing them along the way, or what skills have to be mastered along the way.

• Almost half of the elementary (43.7%) parents feel we are moving on to math concepts before we can master them. Either we are not communicating the spiral of our curriculum or the spiral is not working.

• 86% of elementary parents are satisfied with our math program, 90% of the elementary children enjoy math and 87% of the students have a positive attitude about math. These two statements speak loudly about the elementary program (Everyday Mathematics).

• Everyday Math assessments don’t provide enough opportunities for teachers to assess student learning.

• Communication about the spiral and what does and does not need to be mastered • The weak link in EDM is assessment of the secure goals for learning. We can utilize our formative

assessments in a different way or rethink our summative assessments. We don’t always have enough information to make decisions of children are truly secure in specific skills.

• There is a disconnect and lack of communication about what skills need to be secure and which are developing along the way. We need a communication with parents to clarify the spiral.

• Computation skills are satisfactory in elementary and middle but not in high school for parents. It speaks to the fact that the FASTT Math is plugging a hole that we have seen for quite some time at the elementary level.

• 30% of elementary parents felt their child is not challenged in math. We hope that the new staffing changes including the push in of gifted specialist, math specialist, and the introduction of interim assessments address this concern.

• Middle school teachers are very satisfied. • More high school parents are dissatisfied with the communication than elementary and middle. Is

power school providing the right information? Looking at the score is not the same as communicating with the teacher. Elementary parents are easy to find and talk to. Also, maybe high school grades and scores are not current. More communication with parents is needed, via phone calls, emails, etc.

• About half of our secondary parents can’t assist with math homework or don’t have the ability to help with homework. As math teachers, we need to communicate better with parents on how to help student with homework, and teachers need to provide more time outside of class to help students.

• Communication – when available, how often available to provide help • We need to cut down the number of CHS topics covered in our classes and go deeper into the topics

offered. • CHS teachers need more communication with administration, 47% say that ¼ received extra help

outside of school • High School: almost 1/3 of our students think we are going too fast and they need a tutor to keep up.

We learned we are covering too much material too quickly and maybe not doing mini assessments to see where they stand. We also need to determine if the outcomes in the previous course are rigorous enough to prepare the students for a current class.

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Section IV: Guiding Principles and Program Specifications Add final guiding principles and program specifications after committee reviews them at December 14th committee meeting

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Appendix A Student Achievement Data

• Average Scale Scores for Algebra I End of Course Exam (2009, 2010) • Percent Scoring Proficient or Advanced on Algebra I End of Course Exam (2009, 2010) • National Percentiles on the PLAN Mathematics 2006-2009 • EXPLORE to PLAN and PLAN to ACT Growth, Class of 2009, 2010, 2011 • EXPLORE, PLAN and ACT Mathematics Performance by Math Sequences, Class of 2009

through Class of 2014 • Percent of Students Meeting ACT College Readiness Benchmark Scores by Race/Ethnicity:

MATHEMATICS (2009) • Percent of Students Ready for College-Level Coursework (2009) • SAT Math Scores for the top ten highest achieving school districts in the State of Massachusetts,

2006-2007 as reported on Massachusetts State Department of Education website, including data on Percentage of students taking Advanced Placement Calculus, AP Calculus AB, and AP Calculus BC

• Cohort Mathematics Data Over Time – this report looks at the total population of students as well as the cohort of African-American students and Caucasian students over time with regards to their performance on the MAP-Mathematics Assessment grades 3, 4, 5, 6, 7 and 8.

• Longitudinal Grade-Level Expectation Analysis Data – this report looks at each Grade-Level Expectation for grades 3, 4, 5, 6, 7 and 8 and the questions asked for the past 5 years on the MAP-Mathematics Assessment.

• Item Analysis of 6th Grade Placement Tests – this report looks at the mean and median of the Orleans-Hanna Algebra Readiness Test and the mean, median and item analysis of the District Computation Test.

• Grades 3-8 MAP Student Achievement 2006 – 2010 Percent Advanced/Proficient for White and African American Students

• Assessment Report presented by Heidi Shepard, Director of Assessment on December 1, 2010 to the Board of Education. Can be found on the math curriculum website - http://www.clayton.k12.mo.us/40372063214152777/site/default.asp?403610321114854303Nav=|&NodeID=350&40372063214152777Nav=|2478|&NodeID=2478

• Need to put in all the African American achievement graphs completed for VICC

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Algebra 1 End-Of-Course Exams Data

The graphs below contain information from the 2008-2009 and 2009-2010 school years with regards to the average scale score and percentage of students with an achievement level of proficient or advanced for the Algebra 1 End-of-Course Exam. Achievement Levels for the Algebra 1 End-of-Course Exam are Advanced (225-250), Proficient (200-224), Basic (177-199), and Below Basic (100-176). • Students take the exam at different times of the year and different years depending on their sequence. • Students in the Honors Sequence take the Algebra 1 EOC in the spring when they are in 8th grade

enrolled in Challenge Algebra. • Students in the Integrated Sequence take the exam in the spring when they are enrolled in Integrated

Math 1. • Students in the Alternate Sequence take the exam in fall when they are enrolled in Algebra 2. • Students in the Informal Sequence take the exam in the fall of their junior year. • Currently we have two years of data for the Honors and Integrated Sequences and one year of data for

the Traditional and Informal Sequences.

• All groups of students meet or exceed the Proficient mark of 200 except the 2010 Informal

Mathematics Junior Level Course. • There was a slight decrease in the average scale score at Wydown Middle School, which is also

reflected in the Total’s group. However, both groups at Wydown Middle School are in the Advanced Range for the average score.

• The WMS group represents our honors track students on track for ending CHS in AP Calculus • A total of 229 students took the Alg 1 EOC in 2010. 75 8th graders, 78 Integrated I students, 45

Algebra 2 students, and 29 students in the Informal track. (2 collaborative school students also took the test)

• A total of 148 students took the Alg 1 EOC in 2009. 68 8th graders, 80 Integrated I students • The information for the Algebra 1 End-of-Course is limited in nature due to its new arrival to the

testing matrix and the test is going through changes this year which will make comparisons for the following years difficult.

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The graph above displays the percentage of students scoring proficient or advanced on the Algebra 1 End-of-Course Exam. • The expectation from the State was that 54.1% of the students score proficient or advanced for the

2008-2009 school year and 63.3% for the 2009-2010 school year. Clayton has met Adequate Yearly Progress for the Algebra 1 End-of-Course Exam for both years.

• The expectation for the 2010-2011 school year is 72.5%. Currently CHS as a total group or the subgroups of Integrated Math 1 and Informal (Jr. level ) Sequence Math Course would not meet expectations, though both the Total and Integrated Math 1 showed an increase of approximately 10% points from the 2008-2009 school year to the 2009-2010 school year.

• A total of 229 students took the Alg 1 EOC in 2010. 75 8th graders, 78 Integrated I students, 45 Algebra 2 students, and 29 students in the Informal track. (2 collaborative school students also took the test)

• A total of 148 students took the Alg 1 EOC in 2009. 68 8th graders, 80 Integrated I students

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The graph above displays the National Percentiles for PLAN scores for mathematics as well as subscores in the areas of algebra and geometry. Data is broken down in HAT (Honors Algebra/Trigonometry course), IM II (Integrated Mathematics II course) and ALG II (Algebra II course). Students in the Honors Math course score in the 90%ile math composite and algebra and geometry. Integrated Mathematics score around the 60%ile, except in 2006 when scores were in the 70%ile. Students in Algebra II show the greatest variance in their percentile with the geometry percentile being the largest. The geometry percentile being larger is appropriate considering the freshmen course for these students is geometry and the PLAN is taken in the Fall of their sophomore year.

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EXPLORE to PLAN and PLAN to ACT Growth

This set of data looks at the amount of growth between the EXPLORE test and the PLAN test and the PLAN test and the ACT test. Adequate growth for the EXPLORE to PLAN is two or more points and for the PLAN to ACT three or more points. ACT data for the Class of 2011 is not complete, students are still opting to retake the ACT test and final numbers will not be in until the summer of 2011.

Findings: • The greatest percentage of growth for students in the Honors Mathematics Sequence is between

the EXPLORE test and the PLAN test. Students growth between the EXPLORE to PLAN ranged from about 84% to 91%.

• Growth between the PLAN and ACT ranged between the mid 70%’s to 80%. One explanation for this decrease in growth is how high the scores were on the PLAN. Students in the Honors Sequence have shown continued success in other measures of data, such as the AP test scores for both AP Calculus AB and AP Calculus BC.

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Findings:

• For the Class of 2010 and 2011 the greatest growth occurred between the PLAN test and the ACT test. One explanation for the growth could be the alignment of the curriculum to the test. Since the Integrated Math curriculum is not topic specific like many high school curriculums the test would not show the entirety of its topics until later grades.

Findings:

• There is no consistency in the growth data from one graduating class to another. The Class of 2009 grew the post between the PLAN and the ACT; the Class of 2010 had about the same growth between both pairs of tests; and the Class of 2011 had the greatest growth between the EXPLORE and the PLAN. One explanation for this data is the low number of students taking the Traditional Mathematics Sequence. There were 8 to 15 students in the Traditional Sequence who participated in both the EXPLORE and the PLAN and 12 to 22 students who participated in both the PLAN and the ACT. The lower the set of the data the less likely one can draw conclusions from the data.

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EXPLORE, PLAN and ACT Mathematics Performance by Math Sequences

This set of data compares mathematics performance for the EXPLORE, PLAN and ACT tests. The sets of data are average scores on the different tests and the percent of students who met the College Readiness Benchmark in the area of mathematics for a particular test. The data compared the total population with students in the different math sequences. College Readiness Benchmarks predict success in the college freshman mathematics course – College Algebra. [EXPLORE Math Benchmark = 17, PLAN Math Benchmark = 19, ACT Math Benchmark = 22].

Findings:

• The average score for the total population of Clayton and students in Challenge Algebra met or exceeded the EXPLORE mathematics benchmark

• The average score for the Algebra 8 was slightly below the EXPLORE mathematics benchmark of 17. It will be important for the Mathematics Committee and Mathematics Department at Wydown Middle School to determine what skills and concepts need reinforcement in order to improve the overall performance of the students in this math sequence.

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Findings:

• The average score for the total population of Clayton, students in Honors Algebra/Trigonometry and students in Algebra II met or exceeded the PLAN mathematics benchmark

• The average score for the Integrated Math II was slightly below the PLAN mathematics benchmark of 19 for 3 out of 4 of the reported years. It will be important for the Mathematics Committee and Mathematics Department at Clayton High School to determine what skills and concepts need reinforcement in order to improve the overall performance of the students in this math sequence.

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Findings:

• The average score for the total population of Clayton, students in Honors Pre Calculus, students in Integrated Math III and students in FST (Functions, Statistics and Trigonometry) met or exceeded the ACT mathematics benchmark of 22.

• Students in the College Prep – Integrated Math Sequence for all groups met the College Readiness benchmark for mathematics for the ACT, unlike their pervious performances on the EXPLORE and the PLAN. One explanation for the growth could be the alignment of the curriculum to the test. Since the Integrated Math curriculum is not topic specific like many high school curriculums the test would not show the entirety of its topics until later grades.

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Findings:

• Over 90% of the students in Challenge Algebra for each graduating class are meeting the EXPLORE mathematics benchmark, with 100% meeting the benchmark for the Class of 2009, 2012 and 2014.

• Less than half of the Algebra 8 students are meeting the EXPLORE mathematics benchmark. The Mathematics Committee and Mathematics Department at Wydown Middle School will need to look at the alignment between the current curriculum and the skills and concepts measured on the EXPLORE test.

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Findings: • Over 90% of the students in Honors Algebra/Trigonometry for each graduating class are meeting

the PLAN mathematics benchmark, with 100% meeting the benchmark for the Class of 2011 and 2012.

• Less than half of the Integrated Math II students for the Class of 2010, 2011 and 2012 met the PLAN mathematics benchmark. Approximately half of the students in Algebra II for the Class of 2009, 2010 and 2012 met the PLAN mathematics benchmark. The Mathematics Committee and Mathematics Department at Clayton High School will need to look at the alignment between the current curriculum and the skills and concepts measured on the PLAN test.

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Findings: • Over 90% of the students in Honors Precalculus for each graduating class are meeting the ACT

mathematics benchmark, with 100% meeting the benchmark for the Class of 2006, 2008, 2009, 2010 and 2011.

• Over half of the students in both Integrated Math III and FST (Functions, Statistics and Trigonometry) met the ACT mathematics benchmark. The percentages in Integrated Math III approximately doubled from the percentage met for the PLAN.

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Percent of Students Meeting ACT College Readiness Benchmark Scores by Race/Ethnicity: MATHEMATICS (2009)

Clayton Massachusetts Race/Ethnicity N % Ready N % Ready All Students 207 65 13,093 68 African American/Black 36 19 462 33 American Indian/Alaska Native . . 21 67 Caucasian American/White 121 76 10,008 69 Hispanic 7 57 360 45 Asian American/Pacific Islander 14 93 593 80

100 80 60 40 20 0 20 40 60 80 100

65 All Students 35 68 All Students 32

19 AA 81

67 33 AA

33 67 American Indian

76 Caucasian American 24 69 Caucasian American 31

57 Hispanic 43

45 Hispanic 55

7 93 Asian American

20 80 Asian American

Clayton Percent Ready

Massachusetts Percent Ready

Percent Not Ready

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Percent of Students Ready for College-Level Coursework

ACT English Benchmark Score=18

ACT Math Benchmark Score=22

ACT Reading Benchmark Score=21

ACT Science Benchmark Score=24

A benchmark score is the minimum score needed on an ACT subject-area test to indicate a 50% chance of obtaining a B or higher or about a 75% chance of obtaining a C or higher in the corresponding credit-bearing college course.

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Cohort Mathematics Data Over Time

This report looks at various cohorts of students over time with regards to two sets of data related to mathematics: MAP Index and Mean Scale Score. The MAP Index assigns a weight to the different achievement levels (Advanced, Proficient, Basic and Below Basic) and multiplies that by the number of students in each level to determine the score. The MAP Index is similar in concept to a Grade Point Average. The Scale Score describes achievement on a continuum that spans the range of grades 3 – 8. Scale scores can be added, subtracted, and averaged. The Scale Score determines the student’s achievement level. This report looks at the MAP Index and Mean Scale Score over time for total population of students as well as African-American students and Caucasian students. All three graphs displaying Mean Scale Score data shows an increase from one school year to the next except for current 11th grade students during their 7th grade school year. The MAP Index graph for the total population of a cohort over time shows upward growth for current 6th, 7th and 8th grade students. Current 9th grade students showed a slight dip in 6th grade; current 10th grade students showed a drop in the MAP Index in both 6th and 8th grade; and current 11th graders’ drop in 7th grade, which was also seen in the MAP Index graph. The MAP Index graph for African-American students cohort groups over time shows upward growth for current 6th and 8th grade students. Current 7th grade students show a dip in grade 6; current 9th grade students show no consistent movement, upward or downward (though there is a more noticeable drop between grades 5 and 6); current 10th grade students show a steady decline in their MAP Index scores; and current 11th grade students drop in 7th grade as displayed in previous graphs. The MAP Index graph for Caucasian students cohort groups over time shows upward growth for current 6th, 7th and 8th grade students. Current 9th grade students show a slight dip in 6th grade; current 10th grade students show no consistent movement, upward or downward (though there is a noticeable drop between grades 6 and 7); and current 11th grade students drop in 7th grade as displayed in previous graphs.

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MAP Mathematics 2006 to 2010

Longitudinal Grade-Level Expectation Analysis Data

The School District of Clayton has been participating in the MAP-Mathematics in its current form since 2006. Students in grades 3, 4, 5, 6, 7 and 8 are testing each spring in the area of mathematics. The information in this report analyzes the grade-level expectations (GLEs) for the past 5 years using content analysis reports from the Department of Elementary and Secondary Education. In this report a GLE was identified as a concern if an item on one of the MAP-Mathematics tests had an “earned points” of less than 70%, meaning that less than 70% of the student population earned points on that particular item. The majority of the items on the assessments are one point multiple choice problems; there are some constructed response items worth 2 points and performance events in grades 4 and 8. Grade-Level Expectations were also identified for the frequency in which they occurred in the past 5 years, with a focus on those that had occurred 10 or more times. Mathematics is broken down into five standards:

• Number and Operations • Algebraic Relationships • Geometric and Spatial Relationships • Measurement • Data and Probability

The overall percentage for students earning points on each standard is: Mathematics Standard Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 Number and Operations 86.6% 80.1% 85.0% 81.1% 77.8% 78.2% Algebraic Relationships 83.7% 85.2% 80.0% 75.5% 71.0% 67.3% Geometric and Spatial Relationships

84.2%

82.8%

78.4%

75.6%

70.3%

68.4%

Measurement 80.0% 82.9% 76.1% 74.6% 65.0% 62.1% Data and Probability 85.3% 87.1% 85.3% 81.9% 74.1% 73.0%

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Summary of the report When determining Grade-Level Expectations of great concern from the MAP-Mathematics over the past five years, the report looked at both the frequency in which a grade-level expectation was covered (10 or more questions) and the percentage the student population scoring below 70% on earned points:

• In third grade, Grade-Level Expectations in the area of Number and Operations, Algebraic Relationships, Geometric and Spatial Relationships and Data and Probability have no areas of great concern. In the Mathematics strand of Measurement there was one GLE that is of concern:

o The GLE – M1D of the Measurement strand [determine change from $5.00 and add and subtract money values to $5.00], which has an average earned points of 69.5% and 8 out of 12 questions in the past 5 years scoring below the 70% mark.

• In fourth grade, Grade-Level Expectations in the area of Algebraic Relationships, Geometric and Spatial Relationships and Measurement have no areas of great concern. In the Mathematics strand of Number and Operations and Data and Probability there was one GLE in each strand this is of concern:

o The GLE – N3D of the Numbers and Operations strand [estimate and justify the results of multiplication of whole numbers], which has an average earned points of 60% and 6 out of 15 questions scoring below the 70% mark

o GLE – D2A of the Data and Probability [describe important features of the data sent], which has an average earned points of 64.5% and 2 out of 10 questions scoring below the 70% mark.

• In fifth grade, Grade-Level Expectations in the area of Number and Operations, Algebraic Relationships, Geometric and Spatial Relationships, Measurement and Data and Probability have no areas of great concern.

• In the sixth grade, Grade-Level Expectations in the area Number and Operations, Algebraic Relationships, Geometric and Spatial Relationships, Measurement and Data and Probability had no areas of great concern.

• In the seventh grade, Grade-Level Expectations in the area of Number and Operations, Algebraic Relationships, Geometric and Spatial Relationships and Data and Probability have no areas of great concern. In the Mathematics strand of Measurement there was one GLE that is of concern:

o The GLE – M2C of the Measurement strand [describe how to solve problems involving circumference and/or area of a circle], which has an average earned points of 69.82% and 6 out of 11 questions in the past 5 years scoring below the 70% mark.

• In eighth grade, Grade-Level Expectations in the area of Number and Operations had no areas of great concern. In the Mathematics strand of Algebraic Relationships, Geometric and Spatial Relationships, Measurement and Data and Probability there were GLEs that are of concern:

o The GLE – A1B of the Algebraic Relationships strand [generalize patterns represented graphically or numerically using words or symbolic rules, including recursive notation], which has an average earned points of 65.7% and 8 out of 14 questions scoring below the 70%

o The GLE – A2B of the Algebraic Relationships strand [generate equivalent forms for linear expressions], which has an average earned points of 57.18% and 10 out of 11 questions scoring below the 70% mark.

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o The GLE – A3A of the Algebraic Relationships strand [model and solve problems, using multiple representations such as graphs, tables, equations or inequalities], which has an average earned points of 58.58% and 11 out of 13 questions scoring below the 70% mark.

o The GLE – G4B of the Geometric and Spatial Relationships strand [draw or use visual models to represent and solve problems], which has an average earned points of 65.18% and 6 out of 11 questions scoring below the 70% mark.

o The GLE – M2B of the Measurement strand [use tools to determine the measure of reflex angles to the nearest degree], which has an average earned points of 51.85% and 11 out of 13 questions scoring below the 70% mark.

o The GLE – M2C of the Measurement strand [describe how to solve problems involving surface area and/or volume of a rectangular or triangular prism, or cylinder], which has an average earned points of 64.61% and 11 out of 19 questions scoring below the 70% mark.

o The GLE – D2A of the Data and Probability strand [find, use and interpret measures of center, outliers and spread, including range and interquartile range], which has an average earned points of 67.83% and 7 out of 13 questions scoring below the 70% mark.

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GRADE 3 – MAP Mathematics Longitudinal Item Analysis 31 GLEs were measured on the grade 3 mathematics assessment over the past 5 years; 4 GLEs were in the 90% range for students earning points on the given GLE, 22 GLEs were in the 80% range, 4 GLEs were in the 70% range and 1 GLE was in the 60% range. Number and Operations – 86.6% average 96 out of 293 (32.8%) questions over the past 5 years covered the Number and Operations strand. The GLEs with 10 or more questions over the past 5 years:

• N1A (12 questions) – read, write and compare whole numbers up to 3 digit numbers [93.58%] • N2A (10 questions) – represent a given situation involving multiplication [86.4%] • N3B (14 questions) – develop fluency with basic number relationships (12 x 12) of multiplication

and division [88.36%] • N3C (20 questions) – apply and describe the strategy used to compute using up to a 3-digit

number in addition or subtraction problems [87.13%] • N3D (12 questions) – estimate and justify the results of addition and subtraction of whole numbers

[73.92%] There were 6 questions out of the 96 that less than 70% of the students earned points. No overall GLE average had a percentage below 70%. Algebraic Relationships – 83.7% average 55 out of 293 (18.8%) questions over the past 5 years covered the Algebraic Relationships strand. The GLEs with 10 or more questions over the past 5 years:

• A1A (16 questions) – extend geometric (shapes) and numeric patterns to find the next term (83.72%)

• A1B (10 questions) – represent patterns using words, tables or graphs (85.25%) • A2A (11 questions) – represent a mathematical situation as an expression or number sentence

(88.45%) There were 2 questions out of the 55 that less than 70% of the students earned points. No overall GLE average had a percentage below 70%. Geometric and Spatial Relationships – 84.2% average 57 out of 293 (19.5%) questions over the past 5 years covered Geometric and Spatial Relationships. The GLEs with 10 or more questions over the past 5 years:

• G1A (13 questions) – compare two-and three-dimensional shapes by describing their attributes (circle, rectangle, rhombus, trapezoid, triangle, rectangular prism, cylinder, pyramid and sphere) (84.62%)

• G3A (12 questions) – determine if two objects are congruent through a slide, flip or turn (85.25%) • G3C (12 questions) – identify lines of symmetry in polygons (85.38%)

There were 4 questions out of the 57 who earned less than 70%. No overall GLE average was below 70%. Measurement – 80.0% average 48 out of 293 (16.4%) questions over the past 5 years covered the Measurement strand. The GLEs with 10 or more questions over the past 5 years:

• M1C (10 questions) – tell time to the nearest five minutes (83.10%) • M1D (12 questions) - determine change from $5.00 and add and subtract money values to $5

(69.5%) There were 16 questions out of 48 that earned less than 70%.

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The GLE – M1D determine change from $5.00 and add and subtract money values to $5.00 had an average of 69.5%, with 8 out of the 12 questions scoring below 70%. Data and Probability – 85.3% average 37 out of 293 (12.6%) questions over the past 5 years covered the Data and Probability strand. The GLEs with 10 or more questions over the past 5 years:

• D1C (26 questions) - read and interpret information from line plots and bar, line, pictorial graphs (84.08%)

There were 3 questions out of 37 that earned less than 70% No overall GLE average was below 70%.

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GRADE 4 – MAP Mathematics Longitudinal Item Analysis 31 GLEs were measured on the grade 4 mathematics assessment over the past 5 years; 1 GLE earned 100% for students earning points on the given GLE, 4 GLEs were in the 90% range, 17 GLEs were in the 80% range, 6 GLEs were in the 70% range and 3 GLEs were in the 60% range. Number and Operations – 80.1% average 95 out of 322 (17.7%) questions over the past 5 years covered the Number and Operations strand. The GLEs with 10 or more questions over the past 5 years:

• N1C (14 questions) – recognize equivalent representations for the same number and generate them by decomposing and composing numbers [88.0%]

• N2A (17 questions) – represent and recognize multiplication using various models, including sets and arrays [83.0%]

• N3C (36 questions) – apply and describe the strategy used to compute a multiplication problem up to a 2-digit number by 2-digit number | apply and describe the strategy used to compute a division problem up to a 3-digit number by 1-digit number [83.0%]

• N3D (15 questions) – estimate and justify the results of multiplication of whole numbers [60.0%] There were 15 questions out of the 95 that less than 70% of the students earned points. The GLE – N3D estimate and justify the results of multiplication of whole numbers had an average of 60%, with 6 out of 15 questions scoring below 70%. Algebraic Relationships – 85.2% average 57 out of 322 (17.7%) questions over the past 5 years covered the Algebraic Relationships strand. The GLEs with 10 or more questions over the past 5 years:

• A1A (13 questions) – describe geometric and numeric patterns [93.0%] • A1B (12 questions) – analyze patterns using words, tables and graphs [78.0%] • A2A (19 questions) – represent a mathematical situation as an expression or number sentence

[89%] There were 11 questions out of the 57 that less than 70% of the students earned points. The GLE – A3A model problem situations, using representations such as graphs, tables or number sentences had an average of 64%, with 3 out of 5 questions scoring below 70%. Geometric and Spatial Relationships – 82.8% average 63 out of 322 (19.6%) questions over the past 5 years covered the Geometric and Spatial Relationships strand. The GLEs with 10 or more questions over the past 5 years:

• G1A (22 questions) – identify and describe the attributes of two- and three-dimensional shapes (prisms, cones, parallelism, perpendicularity) [83.0%]

• G3A (12 questions) – predict the results of transformations including slide/translation, flip/reflection or turn/rotations around the center point of a polygon [78.0%]

• G3C (11 questions) – construct a figure with multiple lines of symmetry and identify the lines of symmetry [78.0%]

There were 5 questions out of the 63 that less than 70% of the students earned points. No overall GLE average had a percentage below 70%.

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Measurement – 82.9% average 61 out of 322 (18.9%) questions over the past 5 years covered the Measurement strand. The GLEs with 10 or more questions over the past 5 years:

• M1D (11 questions) – determine change from $10.00 and add and subtract money values to $10.00 [72.0%]

• M2A (13 questions) – select and use benchmarks to estimate measurements (linear, capacity, weight) [91.0%]

• M2C (15 questions) – determine the area of a polygon on a rectangular grid [78.0%] There were 15 questions out of 61 that less than 70% of the students earned points. No overall GLE average had a percentage below 70%. Data and Probability – 87.1% average 46 out of 322 (14.3%) questions over the past 5 years covered the Data and Probability strand. The GLEs with 10 or more questions over the past 5 years:

• D1C (22 questions) – create tables or graphs to represent categorical and numerical data including line plots [100%]

• D2A (10 questions) – describe important features of the data set [64.5%] • D3A (12 questions) – given a set of data, propose and justify conclusions that are based on the

data [82.0%] There were 5 questions out of 46 that less than 70% of the students earned points. The GLE – D2A describe important features of the data set had an average of 64.5%, with 2 out of 10 questions scoring below 70%.

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GRADE 5 – MAP Mathematics Longitudinal Item Analysis 34 GLEs were measured on the grade 4 mathematics assessment over the past 5 years; 3 GLEs were in the 90% range for students earning points on the given GLE, 15 GLEs were in the 80% range, 13 GLEs were in the 70% range and 3 GLEs were in the 60% range. Number and Operations – 85.0% average 77 out of 296 (26%) questions over the past 5 years covered the Number and Operations strand. The GLEs with 10 or more questions over the past 5 years:

• N1A (11 questions) – read, write, compare and order unit fractions and decimals to thousandths [88.82%]

• N3C (38 questions) – apply and describe the strategy used to compute a given division problem up to a 3-digit number by 2-digit number [84.47%]

There were 3 questions out of 77 that less than 70% of the students earned points. The GLE – N1D describe numbers according to their characteristics including whole number, common factors and multiples, prime or composite, and square numbers had an average of 64.0%, with 1 out of 1 question scoring below 70%. Algebraic Relationships – 80.0% average 50 out of 296 (16.9%) questions over the past 5 years covered the Algebraic Relationships strand. The GLEs with 10 or more questions over the past 5 years:

• A1A (11 questions) – make and describe generalizations about geometric and numeric patterns [79.95%]

• A2A (22 questions) – represent a mathematical situation as an expression or number sentence using a letter or symbol [81.52%]

There were 13 questions out of 50 that less than 70% of the students earned points. No overall GLE average had a percentage below 70%.

Geometric and Spatial Relationships – 78.4% average 56 out of 296 (18.9%) questions over the past 5 years covered the Geometric and Spatial Relationships strand. The GLEs with 10 or more questions over the past 5 years:

• G1A (12 questions) – analyze two- and three-dimensional shapes by describing the attributes [74.71%]

• G2A (12 questions) – use coordinate systems to specify locations, describe paths and find the distance between points along horizontal and vertical lines [76.15%]

• G3C (11 questions) – identify polygons and designs with rotational symmetry [85.23%] There were 16 questions out of 56 that less than 70% of the students earned points. No overall GLE average had a percentage below 70%. Measurement – 76.1% average 60 out of 296 (20.3%) questions over the past 5 years covered the Measurement strand. The GLEs with 10 or more questions over the past 5 years:

• M1A (12 questions) – identify and justify the unit of measure for area including customary and metric measurements [82.58%]

• M2C (12 questions) – describe how to solve problems involving the area of polygons and non-polygonal regions imposed on a rectangular grid [73.63%]

• M2E (13 questions) – convert from one unit to another within a system of measurement (linear) [73.73%]

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There were 12 questions out of 60 that less than 70% of the students earned points. The GLE – M1B identify the equivalent weights and equivalent capacities within a system of measurement had an average of 64.28%, with 5 out of 9 questions scoring below 70%. Data and Probability – 85.3% average 53 out of 296 (17.9%) questions over the past 5 years covered the Data and Probability strand. The GLEs with 10 or more questions over the past 5 years:

• D1C (20 questions) – describe methods to collect, organize and represent categorical and numerical data [92.43%]

There were 5 questions of 53 that less than 70% of the students earned points. The GLE – D2B compare different representations of the same data and evaluate how well each representation shows important aspects of the data had an average of 68.38%, with 2 out of 4 questions scoring below 70%.

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GRADE 6 – MAP Mathematics Longitudinal Item Analysis 36 GLEs were measured on the grade 6 mathematics assessment over the past 5 years; 9 GLEs were in the 80% range for students earning points on the given GLE, 19 GLEs were in the 70% range, 7 were in the 60% range and 1 GLE was in the 50% range. Number and Operations – 81.1% average 87 out of 302 (28.8%) questions over the past 5 years covered the Number and Operations strand. The GLEs with 10 or more questions over the past 5 years:

• N3C (49 questions) – add and subtract positive rational numbers [84.27%] • N3E (10 questions) – solve problems using equivalent rations [78.25%]

There were 10 questions out of 87 that less than 70% of the students earned points. The GLE – N1A compare and order integers, positive rational numbers and percents, including finding their approximate location on a number line had an average of 67.67%, with 2 out of 3 questions scoring below 70%. The GLE – N2A represent and recognize division using various models, including quotative and partitive had an average of 62.5%, with 2 out of 2 questions scoring below 70%. The GLE – N2D identify square and cubic numbers and determine whole number roots and cubes had an average of 68%, with 1 out of 1 question scoring below 70%. Algebraic Relationships – 75.5% average 52 out of 302 (17.2%) questions over the past 5 years covered the Algebraic Relationships. The GLEs with 10 or more questions over the past 5 years:

• A1B (17 questions) – represent and describe patterns with tables, graphs, pictures, symbolic rules or words [79.5%]

There were 19 questions out of 52 that less than 70% of the students earned points. The GLE – A1C compare various forms of representations to identify a pattern had an average of 68.5%, with 3 out of 4 questions scoring below 70%. The GLE – A1D identify functions as linear or nonlinear from a table or graph had an average of 54.67%, with 3 out of 3 questions scoring below 70%. The GLE – A4A compare situations with constant or varying rates of change had an average of 69.17%, with 3 out of 6 questions scoring below 70%. Geometric and Spatial Relationships – 75.6% average 56 out of 302 (18.5%) questions over the past 5 years covered Geometric and Spatial Relationships strand. The GLEs with 10 or more questions over the past 5 years:

• G1A (13 questions) – identify the properties of one-, two- and three-dimensional shapes using the appropriate geometric vocabulary [78.04%]

• G2A (12 questions) – use coordinate geometry to construct geometric shapes There were 18 questions out of 56 that less than 70% of the students earned points. The GLE – G1B describe relationships between the corresponding angles and the length of corresponding sides of similar triangles (whole number scale factors) had an average of 62.0%, with 5 out of 7 questions scoring below 70%.

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Measurement – 74.59% average 50 out of 302 (16.6%) questions over the past 5 years covered Measurement strand. The GLEs with 10 or more questions over the past 5 years:

• M1A (12 questions) – identify and justify an angle as acute, obtuse, straight or right [82.46%] • M2C (10 questions) – describe how to solve problems involving the area of perimeter of polygons

[72.1%] • M2E (11 questions) – convert from one unit to another within a system of measurement (mass and

weight) [78.32%] There were 19 questions out of 50 that less than 70% of the students earned points. The GLE – M1C solve problems involving elapsed time (hours and minutes) had an average of 63.17%, with 5 out of 7 questions scoring below 70%. Data and Probability – 81.9% average 57 out of 302 (18.9%) questions over the past 5 years covered Data and Probability strand. The GLEs with 10 or more questions over the past 5 years:

• D1C (27 questions) – interpret circle graphs; create and interpret stem-and-leaf plots [84.72%] • D4A (11 questions) – use a model (diagrams, list, sample space, or area model) to illustrate the

possible outcomes of an event [80.95%] There were 9 questions out of 57 that less than 70% of the students earned points. No overall GLE average was below 70%.

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GRADE 7 – MAP Mathematics Longitudinal Item Analysis 37 GLEs were measured on the grade 7 mathematics assessment over the past 5 years; 3 GLEs were in the 80% range for students earning points on a given GLE, 21 GLEs were in the 70% range, 9 GLEs were in the 60% range, 2 GLEs were in the 50% range, 1 GLE was in the 40% range and 1 GLE was in the 30% range. Number and Operations – 77.8% average 85 out of 309 (27.5%) questions over the past 5 years covered the Number and Operations strand. The GLEs with 10 or more questions over the past 5 years:

• N3C (45 questions) – multiply and divide positive rational numbers [76.93%] There were 14 questions out of 85 that less than 70% of the students earned points. No overall GLE average was below 70%. Algebraic Relationships – 71.0% average 62 out of 309 (20.1%) questions over the past 5 years covered the Algebraic Relationships strand. The GLEs with 10 or more questions over the past 5 years:

• A2A (15 questions) – use variables to represent unknown quantities in equations and inequalities [77.3%]

• A3A (11 questions) – model and solve problems, using multiple representations such as graphs, tables, expressions, equations or inequalities [71.05%]

There were 27 questions out of 62 that less than 70% of the students earned points. The GLE – A1D identify functions as linear or nonlinear from tables, graphs or equations had an average of 69.9%, with 3 out of 5 questions scoring below 70%. The GLE – A2B generate equivalent forms for simple algebraic expressions had an average of 50.6%, with 4 out of 5 questions scoring below 70%. The GLE – A4A compare situations with constant or varying rates of change had an average of 68.57%, with 3 out of 7 questions scoring below 70%. Geometric and Spatial Relationships – 70.3% average 54 out of 309 (17.5%) questions over the past 5 years covered the Geometric and Spatial Relationships strand. The GLEs with 10 or more questions over the past 5 years:

• G1A (22 questions) – classify two- and three-dimensional shapes based on their properties [71.39%]

There were 26 questions out of 54 that less than 70% of the students earned points. The GLE – G1B describe relationships between corresponding sides, corresponding angles and corresponding perimeters of similar polygons had an average of 61.33%, with 4 out of 6 questions scoring below 70%. The GLE – G2A given ordered pairs, identify geometric shapes in the coordinate plane using their properties with an average of 68.0%, with 2 out of 4 questions scoring below 7-0%. The GLE – G3A reposition shapes under informal transformations, such as reflection (flip), rotation (turn) and translation (slide) had an average of 69.0%, with 2 out of 4 questions scoring below 70%. The GLE – G3C determine all lines of symmetry of objects had an average of 66.75%, with 3 out of 4 questions scoring below 70%.

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Measurement – 65% average 49 out of 309 (15.9%) questions over the past 5 years covered the Measurement strand. The GLEs with 10 or more questions over the past 5 years:

• M2C (11 questions) – describe how to solve problems involving circumference and/or area of a circle [69.82%]

There were 23 questions out of 49 that less than 70% of the students earned points. The GLE – M2B use tools to measure angles to the nearest degree with an average of 65%, with 1 out of 1 question scoring below 70%. The GLE – M1C solve problems involving addition and subtraction of time (hours, minutes and seconds) with an average of 62.25%, with 5 out of 8 questions scoring below 70%. The GLE – M2B use tools to measure angles to the nearest degree with an average of 36%, with 4 out of 4 questions scoring below 70%. The GLE – M2C describe how to solve problems involving circumference and/or area of a circle with an average of 69.82%, with 6 out of 11 questions scoring below 70%. Data and Probability – 74.1% average 59 out of 309 (19.1%) questions over the past 5 years covered the Data and Probability strand. The GLEs with 10 or more questions over the past 5 years:

• D4A (12 questions) – use models to compute the probability of an event [75.92%] There were 17 questions out of 59 that less than 70% of the students earned points. The GLE – D2A find, use and interpret measures of center and spread, including ranges and interquartile range with an average of 58.5%, with 6 out of 9 questions scoring below 70%. The GLE – D2B compare different representations of the same data and evaluate how well each representation shows important aspects of the data with an average of 40.38%, with 3 out of 4 questions scoring below 70%.

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GRADE 8 – MAP Mathematics Longitudinal Item Analysis 39 GLEs were measured on the grade 8 mathematics assessment over the past 5 years; 2 GLEs were in the 90% range for students earning points on a given GLE, 8 GLEs were in the 80% range, 12 GLEs were in the 70% range, 7 GLEs were in the 60% range, 9 GLE was in the 50% range and 1 GLE was in the 40% range. Number and Operation – 78.2% average 75 out of 317 (23.7%) questions over the past 5 years covered Number and Operations strand. The GLEs with 10 or more questions over the past 5 years:

• N1B (13 questions) use fractions, decimals and percents to solve problems [74.92%] • N3C (30 questions) apply all operations on rational numbers [80.37%] • N3E (10 questions) solve problems involving proportions, such as scaling and finding equivalent

ratios [82.9%] There were 17 questions out of 75 that less than 70% of the students earned points. The GLE – N1D use factors and multiples to describe relationships between and among numbers and justify characteristics of numbers with an average of 46%, with 2 out of 2 questions scoring below 70%. Algebraic Relationships – 67.3% average 87 out of 317 (27.4%) questions over the past 5 years covered Algebraic Relationships strand. The GLEs with 10 or more questions over the past 5 years:

• A1B (14 questions) generalize patterns represented graphically or numerically using words or symbolic rules, including recursive notation [65.79%]

• A2A (21 questions) use symbolic algebra to represent and solve problems that involve linear relationships, including recursive relationships [71.64%]

• A2B (11 questions) generate equivalent forms for linear expressions [57.18%] • A3A (13 questions) model and solve problems, using multiple representations such as graphs,

tables, equations, or inequalities [58.58%] There were 48 questions out of 87 that less than 70% of the students earned points. The GLE – A1B generalize patterns represented graphically or numerically using words or symbolic rules, including recursive notation had an average of 65.70%, with 8 out of 14 questions scoring below 70%. The GLE – A1D compare properties of linear functions between or among tables, graphs and equations with an average of 62.86%, with 5 out of 7 questions scoring below 70%. The GLE – A2B generate equivalent forms for linear expressions with an average of 57.18%, with 10 out of 11 questions scoring below 70%. The GLE – A3A model and solve problems, using multiple representations such as graphs, tables, equations, or inequalities with an average of 58.58%, with 11 out of 13 questions scoring below 70%. Geometric and Spatial Relationship – 68.4% average 58 out of 317 (18.3%) questions over the past 5 years covered the Geometric and Spatial Relationships strand. The GLEs with 10 or more questions over the past 5 years:

• G1A (11 questions) – describe, classify and generalize relationships between and among types of a) two-dimensional objects and b) three-dimensional objects using their defining properties (of shapes) including Pythagorean Theorem | describe, classify and generalize relationships between and among types of a) two-dimensional objects and b) three-dimensional objects using their defining properties (of shapes) including cross section of a three-dimensional object results in what two-dimensional shape [73.32%]

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• G4B (11 questions) – draw or use visual models to represent and solve problems [65.18%] There were 28 questions out of 58 that less than 70% of the students earned points. The GLE – G1B apply relationships between corresponding sides and corresponding areas of similar polygons to solve problems with an average of 59.94%, with 6 out of 8 questions scoring below 70%. The GLE – G2A use coordinate geometry to analyze properties of right triangles and quadrilaterals with an average of 56.57%, with 6 out of 7 questions scoring below 70%. The GLE – G3A reposition shapes under formal transformations, such as reflection, rotation and translation with an average of 66.81%, with 4 out of 8 questions scoring below 70%. The GLE – G3B describe the relationship between the scale factor and the area of the image using a dilation (stretching/shrinking) with an average 52%, with a 1 out of 1 questions scoring below 70%. The GLE – G4B draw or use visual models to represent and solve problems with an average of 65.18%, with 6 out of 11 questions scoring below 70%. Measurement – 62.1% average 43 out of 317 (13.6%) questions over the past 5 years covered the Measurement strand. The GLEs with 10 or more questions over the past 5 years:

• M2B (13 questions) – use tools to determine the measure of reflex angles to the nearest degree [51.85%]

• M2C (19 questions) – describe how to solve problems involving surface area and/or volume of a rectangular or triangular prism, or cylinder [64.61%]

There were 26 questions out of 43 that less than 70% of the students earned points. The GLE – M1B identify the equivalent volume measures within a system of measurement (e.g., m3 to cm3) with an average of 58.25%, with 2 out of 4 questions scoring below 70%. The GLE – M2B use tools to determine the measure of reflex angles to the nearest degree with an average of 51.85%, with 11 out of 13 questions scoring below 70%. The GLE – M2C describe how to solve problems involving surface area and/or volume of a rectangular or triangular prism, or cylinder with an average of 64.61%, with 11 out of 19 questions scoring below 70%. The GLE – M2D analyze precision and accuracy in measurement situations and determine number of significant digits with an average of 54%, with 1 out of 1 question scoring below 70%. The GLE – M2E convert square or cubic units to equivalent square or cubic units within the same system of measurement with an average of 68.25%, with 1 out of 2 questions scoring below 70%. Data and Probability – 73.0% average 54 out of 317 (17%) questions over the past 5 years covered the Data and Probability strand. The GLEs with 10 or more questions over the past 5 years:

• D2A (13 questions) find, use and interpret measures of center, outliers and spread, including range and interquartile range [67.83%]

There were 17 questions out of 54 that less than 70% of the students earned points. The GLE – D2A find, use and interpret measures of center, outliers and spread, including range and interquartile range with an average of 67.83%, with 7 out of 13 questions scoring below 70%. The GLE – D2B compare different representations of the same data and evaluate how well each representation shows important aspects of the data with an average of 53.65%, with 5 out of 5 scoring below 70%.

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Item Analysis of 6th Grade Placement Tests

As part of math placement for sixth grade, students take the Orleans-Hanna Algebra Readiness Test and the District Computation Test. The District Computation Test is designed to test both secure and developing skills from elementary school. It is not intended to measure the success of the curriculum itself but the level of proficiency of students even if the topic has only been introduced to students. The computation test covers the computation skills of ordering numbers; adding, subtracting, multiplying and dividing whole numbers, fractions and decimals; factors and multiples; and finding the perimeter and area of various geometric shapes. This report compares Captain Elementary School’s, Glenridge Elementary School’s and Meramec Elementary School’s average and median scores on the Orleans-Hanna Algebra Readiness Test and the District Computation Test from 2006 to 2010 and the percent correct for each item on the 2008 District Computation Test and the 2010 District Computation Test. The Orleans-Hanna Algebra Readiness Test graphs displaying average test scores and median test scores from all three elementary schools show that gaps between the schools have closed over time. The same is true for the average test scores and median test scores for the District Computation Test. Both 2008 and 2010 graphs on item analysis for the District Computation Test show similar performances between all three elementary schools for the items on the test. The information was also separated into individual elementary school graphs allowing for a comparison between the 2008 and 2010 school years on the same graph. The Mathematics Committee will continue to gather item analysis data on future tests in order to make any necessary adjustments to the elementary math program.

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Grades 3-8 MAP Student Achievement 2006 – 2010 Percent Advanced/Proficient for

White and African American Students

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Appendix B Comparative Schools Studies

• SAT Math Scores for the top ten highest achieving school districts in the State of Massachusetts, 2006-2007 as reported on Massachusetts State Department of Education website, including data on Percentage of students taking Advanced Placement Calculus, AP Calculus AB, and AP Calculus BC

• Comparison School Study Massachusetts and School District of Clayton as measured by ACT scores 2009

• Comparison of Instructional resources utilized by highest-performing school districts nationally in terms of Math ACT scores, 2009 (Project Blueprint Consortium, Ladue Consortium, ACT schools)

• Comparison of College Prep Study Achievement Data as measured by ACT Quartile Scores • Comparison of Neighboring Districts’ MAP Math Scores Grades 3-Algebra I

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MEMO To: Board of Education From: Dottie Barbeau Date: October 22, 2010 Re: Math review update – comparison between the School District of Clayton and

Massachusetts mathematics performance As part of our mathematics curriculum review we are now analyzing academic achievement of our School District of Clayton students. The student performance analysis requires comparisons at the local, national, and international level to determine the level of achievement and competency our students are attaining as a result of their current mathematics education. Last week you received elementary student achievement data from Heidi, and next week you will receive secondary student achievement data. As you know, in December we expect to receive results of the PISA (Programme for International Student Assessment) which will provide a direct international comparison for Clayton against the highest achieving countries in the world. For most of the school districts in the country, international comparisons are hard to do given the few international assessments available. The purpose of this memo is to provide to you an indirect global competency measure of Clayton student achievement in mathematics using a comparison of Clayton student data against student achievement in the State of Massachusetts. As you know, Massachusetts is recognized worldwide as globally competitive as a result of their outstanding performance in mathematics on the TIMSS and PISA international assessments. The comparison between Clayton and Massachusetts gives us a picture of how our students collectively “stack up” against some of the highest achieving mathematics students in the world. The following charts compare Clayton and Massachusetts on the following measures: • Advanced Placement Performance scores for Calculus – both AB and BC Calc (2009)

Also attached to the Friday Memo is the following ACT comparison: • ACT-Massachusetts comparisons in mathematics performance (2009); We tested 90+% of our

students on the ACT; less than 20% of Massachusetts students took the ACT. Heidi will be providing a more in depth analysis of the ACT in her assessment report. This comparison is not intended to replace her presentation on the ACT.

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(AP data was not reported for the Massachusetts Math and Science Academy) On the graph above for each school district you’ll see three bars – the bar on the left represents the total number of students taking AP Calculus, and then you see both AB and BC Calc measures. You’ll note that Clayton is competitive in the number of students taking AP Calculus, but also note that Clayton has the second highest percentage of students taking BC Calc. On the following graphs you’ll see the percentage of students taking AB and BC Calc and the percentage of students scoring a 3 or higher in those classes. The Advanced Placement performance measure is a truly reliable comparison measure across districts. The school districts on the graph are in descending order from the #1 top school district to #10.

Comparison School Study Massachusetts Top Ten School Districts in the Area of

Mathematics as Measured by SAT Math Scores reported on Massachusetts DESE Website

State Report (most current data 2006-‐07) % Students Taking

Advanced Placement Courses in Calculus

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Clayton Math Curriculum Review Massachusetts School Districts

Demographic Data (2009)

School District

Number of students in district

%

AA

% Asian

% White

Expenditures per Pupil

School District of Clayton

[email protected]

High School 845 Total 2508

22.4 9.4 $16,104

Massachusetts Academy for Math and Science

Grades 11 & 12 only

Total: 91

4.4 16.5 79.1 NA

Acton Boxborough

High School 1953

.8 21.3 73.0 $12,228

Lexington Regional School District

High School 1955

Total 6182

4.5 26.2 62.2 $14,469

Boston Latin

High School 1622

(7-12 only)

12.1 27.8 49.0 NA

Weston School District

High School 715

Total 2388

6.2 10.0 76.7 $17,017

Newton School District

Newton South

High School 1245

Total 11,765

4.7 19 69.1 $15,498

Wellesley School District High School 1220

Total 4868

3.8 7.2 81.8 $13,916

Concord Carlisle

High School

1245

5.2 5.9 83.5 $17,486

Wayland

High School 891

Total 2738

4.5 11.9 76.8 $14,033

Dover Sherborn

High School 608

1.7 4.3 91.8 $15,690

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ACT Profile Report Comparing Clayton and Massachusetts Graduating Class 2009

Note: Clayton tested 90+% of our students on the ACT. Massachusetts tested less than 20% of their students on the ACT.

Five Year Trends

Percent of Students Meeting College Readiness Benchmarks Mathematics

Year Clayton Massachusetts National 2005 69 58 41 2006 65 62 42 2007 66 65 43 2008 69 65 43 2009 65 68 42

Average ACT Scores

Mathematics

Year Clayton Massachusetts National 2005 25.1 22.8 20.7 2006 24.4 23.3 20.8 2007 24.8 23.6 21.0 2008 24.6 23.9 21.0 2009 24.5 24.3 21.0

Average ACT Scores by Level of Preparation

Mathematics

Clayton Massachusetts Year Core or More Less than Core Core or More Less than Core 2005 25.6 24.9 22.9 22.5 2006 25.6 22.7 23.5 23.1 2007 25.0 23.0 23.7 23.4 2008 25.2 22.5 23.9 23.7 2009 25.3 21.4 24.3 24.3

Percent and Average Composite Score by Race/Ethnicity

Clayton Massachusetts 2009 2009 N % Avg N % Avg All Students 207 100 25.4 13,093 100 23.9 African American/Black 36 17 19.3 462 4 19.1 American Indian/Alaska Native 0 0 21 0 23.8 Caucasian American/White 121 58 26.7 10,008 76 24.1 Hispanic 7 3 26.4 360 3 21.2 Asian American/Pacific Islander 14 7 30.5 593 5 25.2 Other/No Response 29 14 25.1 1649 13 24.5

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Academic Achievement

Average ACT Scores by Race/Ethnicity

Student Group Race/Ethnicity Mathematics All Students 24.5 African American/Black 18.8 American Indian/Alaska Native Caucasian American/White 25.5 Hispanic 25.6 Asian American/Pacific Islander 31.1

Clayton

Other/No Response 23.7 All Students 24.3 African American/Black 19.9 American Indian/Alaska Native 23.7 Caucasian American/White 24.3 Hispanic 21.3 Asian American/Pacific Islander 27.1

Massachusetts

Other/No Response 24.9 All Students 21.0 African American/Black 17.1 American Indian/Alaska Native 18.7 Caucasian American/White 21.9 Hispanic 19.1 Asian American/Pacific Islander 24.5

National

Other/No Response 21.0 Note: Clayton tested 90+% of our students on the ACT. Massachusetts tested less than 20% of their students on the ACT.

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Percent of Students in College Readiness Standards (CRS) Score Ranges Student Group CRS Range Mathematics

N % 33 to 36 25 12 28 to 32 44 21 24 to 27 45 22 20 to 23 42 20 16 to 19 42 20 13 to 15 9 4

Clayton

01 to 12 0 0 33 to 36 982 8 28 to 32 2551 19 24 to 27 4032 31 20 to 23 2672 20 16 to 19 2396 18 13 to 15 446 3

Massachusetts

01 to 12 14 0 33 to 36 45,198 3 28 to 32 139,060 9 24 to 27 293,477 20 20 to 23 300,212 20 16 to 19 495,592 33 13 to 15 198,214 13

National

01 to 12 8716 1 Note: Clayton tested 90+% of our students on the ACT. Massachusetts tested less than 20% of their students on the ACT.

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Average ACT Scores by Gender Student Group Gender Average ACT Scores

Mathematics Males 24.6

Females 24.3

Clayton Missing . Males 25.1

Females 23.7

Massachusetts Missing 26.0 Males 21.6

Females 20.4

National Missing 21.2

Percent of Students Meeting College Readiness Benchmark Scores by Gender

Student Group Gender Percent of Students Mathematics

Males 64 Clayton Females 65

Males 73 Massachusetts Females 65

Males 47 National Females 38

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ACT Subscore Distributions, Cumulative Percentages (CP), and Subtest Score Averages

Clayton Massachusetts Pre/Elementary

Algebra Algebra/

Coordinate Geometry

Plane Geometry/

Trigonometry

Pre/Elementary Algebra

Algebra/ Coordinate Geometry

Plane Geometry/

Trigonometry

ACT Scale Score

N CP N CP N CP N CP N CP N CP

18 24 100 4 100 9 100 1094 100 345 100 380 100 17 29 88 11 98 6 96 1512 92 277 97 126 97 16 14 74 14 93 21 93 1072 80 857 95 910 96 15 17 68 14 86 24 83 1310 72 854 89 1387 89 14 21 59 28 79 24 71 1243 62 2133 82 1665 79 13 9 49 14 66 32 59 1190 52 1295 66 2198 66 12 22 45 23 59 18 44 1605 43 1934 56 1148 49 11 13 34 23 48 17 35 961 31 1223 41 1621 40 10 14 28 35 37 20 27 978 24 1995 32 1280 28 9 11 21 21 20 14 17 623 16 1012 17 891 18 8 13 16 11 10 10 11 783 11 588 9 751 11 7 13 10 5 4 5 6 535 6 254 4 195 6 6 4 3 1 2 4 3 144 1 82 2 232 4 5 1 1 1 1 2 1 27 1 166 2 144 2 4 1 1 0 1 1 1 11 1 31 1 66 1 3 0 1 2 1 0 1 1 1 25 1 62 1 2 1 1 0 1 0 1 3 1 10 1 21 1 1 0 1 0 1 0 1 1 1 12 1 16 1

Avg (SD)

13.0 (3.8) 12.0 (3.0) 12.5 (3.0) 13.1 (3.) 12.1 (2.8) 12.1 (2.9)

ACT Score Quartile Values Quartile Clayton Massachusetts

Q3 (75th Percentile) 29 22.8 Q2 (50th Percentile) 25 23.3 Q1 (25th Percentile) 20 23.6

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College Readiness & The Impact of Course Rigor

Average ACT Scores and Average ACT Score Changes by Common Course Patterns

Clayton Massachusetts Mathematics Course Pattern

N Percent ACT Math

Course Value Added

N Percent ACT Math

Course Value Added

Alg 1, Alg 2, Geom, Trig, & Calc

29 14 28.8 8.5 1480 11 26.6 6.1

Alg 1, Alg 2, Geom, Trig, & Other Adv Math

23 11 22.7 2.4 1246 10 23.1 2.6

Alg 1, Alg 2, Geom, & Trig

13 6 19.3 -1.0 807 6 21.1 0.6

Alg1, Alg 2, Geom, & Other Adv Math

11 5 19.5 -0.8 1675 13 21.3 0.8

Other comb of 4 or more years of Math

97 47 26.4 6.1 6171 47 26.0 5.5

Alg 1, Alg 2, Geom (Min. Core)

6 3 15.0 -5.3 590 5 18.8 -1.7

Other comb of 3 or 3.5 years of Math

8 4 25.3 5.0 674 5 23.3 2.8

Less than 3 years of Math 15 7 20.3 - 179 1 20.5 - No Math course/grade info reported

5 2 17.6 - 271 2 22.4 -

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Clayton Math Curriculum Review – Comparison Schools Study -‐ March 2010 Includes School District of Clayton Project Blueprint Schools, Ladue’s Benchmarking Consortium, and Demographically Matched Schools for ACT Comparison

Clayton’s Project Blueprint Consortium of Schools

School District

Location

K-‐5 Math Program

6-‐8 Math Program

9-‐12 courses & texts

(not all courses are listed for all schools)

Composite

ACT

ACT Math

SAT where ACT is

secondary in use 620=25 ACT

School District of Clayton [email protected] Total district enrollment: 2487 Asian: 9.4% African American: 22.4% Hispanic: 2.3% Free/Reduced Lunch 16.1% High School enrollment: 827 Enrollment type: Resident: 75% Voluntary Transfer Desegregation Program: 18%, Other 7%

St. Louis, MO Everyday Math Connected Math 8th Grade Challenge Algebra (Holt) 7th Grade Supplements Pre-‐Algebra II Extensions, Gateways to Algebra and Geometry – An Integrated Approach (McDougal-‐Little)

Core Plus IM1, IM2, IM3, IM4 Honors Track: Key Curriculum Press, Foerster Alternate sequence: Pearson and UCSMP

25.4 90+% took

ACT

24.5 Math 661 (less than 80% took the test)

Edina "Norlin-‐Weaver, Jenni" [email protected]

Edina, Minnesota

Everyday Math UCSMP UCSMP PreCalc and Calc use Glencoe Math

25.7 Math 630 (less than 80% took the test)

Pallasaides [email protected]

Kintnersville, PA

Everyday Math 6th Pearson 6-‐8 Pre Alg Prentice Hall 8th Glencoe

Alg I and II Prentice Hall, Geometry Key Curriculum Press, Pre Calc Houghton Mifflin, Integrated AGS – Contemporary Mathematics Glencoe

Math 533 (less than 80% took the test)

Whitefish Bay [email protected]

Whitefish Bay, WI

Everyday Math McDougal Littell 2007 Algebra I McDougal Littell Math Matters, Glencoe Geometry, McDougal Littell 2008 Algebra 2, Key Curriculum Press 2006 Adv Algebra 2 McDougal Littell 2007 PreCalc Pearson 2004 AP Calc AB/BC Wiley & Sons AP stats Pearson Education 2007

26.2 90+% took

ACT

26.5

Guilford Anne Keene [email protected]

Guilford, CT Everyday Math Connected Math 2003 Algebra I Prentice Hall 2007 Algebra II Heath 1997 Geometry Glencoe 1998 Precalc Houghton Mifflin 2008 Calc I Thompson 2007 NOTE: Guilford is in the process of adopting a new

Math 534

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Geometry text for 2010-‐2011. (Geometry, Holt McDougal, 2011). We anticipate an Algebra II adoption next year; hopefully, it will be the same publisher as the Algebra I.

Wayland Brad Crozier [email protected]

Wayland, MA Everyday Math 6th Grade Level 1 -‐ Everyday Mathematics (grade 4 spiral) -‐ In use for the third year Level 2 -‐ Middle School Mathematics Course 1 (Scott Foresman) -‐ In use for the 12th year also Impact Mathematics (2 units) -‐ in use for the 6th year, and Zero to One (Mathscape) -‐ In use for the ninth year Level 3 -‐ Middle School Mathematics Course 2 (Scott Foresman) -‐ In use for the 12th year -‐ plus tons of materials from a wide variety of sources -‐ MathCounts etc. 7th Grade -‐ Pre-‐ Algebra Level 1 -‐ Everyday Mathematics (grade 5 spiral) -‐ In use for the third year Level 2 -‐ Passport to Algebra and Geometry -‐ (Larson) -‐ In use for the sixth or seventh year Level 3 -‐ Gateways to Algebra and Geometry -‐ An Integrated Approach -‐ (McDougal Littel) -‐ In use for a second year 8th Grade -‐ Algebra Level 1 -‐ Modified Algebra -‐ Everyday Mathematics (grade 6 spiral) Level 2 -‐ Algebra I (Larson) -‐ In use for the sixth or

Algebra I: Teacher made and pulled from many resources Algebra II: Intro and College: Holt Honors: McDougal Littel Geometry: Intro and College: Geometry; Explorations and Applications McDougal Littel (We are not a big fan of this one and would like to switch but haven't found anything significantly better) Honors: Geometry for Enjoyment and Challenge, McDougal Littel Precalculus: Intro and College: Stewart Honors: Demana Waits Calculus: College: Best AB and BC (AP) Finney, Demana, Waits Statistics: College: Larson AP: Bock

Math 618 (less than 80% took the test)

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seventh year Level 3 -‐ Algebra -‐ An Integrated Approach -‐ (McDougal Littel) -‐ -‐ In use for the 12th year The recent text adoptions for seventh and eighth grade accelerated math courses aligned with what the high school was using in grades 9 and 10. The McDougal Littel books were favored by WMS math teachers due to the high incidence of non-‐routine problem solving problems they offered.

Cape Elizabeth [email protected]

Cape Elizabeth, ME

Everyday Math Everyday Math 6 & 7 8th UCSMP

UCSMP Math 580 (All 11th grade take the test)

Ladue Consortium Schools

School District

Location

K-‐5 Math Program

6-‐8 Math Program



Composite

ACT

ACT Math

SAT where ACT is


Eanes ISD "Jerri LaMirand" [email protected]

Austin, Texas Everyday Math Holt Alg, Geo, Alg II Pre Calc Holt Calc AB BC Houghton Mifflin

26.3 (65% took test)

27.0 615 (80% took the test)

Edina (Also a member of Project Blueprint consortium – please see data above)

Edina, Minnesota

See data above in Project Blueprint Schools

25.7

Highland Park ISD (Dallas, Texas) [email protected] [email protected]

Dallas, Texas 4 elementary schools. Recently adopted EnVision (2nd year) Not aligned across all schools. Some of the elementary schools still use

Holt Algebra I: McDougal Littel Geometry: Glencoe Texas Geometry Pre Calc: Thompson Learning/Brooks-‐Cole (Precalc-‐Mathematics for Calculus) Calc AB: Thompson Learning Brooks-‐Cole (Sing Var Calc w/vector functions) Calc BC: John Wiley & Sons (Calc Early Trans Single Variables 8th ed) Note: Estimate 60% of work done in any one course is

26.1 (70% took the test)

26.8

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Investigations. based on text) Ladue "Donna Jahnke" [email protected]

St. Louis Investigations Holt (6th and 7th) Glencoe (7th and 8th)

Algebra I: Glencoe Geometry: Glencoe Pre Calc: Glencoe Calc AB and BC: Prentice Hall


25.8

Palo Alto Unified [email protected] [email protected] [email protected]

Palo Alto, California

Everyday Math 6-‐8 Holt used as Core 8th grade supplemental for algebra: Key Curriculum Press Connected Math is used supplemental for grades 6-‐8

Alg : Prentice Hall (California Geometry) Geo: Prentice Hall (California Geometry) Honors Geometry: Jurgensen (McDouglal Littel) PreCalc and Calc BC: Graphical, Numerical, Algebraic by Demana Waits (Pearson) Also use Intro to Analysis and Calculus

26.5 (less than 80% took the test)

644 (less than 80% took the test)

Westside Community "Bert Jackson" [email protected]

Omaha, Nebraska

Everyday Math McDougal Littel and Pearson

Alg I Holt, Alg 2 Coxford, Geometry McDougal Littel and Glencoe, Pre Calc Pearson, many texts across courses, (list available)


24.1

Wilmette/New Trier Public (see note *) [email protected] [email protected]

Wilmette, Illinois

Everyday Math McDougal Littel (grades 5-‐8)

Alg I McDougal Littel Level II Alg I Prentice Hall Level III Alg I Integrated Approach Geometry Level III and IV McDougal Littel and Geometry for Enjoyment Pre Calc? Calc ?

26.9 (more than 90% took the test)

28

Wilton Public Schools "gottesmana" [email protected]

Wilton, Connecticut

Everyday Math 6th grade Everyday Math 7-‐8 UCSMP

UCSMP is used for level 2. (normal college bound). Foerster and Larson are used for Honors track (including multivariable Calc). AGS series for level 1 (weak).

SAT 605 (less than 80% took the test)

*Wilmette/New Trier is a high school district with four feeder districts. The smallest feeder district uses a different program.

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Schools With Close Demographic Match to Clayton* Comparison of ACT Math scores

(matched by high school size, more than 80% take the ACT, percent minority, percent low income) Math Programs and texts shown only for schools performing as well or better than School District of Clayton

School District

Location

K-‐5 Math Program

6-‐8 Math Program



Composite

ACT

ACT Math

SAT where ACT is


Whitefish Bay (a Project Blueprint School as shown above) Math program data is entered above under Project Blueprint schools.

Whitefish Bay, Wisconsin


26.5

Hume Fogg High School Magnet (High School only) [email protected]

Nashville, Tennessee

N/A – High school only

N/A – high school only Alg I & Geo McDougal Littell, Alg II Glencoe, Pre Calc state required Glencoe, Calc Kennedy Book, Adv Calc Carson Calculus

25.7

Orono "Aaron Ruhland" [email protected] *(10-‐15% less minority population than Clayton)

Orono, Minnesota

Everyday Math McDougal Littell/Holt Through Algebra II – McDougal Littell and Holt. AP Calc: Calculus with Analytic Geometry, 8th Ed.”(Larson). Pre-‐Calculus: “Pre-‐Calculus” (Larson)

25.3

Greendale *(10-‐15% less minority population than Clayton) [email protected]

Greendale, WI Everyday math McDougal Littel Bulk of lower level McDougal Littel, Honors Key Curriculum Press, Calc & higher levels Prentice Hall

25.2

Shorewood "Dean Schultz" [email protected]

Shorewood, WI

Everyday Math Connected Math Core Plus – IM1, IM2, IM3 PreCalc: "Calculus from Graphical, Numerical, and Symbolic Points of View, Second Edition" by Ostebee & Zorn. Published by Brooks/Cole Copyright 2002. BC is not offered, though students are offered individual help if they wish to pursue some topics in BC. (no other course is offered – no tracks)

25.0

Dunlap *(10-‐15% less minority population than Clayton) [email protected]

Dunlap, Illinois Harcourt Prentice Hall 6 & 7 Middle Grades Math 8th (Prentice Hall)

Algebra Glencoe, Geometry: Geo Concepts and Applications, Calc Prentice Hall

24.6



24.5

Deer Creek Edmond, 23

115

Oklahoma Johnsburg McHenry,

Illinois 22

Mascoutah Mascoutah, Illinois

22

Mahomet-‐Seymour Mahomet, Illinois

21.8

Effingham Effingham, Illinois

21

Evergreen park Evergreen Park, Illinois

20.9

Ridgewood Norridge, Illinois

20.5

Glenwood Springs Glenwood Springs, Colorado

20.4

Marengo Marengo, Illinois

20.2

Summit Frisco, Colorado

20

Windsor Windsor, Colorado

19.7

Elmwood Park Elmwood Park, Illinois

19.6

Falcon Falcon, Colorado

18.8

*CLAYTON demographics: Total district enrollment: 2487 Asian: 9.4% African American: 22.4% Hispanic: 2.3% Free/Reduced Lunch 16.1% High School enrollment: 827 Enrollment type: Resident: 75% Voluntary Transfer Desegregation Program: 18% Private Tuition: 3% Other: 4%

Contact: Dr. Dottie Barbeau, Assistant Superintendent for Teaching and Learning, School District of Clayton 314-‐854-‐6022, [email protected]

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Comparison of College Prep Study Achievement Data as measured by ACT Quartile Scores (2010)

November 5, 2010 Following the out of state math comparison data that was sent to the Board of Education, several questions pertaining to our “nonhonors,” or College-Prep, math students were raised by Board of Education members. Therefore, provided below is math data regarding a comparison of our College-Prep math students to students in other high performing districts. In order to compare College-Prep achievement groups across out of state districts we have to first be able to identify one of Clayton’s norm referenced sources that would provide meaningful data, and secondly identify comparable districts using the same norm referenced assessments, administered to similar percentages of students taking the assessment. In Clayton, the best tool we have for this purpose is the ACT, as 90+% of our students take the test and the ACT Profile Report provides data broken down by quartile scores. (The use of quartile scores for this comparison was mentioned by Mr. Singer in his questions regarding collecting the data for comparison.) In looking for meaningful district comparisons, it is important to note that only 16% of Massachusetts students take the ACT. In each district there are only a handful of students who use that test for college admission so it is not possible to use that as a measure for students in any particular track. To locate this data for you, we turned to two of our Project Blueprint schools, Edina, Minnesota, and Whitefish Bay, Wisconsin. Both districts are in the Midwest area and both primarily use the ACT for college placement and determining College Readiness. (The other Project Blueprint schools are located on or near the east coast and primarily use the SAT.) The section of the ACT Profile Report that was used for this comparison is Section II, Academic Achievement, Table 2.3 ACT Score Quartile Values.

Table 2.3 ACT Score Quartile Values (2010)

Mathematics

Quartile

Clayton

ACT Comp: 25.4

Edina, Minnesota

ACT Comp: 25.7

Whitefish Bay, Wisc.

ACT Comp: 25.7

Q3 (75th Percentile) 30 30 30 Q2 (50th Percentile) 26 27 26 Q1 (25th Percentile) 22 23 23 The quartiles shown above break up the district’s total number of ACT scores into four equal parts. Quartiles can be thought of as percentile measure. If 100% of the scores are broken into four equal parts, we have subdivisions at the 25th percentile, 50th percentile, and 75th percentile. As you see above, Clayton’s ACT score at Quartile 3, or at the 75th percentile, is 30. That means that the top 25% of our students, the group of students that would be in the 75th percentile or above scored a 30 or higher on their ACT. The next 25% (quartile) of the students, those between the 50th

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and 75th percentile, scored between a 26 and 30 on their ACT test. The next quartile of the students, or those between the 25th and 50th percentile, scored between a 22 and 26 on their ACT, and the last quartile of the students scored below a 22. (22 is considered to be College Ready by ACT.) Clayton’s scores are comparable to Edina and Whitefish Bay. When looking at quartiles, we can generally consider that the top 25% of students, or the scores above Q3, represent our honors students, and that students between the 25th and 75th percentile represent our College-Prep students. Across all three schools, the top 25% of the students are scoring 30+ on the ACT mathematics assessment. Across all three schools, 75% of the students are considered College Ready in mathematics according the ACT benchmarks. And across all three schools, the College-Prep” students are within 7-8 points of the honors group. Again, Clayton’s scores are comparable to our two high achieving Project Blueprint schools. Comparison District demographic data (2009) Total Enrollment Asian African American Hispanic Clayton

2487 9.4% 22.4% 18% of students attended under the State

Voluntary Transfer Program.

2.3%

Edina 7988 7% 6% 3% Whitefish Bay

2976 6.5% 10.9% 8% of students attended under the State

Chapter 220 Integration Program.

3.1%

118

MAP 2010 Mathematics Comparisons – Percent Advanced and Percent Advanced/Proficient

Comparisons with neighboring school districts Lindbergh, Ladue, Kirkwood, Webster Groves, Wentzville

119

2010 MAP % Advanced/Proficient Mathematics Clayton Lindbergh Kirkwood Ladue Webster Wentzville gr 3 67.5 79.4 74.2 68.4 69.1 55.1 gr 4 73.2 82 78.2 81.6 69.1 56 gr 5 82.5 86.4 79.2 78 64.1 64.2 gr 6 76 77.4 71.1 76.2 71.9 67.2 gr 7 75.5 73.4 72.2 81.9 64.9 68.4 gr 8 75.5 76.6 73.1 77.8 68.8 67.3 AI 75.9 80.4 83.7 73.8 75.2 70.6

2010 MAP % Advanced Mathematics Clayton Lindbergh Kirkwood Ladue Webster Wentzville gr 3 21.7 24.8 23.8 18 14.7 10.4 gr 4 29.6 26.6 25.9 30.9 17.5 12.2 gr 5 41.8 48.7 34.7 34.6 23.9 21.1 gr 6 39.3 30.8 28.1 35.4 25.7 22.8 gr 7 40.6 27.5 33.7 38.1 25.3 25.7 gr 8 46.3 38.4 39.2 51.2 35.4 32.4 AI 32.9 35.9 35.6 36 31.4 27.7

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Appendix C Mathematic Benchmarks Comparisons

• Elementary, Middle, High School benchmarks comparisons (Not Complete only grade 4

attached) • Massachusetts Common Core Plus recommendations October 2010

121

The School District of Clayton Elementary Mathematics Benchmarks Comparison

Grade 4

Correlation with

Common Core State Standards (2010)

Final Report of the National Mathematics Advisory Panel (2008)

National Council of Teachers of Mathematics Principles and Standards for School Mathematics (2000)

Massachusetts Department of Education

Mathematics Curriculum Frameworks (2000) Common Core Plus (2010)

Everyday Mathematics Grade 4 (2007)

Massachusetts comparisons contributed by: Mary Eich, K-8 Mathematics Coordinator, Newton Public School District, Massachusetts

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Common Core State Standards

Massachusetts Core Plus

National Math Advisory Panel NCTM Standard

Grades 3-5

Massachusetts Frameworks Grade

4

Everyday Mathematics Grade 4

Singapore Grade 4

4. Generalize place value understanding for multi-digit whole numbers.

Whole numbers less than or equal to 1,000,000.

1.Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right 2. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. 3. Use place value understanding to round multi-digit whole numbers to any place.

NCTM 3-5 Understand the place value structure of the base-ten number system and be able to represent and compare whole numbers and decimals.

4.N.1 Exhibit an understanding of the base ten number system by reading, modeling, writing, and interpreting whole numbers to at least 100,000; demonstrating an understanding of the values of the digits; and comparing and ordering the numbers. 4.N.6 Exhibit an understanding of the base-ten number system by reading, naming, and writing decimals between 0 and 1 up to the hundredths.

Goal N1 Read and write whole numbers up to 1,000,000,000 and decimals through thousandths; identify places in such numbers and the values of the digits in those places; translate between whole numbers and decimals represented in words and in base-10 notation.

Whole Numbers

Numbers up to 100,000

• Number notation and place values (ten thousands, thousands, hundreds, tens, ones),

• Reading and writing numbers in numerals and words,

• Comparing and ordering numbers,

• Number patterns,

• Rounding off numbers to the nearest 10 or 100,

• Use of approximation symbol

Extend understanding of fraction equivalence and ordering. 3. Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify

NCTM 3-5 Develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers.

4.N.3 Demonstrate an understanding of fractions as parts of unit wholes, as parts of a collection, and as locations on the number line.

Goal N2 Read, write, and model fractions; solve problems involving fractional parts of a region or a collection; describe and explain strategies used; given a fractional part of a region or a collection, identify the unit whole.

Fractions

Fraction of a set of objects

• Include interpretation of fraction as part of a set of objects

Grade 4 - Number and Operations

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

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Grades 3-5


4


Singapore Grade 4

decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.


124




Grades 3-5


4


Singapore Grade 4

Gain familiarity with factors and multiples.

4. Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.

NCTM 3-5 Describe classes of numbers according to characteristics such as the nature of their factors.

4.N.7 Recognize classes (in particular, odds, evens; factors or multiples of a given number; and squares) to which a number may belong, and identify the numbers in those classes. Use these in the solution of problems.

Goal N3 Find multiples of whole numbers less than 10; find whole-number factors of numbers.

Factors and multiples

• Determining if a 1-digit number is a factor of a given number,

• Listing all factors of a given number up to 100,

• Finding the common factors of two given numbers,

(above items taught in Clayton grade 5)

• Recognizing the relationship between factor and multiple,

(taught in Clayton grade 4)

• Determining if a number is a multiple of a given 1-digit number,

• Listing the first 12 multiples of a given 1-digit number,

• Finding the common multiples of a given 1-digit numbers.

Exclude ‘highest common factor’ (H.C.F.) and ‘lowest common multiple’ (L.C.M.)


125




Grades 3-5


4


Singapore Grade 4

NCTM 3-5 Recognize equivalent representations for the same number and generate them by decomposing and composing numbers

4.N.2 Represent, order, and compare numbers through 9,999. Represent numbers using expanded notation (e.g., 853 = 8 x 100 + 5 x 10 + 3), and written out in words (e.g., eight hundred fifty-three).

Goal N4 Use numerical expressions involving one or more of the basic four arithmetic operations and grouping symbols to give equivalent names for whole numbers.

Not covered in Primary 4 Singapore Curriculum

Generate and analyze patterns. 5. with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.2 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. 6. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

NCTM 3-5 Recognize and generate equivalent forms of commonly used fractions, decimals, and percents.

4.N.5 Identify and generate equivalent forms of common decimals and fractions less than one whole (halves, quarters, fifths, and tenths.)

Goal N5 Use numerical expressions to find and represent equivalent names for fractions and decimals; use and explain a multiplication rule to find equivalent fractions; rename fourths, fifths, tenths, and hundredths as decimals and percents.

*Not covered in Primary 4 Singapore Curriculum

Decimals up to 3 decimal places • Notation and place

values (tenths, hundredths, thousandths),

• Indentifying the values of the digits in a decimal,

• Comparing and ordering decimals,

• Conversion of a fraction whose denominator is a factor of 10 or 100 to a decimal,

• Rounding off decimals to the nearest whole number, 1 decimal place, 2 decimal places

7. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals

NCTM 3-5 Use models, benchmarks, and equivalent forms to

4.N.4 Select, use, and explain models to relate common

Goal N6 Compare and order whole numbers up to 1,000,000,000 and

Mixed numbers and improper fractions

• Concepts of mixed numbers and


126




Grades 3-5


4


Singapore Grade 4

refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

judge the size of fractions. NCTM 3-5 Explore numbers less than 0 by extending the number line and through familiar applications.

fractions and mixed numbers (1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/10, 1/12, and 1 1/2), find equivalent fractions, mixed numbers, and decimals, and order fractions. (3-4) 4.N.2 Represent, order, and compare numbers through 9,999. Represent numbers using expanded notation (e.g., 853 = 8 x 100 + 5 x 10 + 3), and written out in words (e.g., eight hundred fifty-three).

decimals through thousandths; compare and order integers between –100 and 0; use area models, benchmark fractions, and analyses of numerators and denominators to compare and order fractions.

improper fractions,

• Expressing an improper fraction as a mixed number, and vice versa,

• Expressing an improper fraction/mixed number in its simplest form.

(Denominators of given fractions should not exceed 12.)

CS

Understand meanings of operations and how they relate to one another.

Compute fluently and make reasonable estimates.

Goal O1 Demonstrate automaticity with basic addition and subtraction facts and fact extensions.


4. Fluently add and subtract multi-digit whole numbers using the standard algorithm. 5. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using

NCTM 3-5 Develop fluency in adding, subtracting, multiplying and dividing whole numbers.

Select appropriate methods and tools for computing with whole numbers form among mental computation, estimation,

4.N.12 Add and subtract (up to five-digit numbers) and multiply (up to three digits by two digits) accurately and efficiently

Goal O2 Use manipulatives, mental arithmetic, paper-and-pencil algorithms, and calculators to solve problems involving the addition and subtraction of whole numbers and decimals through hundredths; describe the

Decimals Addition and subtraction • Addition and

subtraction of decimals (up to 2 decimal places),

• Estimation of answers in calculations,

• Checking reasonableness of


127




Grades 3-5


4


Singapore Grade 4

equations, rectangular arrays, and/or area models. 6. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

calculators and paper and pencil according to the context and nature of the computation and use the selected method or tool

strategies used and explain how they work.

answers Multiplication and division • Division of a whole

number by a whole number with answer in decimal form,

• Multiplication and division of decimals (up to 2 decimal places) by a 1-digit whole number,

• Solving up to 2-step word problems involving the 4 operations,

• Rounding off answers to a specified degree of accuracy,

• Estimation of answers in calculators,

• Checking reasonableness of answers


128




Grades 3-5


4


Singapore Grade 4

MA4NB7.5a Know multiplication facts and related division facts through 12 x 12

4.N.8 (Select, use, and explain various meanings and models of multiplication and division of whole numbers.) Understand and use the inverse relationship between the two operations. 4.N.11 Know multiplication facts through 12 x 12 and related division facts. Use these facts to solve related multiplication problems and compute related problems, e.g., 3 x 5 is related to 30 x 50, 300 x 5, and 30 x 500.

Goal O3 Demonstrate automaticity with multiplication facts through 10* 10 and proficiency with related division facts; use basic facts to compute fact extensions such as 30 * 60.


4. Fluently add and subtract multi-digit whole numbers using the standard algorithm. 5. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 6. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies

NCTM 3-5 Develop fluency in adding, subtracting, multiplying and dividing whole numbers.

4.N.10 Select and use appropriate operations (addition, subtraction, multiplication, and division) to solve problems, including those involving money 4.N.13 Divide up to a three-digit whole number with a single-digit divisor (with or without remainders) accurately and

Goal O4 Use mental arithmetic, paper-and-pencil algorithms, and calculators to solve problems involving the multiplication of multidigit whole numbers by 2-digit whole numbers and the division of multidigit whole numbers by 1-digit whole numbers; describe the strategies used and explain how they work.

Whole Numbers

Multiplication and division

• Multiplication of a 4-digit number by a 1-digit number,

• Multiplication of a 3-digit number by a 2-digit number,

• Division of a 4-digit number by a 1-digit number,

• Solving up to 3-digit number by a 2-digit number,

• Division of a 4-digit


129




Grades 3-5


4


Singapore Grade 4

based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

efficiently. Interpret any remainders.

number by a 1 digit number,

• Solving up to 3-step word problems involving the 4 operations

• Estimation of answers in calculations involving the 4 operations,

• Checking reasonableness of answers

•

1. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. 2. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

NCTM 3-5 Use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals.

4.N.18 Use concrete objects and visual models to add and subtract common fractions.

Goal O5 Use manipulatives, mental arithmetic, and calculators to solve problems involving the addition and subtraction of fractions with like and unlike denominators; describe the strategies used.

Fractions

Addition and subtraction of

• Like fractions,

• Related fractions.

(Denominators of given fractions should not exceed 12.)

Exclude calculations involving more than 2 different denominators.

NCTM 3-5 Develop and use strategies to

4.N.17 Select and use a variety of strategies

Goal O6 Make reasonable estimates for whole



130




Grades 3-5


4


Singapore Grade 4

estimate the results of whole-number computations and to judge the reasonableness of such results. Develop and use strategies to estimate computations involving fractions and decimals in situations relevant to students’ experience.

(e.g., front-end, rounding, and regrouping) to estimate quantities, measures, and the results of whole-number computations up to three-digit whole numbers and amounts of money to $1000, and to judge the reasonableness of the answer. 4.N.16 Round whole numbers through 100,000 to the nearest 10, 100, 1000, 10,000, and 100,000.

number and decimal addition and subtraction problems and whole number multiplication and division problems; explain how the estimates were obtained.

4. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4). Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.) Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction

NCTM 3-5 Understand various meanings of multiplication and division.

Understand the effects of multiplying and dividing whole numbers.

Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

4.N.8 Select, use, and explain various meanings and models of multiplication and division of whole numbers. (Understand and use the inverse relationship between the two operations.)

Goal O7 Use repeated addition, skip counting, arrays, area, and scaling to model multiplication and division.

Multiplication

• Multiplication of a proper/improper fraction and a whole number,

• Solving up to 2-step world problems involving addition, subtraction and multiplication,

• Using unitary method to find the whole given a fractional part


131




Grades 3-5


4


Singapore Grade 4

models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? OAT 1. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. 2. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.1


132




Grades 3-5


4


Singapore Grade 4

4.N.14 Demonstrate in the classroom an understanding of and the ability to use the conventional algorithms for addition and subtraction (up to five-digit numbers), and multiplication (up to three digits by two digits). 4.N.15 Demonstrate in the classroom an understanding of and the ability to use the conventional algorithm for division of up to a three-digit whole number with a single-digit divisors (with or without a remainder)

4.N.9 see Patterns and Algebra


133

Grade 4 – Patterns and Algebra



National math Advisory Panel

NCTM Standards Grades 3-5

Massachusetts Frameworks Grade 4

Everyday Mathematics Grade 4 Singapore Grade 4

Understand patterns, relations and functions.

5. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

NCTM 3-5 Describe, extend, and make generalizations about geometric and numeric patterns; Represent and analyze patterns and functions, using words, tables, and graphs.

4.P.1 Create, describe, extend, and explain symbolic (geometric) and numeric patterns, including multiplication patterns like 3, 30, 300, 3000, . . .

Goal 1 Extend, describe, and create numeric patterns;

describe rules for patterns and use them to solve problems;

use words and symbols to describe and write rules for functions that involve the four basic arithmetic operations and use those rules to solve problems.


Represent and analyze mathematical situations and structures using algebraic symbols.

OAT 3. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown

NCTM 3-5 Represent the idea of a variable as an unknown quantity using a letter or a symbol;

Express mathematical relationships using equations.

4.P.2 Use symbol and letter variables (e.g., Δ, x) to represent unknowns or quantities that vary in expressions and in equations or inequalities (mathematical sentences that use =, <, >). 4.P.3 Determine values of variables in simple equations, e.g., 4106 – ∇ = 37, 5 = + 3, and

Goal 2 Use conventional notation to write expressions and number sentences using the four basic arithmetic operations; determine whether number sentences are true or false; solve open sentences and explain the solutions;


134







quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

– = 3.

write expressions and number sentences to model number stories.

Goal 3 Evaluate numeric expressions containing grouping symbols; insert grouping symbols to make number sentences true.


135







OAT 1. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. 2. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.1

NCTM 3-5 Identify such properties as commutativity, associativity, and distributivity and use them to compute with whole numbers;

4.N.9 Select, use, and explain the commutative, associative, and identity properties of operations on whole numbers in problem situations, e.g., 37 x 46 = 46 x 37, (5 x 7) x 2 = 5 x (7 x 2).

Goal 4 Apply the Distributive Property of Multiplication over the Addition to the partial-products multiplication algorithm.


Use mathematical models to represent and understand quantitative relationships.

NCTM 3-5 Model problem situations with objects and use representations such as graphs, tables, and equations to

4.P.4 Use pictures, models, tables, charts, graphs, words, number sentences, and mathematical notations to interpret mathematical relationships.


136







draw conclusions. 4.P.5 Solve problems involving proportional relationships, including unit pricing (e.g., four apples cost 80¢, so one apple costs 20¢) and map interpretation (e.g., one inch represents five miles, so two inches represent ten miles).


Analyze change in various contexts.

NCTM 3-5 Investigate how a change in one variable relates to a change in a second variable;

Identify and describe situations with constant or varying rates of change and compare them.

4.P.6 Determine how change in one variable relates to a change in a second variable, e.g., input-output tables.


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Grade 4 – Geometry







Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

1. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

4.G.4 Identify angles as acute, right, or obtuse. 4.G.5 Describe and draw intersecting, parallel, and perpendicular lines.

Goal 1 Identify, draw, and describe points, intersecting and parallel line segments and lines, rays, and right, acute, and obtuse angles.


2. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

NCTM 3-5 Identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes;

Classify two- and three-dimensional shapes according to their properties and develop definitions of classes of shapes such as triangles and pyramids;

Investigate, describe, and reason about the results of subdividing, combining, and transforming shapes;

Explore congruence and similarity;

Make and test conjectures about geometric properties and relationships and develop logical arguments to justify conclusions.

4.G.1 Compare and analyze attributes and other features (e.g., number of sides, faces, corners, right angles, diagonals, and symmetry) of two-and three-dimensional geometric shapes. 4.G.2 Describe, model, draw, compare, and classify two- and three-dimensional shapes, e.g., circles, polygons- especially triangles and quadrilaterals- cubes, spheres, and pyramids. 4.G.3 Recognize similar figures.

Goal 2 Describe, compare, and classify plane and solid figures, including polygons, circles, spheres, cylinders, rectangular prisms, cones, cubes, and pyramids, using appropriate geometric terms including vertex, base, face, edge, and congruent.


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Apply transformations and symmetry in geometric situations.

Use visualization, spatial reasoning, and geometric modeling to solve problems.

3. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

NCTM 3-5 Predict and describe the results of sliding, flipping, and turning two-dimensional shapes;

Describe a motion or a series of motions that will show that two shapes are congruent;

Identify and describe line and rotational symmetry in two- and three-dimensional shapes and designs.

NCTM 3-5 Build and draw geometric objects;

Create and describe mental images of objects, patterns, and paths;

Identify and build a three-dimensional object from two-dimensional representations of that object;

Identify and draw a two-dimensional representation of a three-dimensional object;

Use geometric models to solve

4.G.7 Describe and apply techniques such as reflections (flips), rotations (turns), and translations (slides) for determining if two shapes are congruent. 4.G.8 Identify and describe line symmetry in two-dimensional shapes. 4.G.9 Predict and validate the results of partitioning, folding, and combining two- and three-dimensional shapes.

Goal 3 Identify, describe, and sketch examples of reflections; identify and describe examples of translations and rotations.

4 – Measurement

Symmetry

• identifying symmetric figures

• determining whether a straight line is a line symmetry of a symmetric figure

• completing a symmetric figure with respect to a given horizontal/vertical line of symmetry

• designing and making patterns

Exclude

• finding the number of line of symmetry of a symmetric figure

• rotational symmetry

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problems in other areas of mathematics, such as number and measurement.

Recognize geometric ideas and relationships and apply them to other disciplines and to problems that arise in the classroom or in everyday life.

Specify locations and describe spatial relationships using coordinate geometry and other representational systems.

NCTM 3-5 Predict and describe location and movement using common language and geometric vocabulary.

Make and use coordinate systems to specify locations and to describe paths.

Find the distance between points along horizontal and vertical lines of a coordinate system.

4.G.6 Using ordered pairs of numbers and/or letters, graph, locate, identify points, and describe paths. (first quadrant)

See Goal 4, Measurement and reference Frames.


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Grade 4 – Measurement

Common Core State Standards Massachusetts Core Plus

National math Advisory Panel NCTM Standard

Grades 3-5 Massachusetts

Frameworks Grade 4

Everyday Mathematics Grade

4 Singapore Grade 4

Understand measurable attributes of objects and units, systems, and processes of measurement.

Apply appropriate techniques, tools and formulas to determine measurements.

1. Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.

2. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

5. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.

NCTM 3-5 Understand such attributes as length, area, weight, volume, and size of angle and select the appropriate type of unit for measuring each attribute;

Select and use benchmarks to estimate measurements;

Select and apply appropriate standard units and tools to measure length, area, volume, weight, time, temperature, and the size of angles;

Understand the need for measuring with standard units and become familiar with standard units in the customary and metric systems;

Understand that measurements are approximations and how differences in units affect precision;

4.M.1 Demonstrate an understanding of such attributes as length, area, weight, and volume, and select the appropriate type of unit for measuring each attribute. 4.M.5 Identify and use appropriate metric and English units and tools (e.g., ruler, angle ruler, graduated cylinder, thermometer) to estimate, measure, and solve problems involving length, area, volume, weight, time, angle size, and temperature.

Goal 1 Estimate length with and without tools; measure length to the nearest quarter inch and half centimeter; estimate the size of angles without tools.

5 – Geometry

Angles

• estimation and measurement of angles in degrees

• drawing an angle using a protractor

• associating ¼ turn/right angle with 90o; ½ turn with 180o; ¾ turn with 270o; a complete turn with 360o

• 8 point compass

(Exclude drawing and measuring reflex angles)

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Frameworks Grade 4


4 Singapore Grade 4

An angle that turns through n one-degree angles is said to have an angle measure of n degrees. 6. Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. 7. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

3. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

NCTM 3-5 Develop strategies for estimating the perimeters, areas, and volumes of irregular shapes;

Develop, understand, and use formulas to find the area of rectangles and related triangles and parallelograms;

Develop strategies to determine the surface areas and volumes of rectangular solids.

Explore what happens to measurements of a two-dimensional shape such as its perimeter and area

4.M.4 Estimate and find area and perimeter of a rectangle, triangle, or irregular shape using diagrams, models, and grids or by measuring

Goal 2 Describe and use strategies to measure the perimeter and area of polygons, to estimate the area of irregular shapes, and to find the volume of rectangular prisms.

4 – Measurement

Area and perimeter

• finding the area of a composite figure made up of rectangles and squares

• finding one dimension of a rectangle given the other dimension and its area/perimeter

• finding the length of one side of

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Frameworks Grade 4


4 Singapore Grade 4

when the shape is changed in some way.

a square given its area/perimeter

• solving word problems involving the area/perimeter of squares and rectangles

Exclude use of the symbol √‾

Carry out simple unit conversions, such as from centimeters to meters, within a system of measurement;

4.M.2 Carry out simple unit conversions within a system of measurement, e.g., hours to minutes, cents to dollars, yards to feet or inches, etc.

Goal 3 Describe relationships among U.S. customary units of length and among metric units of length.


4.M.3 Identify time to the minute on analog and digital clocks using a.m. and p.m. Compute elapsed time using a clock (e.g., hours and minutes since…) and using a calendar (e.g., days since…).

. 4 – Measurement Time:

• measurement of time in seconds

• 24-hour clock

• Solving word problems involving time in 24-hour clock

Money: • Multiplication

and division of money in decimal notation

• Solving word problems involving

143




Frameworks Grade 4


4 Singapore Grade 4

the 4 operations of money in decimal notation

NCTM 3-5 (Geometry) Describe location and movement using common language and geometric vocabulary;

Make and use coordinate systems to specify locations and to describe paths;

Find the distance between points along horizontal and vertical lines of a coordinate system.

4.G.6 (Geometry) Using ordered pairs of numbers and/or letters, graph, locate, identify points, and describe paths (first quadrant).

Goal 4 Use ordered pairs of numbers to name, locate, and plot points in the first quadrant of coordinate grid.


144

Grade 4 – Data Analysis, Statistics, and Probability




NCTM Standard Grades 3-5



Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.

4. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8).

NCTM 3-5 Design investigations to address a question and consider how data-collection methods affect the nature of the data set;

Collect data using observations, surveys, and experiments;

Represent data using tables and graphs such as line plots, bar graphs, and line graphs;

Recognize the differences in representing categorical and numerical data.

4.D.1 Collect and organize data using observations, measurements, surveys, or experiments, and identify appropriate ways to display the data.

4.D.2 Match a representation of a data set such as lists, tables, or graphs (including circle graphs) with the actual set of data.

Goal 1 Collect and organize data or use given data to create charts, tables, bar graphs, line plots, and line graphs.

6-Data Analysis

Tables

Include:

• completing a table from given data

• reading and interpreting tables

• solving problems using information presented in tables

Select and use appropriate statistical methods to analyze data. Develop and evaluate inferences and predictions that are based on data.

4. cont. Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest

NCTM 3-5 Describe the shape and important features of a set of data and compare related data sets, with an emphasis on how the data are distributed;

Use measures of center, focusing on

4.D.3 Construct, draw conclusions, and make predictions from various representations of data sets, including tables, bar graphs, pictographs, line graphs, line plots, and tallies.

Goal 2 Use the maximum, minimum, range, median, mode, and graphs to ask and answer questions, draw conclusions, and make predictions.

6 – Data Analysis

Line graphs

Include:

• reading and interpreting line graphs

• solving problems using information presented in line

145







specimens in an insect collection.

the median, and understand what each does and does not indicate about the data set;

Compare different representations of the same data and evaluate how well each representation shows important aspects of the data.

NCTM 3-5 Propose and justify conclusions and predictions that are based on data and design studies to further investigate the conclusions or predictions.

graphs

(Excludes the distance-time graph)

Understand and apply basic concepts of probability.

NCTM 3-5 Describe events as likely or unlikely and discuss the degree of likelihood using such words as certain, equally likely, and impossible;

4.D.6 Classify outcomes as certain, likely, unlikely, or impossible by designing and conducting experiments using concrete objects such as counters, number cubes, spinners, or coins.

Goal 3 Describe events using certain; very likely; likely, unlikely, very unlikely, impossible and other basic probability terms; use more likely, equally likely, same chance, 50-50, less likely, and other basic probability terms to compare events’ explain the choice of language.

Not found in Singapore’s curriculum

NCTM 3-5 Predict the probability of outcomes of simple experiments and test the predictions;

4.D.4 Represent the possible outcomes for a simple probability situation, e.g., the probability of drawing a red marble from a bag containing

Goal 4 Predict the outcomes of experiments and test the predictions using manipulatives; summarize the results and use them to


146







Understand that the measure of the likelihood of an event can be represented by a number from 0 to 1.

three red marbles and four green marbles.

predict future events’ express the probability of an event as a fraction.

4.D.5 List and count the number of possible combinations of objects from three sets, e.g., how many different outfits can one make from a set of three shirts, a set of two skirts, and a set of two hats?


147

MEMO To: Board of Education From: Dottie Barbeau Date: October 29, 2010 Re: Update on Math Review – continued focus on Massachusetts and data

Progress on Common Core Standards and Common Core Plus

Progress on Common Core Standards and Common Core Plus I’d like to give you an update on the work Massachusetts has been doing with the Common Core Standards, which as of now have been adopted by at least 37states, including Massachusetts and Missouri. When the first draft of the Common Core Standards was released for general feedback, much was written about how the standards were not as rigorous as the frameworks used by the State of Massachusetts. As you know, Massachusetts was used by many as a comparison benchmark for academic rigor because of their recognition in light of outstanding performance on the TIMSS and PISA international assessments. As expert discussion continued on the rigor of the preliminary Common Core Standards, members of the Massachusetts Board of Elementary and Secondary Education became more involved in the revision of the Core Standards, and Massachusetts convened Curriculum Panels for study and revision. As stated in the meeting minutes by Massachusetts Commissioner Chester at a special meeting of the Massachusetts Board on July 21, 2010:

Massachusetts has been very influential in the Common Core Standards, and we are a state that is recognized for having done standards right…we have made it clear from the start that we would only adopt standards that are as strong as or stronger than our current standards. Commissioner Chester said the evidence is overwhelming that the Common Core Standards are at least as strong as the Massachusetts standards, if not stronger.

At the July 21st meeting, the Massachusetts Board voted to formally adopt the Core Standards to replace the Massachusetts curriculum frameworks, with minor augmentation. In the board minutes from July, many experts were present or provided written statements supporting the Core Standards as at least as rigorous and some felt more rigorous than Massachusetts current standards. The BOE Commissioner felt there were only minor augmentations that should be added to the Core Standards (you can add up to 15% new material) and approved sending the Curriculum Panels back to develop those additions. Just this month on Oct 8th the Massachusetts BOE again met and the Commissioner presented the augmentation, the Common Core Plus, for recommendation. The Common Core Plus was released

148

for comment from educators across Massachusetts until Dec 1st. Any comments will be reported to the BOE at the Dec meeting, and the final steps for Massachusetts to move forward with the Common Core will be completed. If you are interested in reading the minutes from the Massachusetts BOE pertaining to the Common Core Standards, here are the links to both the July and October meetings. (There might pop up a page with a security question, but just click yes to proceed) https://www.doe.mass.edu/boe/minutes/10/0721reg.pdf https://www.doe.mass.edu/boe/docs/1010/item1.html As we continue to move forward with the development and use of a math adoption rubric, I thought it was important to provide this background on Massachusetts’ adoption of the Core Standards, as any new curriculum resources will need to be aligned to the Common Core. We know there has been concern from some members of the Clayton BOE about the rigor associated with the preliminary release of the Common Core, but with input from national expert curriculum panels, as you can see, the quality and rigor is now judged by the majority of the Massachusetts BOE to be “at least as strong as the Massachusetts standards, if not stronger.” As we begin to look at new curriculum resources, the Math Committee will review the augmented improvements of the Common Core Plus as part of our analysis. (The augmented standards can be found as attachments at the bottom of the October BOE minutes link shown above)

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Appendix D Math Survey Overview

• Overview Math Elementary Student Survey • Overview Math Middle School Student Survey • Overview Math High School Student Survey • Overview Math Alumni Survey • Overview Math Elementary Teacher Survey • Overview Math Middle School Teacher Survey • Overview Math High School Teacher Survey • Overview Math Parent Survey • UNICOM ARC PowerPoint Presentations to the Board of Education on September 29, 2010

and October 20, 2010 can be found on the math curriculum website -http://www.clayton.k12.mo.us/40372063214152777/site/default.asp?403610321114854303Nav=|&NodeID=350&40372063214152777Nav=|2478|&NodeID=2478

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School District of Clayton Elementary Student Survey

In May 2010, UNICOM•ARC conducted an online survey of elementary students in the School District of Clayton. The purpose of the survey was to better understand perceptions of and priorities for the District’s math program. Four hundred and thirty nine (439) surveys were completed. This Overview of Data provides overall results of every question asked. We give exact wording of each question, editing only some instructions in the interest of space.

%

3rd grade 24.0%

4th grade 37.5% 1. What is your grade level?

5th grade 38.4%

%

Meramec Elementary 29.0%

Captain Elementary 28.8% 2. Which elementary school

do you go to? Glenridge Elementary 42.2%

Overview of Data

151

%

Kindergarten 65.1%

1st grade 7.1%

2nd grade 6.2%

3rd grade 8.7%

4th grade 9.4%

3. I started in the School

District of Clayton in ______.

5th grade 3.7%

Most of the

time Sometimes Never

% % %

4a. I like my school 76.8% 21.3% 1.8%

4b. I enjoy math 48.5% 48.0% 3.5%

4c. I understand what the

teacher is teaching in math.

72.3% 27.0% .7%

4d. I ask my math teacher for

help if I don’t understand math.

54.7% 42.7% 2.6%

%

Too easy 16.7%

Too hard 7.1% 5. For me, math is:

Just right 76.1%

152

%

Too easy 22.9%

Too hard 6.4% 6. For me, math homework is:

Just right 70.7%

%

Too much 15.2%

Too little 13.4%

7. For me, the amount of

math homework is:

Just right 71.4%

%

Yes 76.8%8. Do you ever have help with your

math homework outside of... No 23.2%

%

Family (mom, dad, sister,

brother, grandma, grandpa,

aunt, uncle, cousin)

83.7%

A friend 28.6%

A teacher 11.4%

I don’t need help 14.7%

Kumon, Sylvan Learning

Center, etc.

7.4%

A tutor/academic coach 3.7%

9. Who helps you with math

(outside of math class)?

I don’t know who to ask 2.1%

153

Questions 10 and 11 are only for those who received help from a tutor outside of the home.

%

I want to be better at math. 62.2%

My parents make me. 46.7%

I need help doing some of my

homework.

15.6% 10. Why do you receive extra

help in math?

Other (please specify) 15.6%

%

I only receive help in math. 55.3%

Reading 21.3%

Science 10.6%

Writing 6.4%

Social science .0%

11. In what other subjects do

you receive help?


154

School District of Clayton Middle School Student Survey

In May 2010, UNICOM•ARC conducted an online survey of middle school students in the School District of Clayton. The purpose of the survey was to better understand perceptions of and priorities for the District’s math program. Four hundred and seventy nine (479) surveys were completed. This Overview of Data provides overall results of every question asked. We give exact wording of each question, editing only some instructions in the interest of space.

%

6th grade 34.0%

7th grade 33.8% 1. What is your grade level?

8th grade 32.1%

%

Great 32.3%

Good 46.9%

Just okay 16.5%

Not very good 2.5%

2. How would you describe your math

experience at Wydown Middle School

this year?

Bad 1.7%

Overview of Data

155

Now think about your math class this year and rate your experience for each of the following…

Good Just okay Not good

% % %

3a. The math class you are taking

this year.

74.3% 22.9% 2.8%

3b. Your overall experience with

your math teacher this year.

78.1% 17.6% 4.2%

3c. The amount of homework you

have in math this year.

43.2% 41.9% 14.9%

3d. The textbook(s) used in the

math class this year.

56.2% 36.3% 7.5%

Please rate the following statements about this year’s math class.

I agree Neutral I disagree

% % %

4a. I enjoy math class. 54.2% 35.6% 10.2%

4b. I feel that I usually understand math

concepts before my teacher moves on to

another concept.

59.2% 34.0% 6.8%

4c. The material in my math class is

challenging.

37.9% 43.4% 18.6%

4d. I feel there is good communication

between my math teacher and myself

about how I am doing in math class.

66.2% 27.2% 6.6%

4e. My teacher really understands the

math concepts he/she is teaching.

89.9% 7.8% 2.4%

4f. I understand the class work in my

math class and do not need a tutor to

understand the basic concepts.

67.7% 26.0% 6.3%

4g. I feel that my math class is taught in

a way that I can learn.

64.4% 29.5% 6.1%

156

%

0 to 15 minutes each day 3.0%

16 to 30 minutes 12.7%



5. How much time you typically spend

each day doing (all) your homework for

all subjects combined?

More than an hour 34.3%

%





6. How much time do you

spend doing a typical (math)

homework assignment?

More than an hour 3.4%

157

%

I spend more time doing math

homework than I do on other core

subjects.

33.6%

I spend the same amount of time on math

homework as I do on other core subjects.

33.0%

I don’t know how much time I spend on

math homework compared to other core

subjects.

16.9%

7. Which statement best

describes the time you spend on

math homework compared to

other core subjects?

I spend less time on math homework than I

do on other core subjects.

16.5%

%

A family member 64.9%

A math teacher 58.0%

A friend 36.4%

Math Think Tank 24.2%

I have not asked for extra help

from anyone in math 11.3%

8. Which of the following

have you used to get extra

help in math?

A professional tutor 10.5%

158

Questions 9 through 12 are only for those who received help from a tutor outside of the home.

%

I am doing fine in math and

understand all the concepts, but I

want to excel beyond my current

level.

31.8%

I mostly understand the concepts

but need a little additional help

with some of the work in my

math classes.

57.6%

I don’t understand my math

homework and need help to

complete it.

13.9%

My parents want me to have extra

help.

11.9%


9. Why do you receive extra

help in math?

I don’t know 7.7%

%

Rarely, only when needed for a

specific project or homework

16.7%

A few times a month 16.7%

One time per week 50.0%

Two times per week 8.3%

10. How often do you receive

outside tutoring for math?

Three or more times per week 8.3%

159

%

Paid private tutor 41.3%

Other tutoring service 28.3%

Kumon 21.7%

Sylvan Learning Center 2.2%

11. What type of tutoring/extra

help do you utilize?

I don’t know 6.5%

%

I only receive help in math. 62.2%

Writing 24.4%

Science 22.2%

Reading 17.8%

12. Please check ALL of the

following other subjects in

which you receive tutoring in.


%

0 to 2 years 18.2%

3 to 5 years 19.3%

6 to 10 years 58.6%

11 to 20 years 2.6%

15. How long have you attended

classes in the School District of

Clayton?

More than 20 years 1.3%

160


High School Student Survey

In May 2010, UNICOM•ARC conducted an online survey of high school students in the School District of Clayton. The purpose of the survey was to better understand perceptions of and priorities for the District’s math program.

Six hundred and sixteen (616) surveys were completed. This Overview of Data provides overall results of every question asked. We give exact wording of each question, editing only some instructions in the interest of space.

%

9th Grade (Freshman) 27.5%

10th Grade (Sophomore) 22.1%

11th Grade (Junior) 20.3% 1. What is your grade level?

12th Grade (Senior) 30.1%

%

Very satisfied 19.2%

Somewhat satisfied 35.7%

Neutral 21.9%

Somewhat dissatisfied 14.0%

Very dissatisfied 9.3%

Total satisfied 54.9%

2. How would you describe your

math experience at Clayton High

School?

Total dissatisfied 23.2%

Overview of Data

161

%

Honors classes 37.6%

College prep integrated 38.3%

College prep alternate 16.2%

3. What type of math class (“track”)

are you taking at Clayton High School

this year?

Informal 7.9%

4. Please rate the following statements about this year’s math class.

Very

satisfied

Very/

somewhat

satisfied

Neutral

Very/

somewhat

dissatisfied

% % % %

4a. The math class you are currently taking 27.9% 64.1% 18.6% 17.3%

4b. Your overall experience with your math

teacher this year

42.6% 69.2% 15.2% 15.5%

4c. The amount of homework you have in math 23.6% 54.5% 32.4% 13.1%

4d. The textbook(s) used in the your math class 23.8% 53.4% 26.4% 20.2%

162

5. For each of the following statements, please indicate how strongly you agree or disagree with each…

I agree

I agree/

I somewhat

agree

I agree/

I somewhat

disagree

% % %

5a. I enjoy math class. 30.0% 67.2% 32.8%

5b. I do feel that I usually understand the math

concepts before my teacher moves on to another

concept.

33.8% 71.5% 28.5%

5c. The material in my math class adequately

challenges me.

47.2% 86.1% 13.9%

5d. I feel there is good communication between my

math teacher(s) and myself about how I am doing

in the class.

42.6% 76.2% 23.8%

5e. My teacher really understands the math

concepts he/she is teaching the class.

70.8% 90.6% 9.4%

5f. I understand the class work in my math class

and do not need a tutor to understand the basic

concepts.

44.2% 71.5% 28.5%

5g. I feel that my math class is taught in a way that I

can learn.

38.9% 74.3% 25.7%

163

%



1 to 2 hours 37.2%

6. How much time you spend each

day doing all your homework for all

subjects combined?

More than 2 hours 37.6%

%





More than one hour 3.6%

7. How much time do you spend doing the

math homework you have on an average

school night?

Don't have math-specific

homework .2%

164

%

I spend more time doing math

homework than I do on other core

subjects.

18.4%

I spend the same amount of time

on math homework as I do on other

core subjects.

35.7%

I spend less time on math

homework than I do on other

core subjects.

38.3%

8. Which statement most closely matches the

time you spend on math homework compared

to other core subjects?

I don't know how much time I

spend on math homework

compared to other core subjects.

7.6%

%

A math teacher 63.2%

A friend 41.4%

A professional tutor 37.8%

A family member 26.9%

Learning center 24.4%

9. Which of the following sources

have you used to receive extra help

specifically in math?

I have not asked for extra

help from anyone in math

12.0%

165

Question 10 is only for those who received help from a math teacher or the Learning center.

%



47.5%




10. How often do you ask a math

teacher or go to the Learning Center

for help specifically for math?


Questions 11 through 14 are only for those who received help from a professional tutor.

%

I am doing fine in math and understand

all the concepts, but I want to excel

beyond my current level.

12.3%

I mostly understand the concepts but

need a little additional help with some

of the math curriculum.

52.1%

I don't understand my math homework

and need help to complete my

homework.

29.4%

I think I need more math help to prepare

for college math classes.

12.8%

My parents want me to have extra help. 10.4%

11. Why do you receive extra help in

math? Please choose which statement

most closely matches your reason.


166

%



53.6%




12. How often do you receive

professional tutoring outside

the school day for math?


%


Kumon 1.3%


13. What type of math tutoring/

extra help do you utilize?

Other professional tutoring service 22.1%

167

%

ACT/SAT prep 71.8%

I only receive tutoring in math 22.7%

Science 18.5%

Writing 5.6%

History (Social studies) 4.6%

Reading 3.2%

World language 3.2%

14. Please check ALL of the following

other subjects that you receive tutoring

in.

Other (Please specify) 2.3%

Question 15 is only for respondents who have had tutoring for ACT/SAT prep.

%

To improve test score 61.4%

Help in all content areas 40.5%

Test taking strategies 39.2%

15. I received ACT/SAT prep

for ________.

Math specific help 15.0%

%

0 - 15 range 1.1%

16 - 20 range 9.9%

21 - 25 range 24.2%

26 - 30 range 37.4%

16. On my previous test I scored

in the _______.

31 - 36 range 27.5%

168

%

Very prepared 30.7%

Math specific help 15.0%

Not very prepared 12.5%

Not at all prepared 6.8%

I do not plan on taking math

classes in college

1.7%

I do not plan on attending college .0%

17. How prepared do you think you

will be for the math classes you will

take in college? Would you say…

I don't know 2.8%

%

0 to 2 years 14.0%

3 to 5 years 24.3%

6 to 10 years 31.1%

20. How long have you attended

classes in the School District of

Clayton?

11 to 14 years 30.7%

169

School District of Clayton Elementary Math Teacher Survey

In May 2010, UNICOM•ARC conducted an online survey of elementary math teachers in the School District of Clayton. The purpose of the survey was to better understand perceptions of and priorities for the District’s math program. Fifty (50) interviews were completed. This Overview of Data provides overall results of every question asked. We give exact wording of each question, editing only some instructions in the interest of space.

%

Kindergarten 20.0%

1st 14.0%

2nd 18.0%

3rd 14.0%

4th 18.0%

1. What grade do you

currently teach?

5th 16.0%

%

High achieving math group 30.3% 2. Which math group do

you currently teach? Heterogeneous math group 69.7%

Overview of Data

179

%



Neutral .0%


Very dissatisfied .0%


3. Please indicate your level of satisfaction with your

overall educational experience teaching in the School

District of Clayton.


4. Now think specifically about the Everyday Math program and indicate your level of satisfaction with each of the following…

Very

satisfied

Very/

somewhat

satisfied

Neutral

Very/

somewhat

dissatisfied

% % % %

4a. The Everyday Math program as a whole in

your school 40.0% 86.0% 4.0% 10.0%

4b. Your overall experience teaching the current

Everyday Math program 42.0% 84.0% 4.0% 12.0%

4c. The resources you have at your disposal to

teach the curriculum (i.e., games, manipulatives,

online materials)

64.0% 94.0% 2.0% 4.0%

4d. The Everyday Math Teacher’s Lesson Guide 61.2% 87.8% 6.1% 6.1%

4e. The Everyday Math student journals 48.9% 70.2% 10.6% 19.1%

4f. The Everyday Math study links 35.4% 56.2% 33.3% 10.4%

4g. The Everyday Math home links 41.7% 77.1% 14.6% 8.3%

180

5. For each of the following statements, please tell me how strongly you agree or disagree with each…

I agree

Agree/

somewhat

agree

Disagree/

somewhat

disagree

% % %

5a. I enjoy teaching math. 83.7% 100.0% .0%

5b. I feel that the majority of my students have mastered a skill

before I have to move on to another math concept. 36.7% 73.5% 26.5%

5c. Students have enough background and are adequately

prepared to take my current math class at the beginning of the

year.

49.0% 81.6% 18.4%

5d. The Everyday Math program adequately challenges a

majority of the students in my class. 53.1% 83.7% 16.3%

5e. There is adequate communication between teachers and

parents regarding how students are progressing in math classes.69.4% 93.9% 6.1%

5f. The majority of the students in my class understand the class

work. 63.3% 91.8% 8.2%

5g. I would prefer the District use a textbook other than Everyday

Math. 12.2% 26.5% 73.5%

5h. I use the current Everyday Math assessments to inform

instruction. 68.8% 89.6% 10.4%

5i. I feel the current Everyday Math assessments give adequate

opportunities for students to demonstrate their understanding of

all the goals for the unit.

24.5% 69.4% 30.6%

5j. I would like more professional development in the area of

mathematics. 35.4% 68.8% 31.2%

181

%





More than one hour .0%

I don't know .0%

6. How much time do you anticipate students in

your class spend doing the math homework you

assign on an average school night?

Don't give math-specific homework. 14.3%

%

0 20.4%

1-2 61.2%

3-5 16.3%

6-9 2.0%

7. How many professional development

courses/workshops in the area of mathematics

have you attended in the past 3 years?

10 or more .0%

182

School District of Clayton Middle School Math Teacher Survey

In May 2010, UNICOM•ARC conducted an online survey of middle school math teachers in the School District of Clayton. The purpose of the survey was to better understand perceptions of and priorities for the District’s math program. Nine (9) interviews were completed. This Overview of Data provides overall results of every question asked. We give exact wording of each question, editing only some instructions in the interest of space.

%

6th 33.3%

7th 33.3% 1. What grade(s) do you

currently teach? 8th 44.4%

%

Extension/Challenge math class 100.0%

Regular math class 88.9% 2. What type of math class(es)

do you teach at Wydown Middle

School? Regular math class with

significant modifications 66.7%

Overview of Data

183

%



Neutral 0.0%




3. Please indicate your level of

satisfaction with your overall

experience teaching in the School

District of Clayton.


4. Now think specifically about the math program and curriculum and indicate your level of satisfaction with each of the following…

Very

satisfied

Very/

Somewhat

satisfied

Neutral

Very/

Somewhat

dissatisfied

% % % %

4a. The math program as a whole in your school 77.8% 88.9% 11.1% 0.0%

4b. Your overall experience teaching the current math

program in this grade level? 77.8% 88.9% 0.0% 11.1%

4c. The textbook(s) used to teach the curriculum 44.4% 88.9% 11.1% 0.0%

4d. The resources (other than textbooks) available to you to

teach the curriculum 55.6% 100.0% 0.0% 0.0%

184


I

agree

Agree/

Somewhat

agree

Agree/

Somewhat

disagree

% % %

5a. At least 20% of my students ask for extra help in math

outside of the core mathematics classroom on a regular

basis.

22.2% 66.7% 33.3%

5b. I feel that I have enough time to teach math so that the

majority of my students are able to learn the next concept. 44.4% 88.9% 11.1%

5c. The majority of my students has enough background and

is adequately prepared to take my current math class at the

beginning of the year/semester.

55.6% 88.9% 11.1%

5d. The current math program provides opportunities to

adequately challenge all of the students in my class. 100.0% 100.0% 0.0%

5e. I often have to make significant adjustments of the

delivery of the curriculum to help students learn key

concepts.

22.2% 55.6% 44.4%

5f. The majority of students in my class do not require a tutor

to be successful. 66.7% 77.8% 22.2%

5g. I feel that the textbooks and additional resources that the

District provides are adequate to teach the curriculum. 55.6% 88.9% 11.1%

185

%






I don't know 0.0%

6. How much time do you anticipate

students in your class spend doing the

math homework you assign on an

average school night?

Don’t give math-specific

homework.

0.0%

%

Students spend more time doing

math homework than they do on

other subjects.

33.3%

Students spend the same amount

of time on math homework as they

do on other subjects.

55.6%

Students spend less time on math

homework than they do on other

subjects.

11.1%

I don’t know how much time students

spend on math homework compared

to other subjects.

0.0%

7. To your knowledge, which statement

most closely matches the time your

students spends on math homework

compared to other subjects?


186

%

I agree 55.6%

I somewhat agree 33.3%

I somewhat disagree 11.1%

I disagree 0.0%

Total agree 88.9%

8. There is adequate communication

between teachers and administration

regarding the math curriculum.

Total disagree 11.1%

%

I agree 77.8%


I somewhat disagree .0%

I disagree 0.0%

Total agree 100.0%

9. There is adequate communication between

teachers and parents regarding how students are

progressing in math class.

Total disagree 0.0%

%

I agree 88.9%



I disagree 0.0%

Total agree 100.0%

10. Decisions that I make regarding

placement concerns are supported

by district leadership.

Total disagree 0.0%

187

%

I agree 55.6%



I disagree 0.0%

Total agree 100.0%


curriculum concerns are supported


Total disagree 0.0%

%

I agree 66.7%



I disagree 0.0%

Total agree 88.9%


classroom concerns are supported


Total disagree 11.1%

188

School District of Clayton High School Math Teacher Survey

In May 2010, UNICOM•ARC conducted an online survey of high school math teachers in the School District of Clayton. The purpose of the survey was to better understand perceptions of and priorities for the District’s math program. Fifteen (15) interviews were completed. This Overview of Data provides overall results of every question asked. We give exact wording of each question, editing only some instructions in the interest of space.

%

9th 53.3%

10th 46.7%

11th 73.3%

1. What grade(s) do you

currently teach?

12th 73.3%

%


College prep Integrated 60.0%

College prep Alternate 40.0%

2. What math “track” do you

teach at Clayton High School?

Informal 33.3%

Overview of Data

189

%



Neutral 13.3%




3. Please indicate your level of satisfaction

with your overall experience teaching in the

School District of Clayton.


4. Indicate your level of satisfaction with each of the following:

Very

satisfied

Very/

Somewhat

satisfied

Neutral

Very/

Somewhat

dissatisfied

% % % %

4a. The math program as a whole in your school 46.7% 93.3% 0.0% 6.7%

4b. Your overall experience teaching the current math

curriculum in this level class? 73.3% 100.0% 0.0% 0.0%

4c. The textbook(s) used to teach the curriculum 86.7% 100.0% 0.0% 0.0%

4d. The resources (other than textbooks) available to you to

teach the curriculum 66.7% 86.7% 0.0% 13.3%

190


I agree

Agree/

Somewhat

agree

Disagree/

Somewhat

disagree

% % %

5a. I have students come in for help on a regular basis. 53.3% 93.3% 6.7%

5b. I feel that I have enough time to teach math so that the

majority of my students are able to learn the next concept.

66.7% 100.0% 0.0%

5c. The majority of my students has enough background

and is adequately prepared to take my current math class

at the beginning of the year/semester.

60.0% 93.3% 6.7%

5d. The curriculum adequately challenges all of the

students in my class.

93.3% 100.0% 0.0%

5e. There is adequate communication between teachers

and administration regarding the math curriculum.

20.0% 60.0% 40.0%

5f. There is adequate communication between teachers

and parents regarding how students are progressing in

math classes.

46.7% 93.3% 6.7%

5g. Decisions I make (regarding placement/ curriculum/

classroom problems) are supported by District leadership.

0.0% 28.6% 71.4%

5h. I often have to adjust the curriculum to help students

learn key concepts.

13.3% 53.3% 46.7%

5i. The majority of students in my class do not require a

tutor to be successful.

92.3% 100.0% 0.0%

5j. I would prefer the District use a different textbook for the

math class I teach.

0.0% 6.7% 93.3%

191

%






I don't know 0.0%

6. How much time do you anticipate

students in your class spend doing

the math homework you assign on

an average school night?

Don’t give math-specific homework. 0.0%

%

Students spend more time doing

math homework than they do on

other subjects.

13.3%

Students spend the same amount

of time on math homework as

they do on other subjects.

40.0%

Students spend less time on math

homework than they do on other

subjects.

13.3%

I don’t know how much time

students spend on math homework

compared to other subjects.

26.7%

7. To your knowledge, which statement

most closely matches the time your

students spends on math homework



192

%

0 - 25% 46.7%

26 -50% 26.7%

51 - 75% .0%

76 -100% .0%

8. To your knowledge, what percentage of

students in your math classes do you estimate

receive extra help specifically in math from

someone other than yourself or a family

member? I don't know 26.7%

193

School District of Clayton Parent Survey

In March and April 2010, UNICOM•ARC conducted an online survey of parent households in the School District of Clayton. The purpose of the survey was to better understand parents’ perceptions of and priorities for the math curriculum in the District. Six hundred and seventy six (676) surveys were completed. Each household was provided a code and each code could be used up to two times, one for each parent. This Overview of Data provides overall results of every question asked. We give exact wording of each question, editing only some instructions in the interest of space. Top responses are bolded for each question.

%

Elementary school 41.6%

Middle school 24.9% 1. I am completing this survey

for my child who attends... High school 33.5%

1a. If answered “Elementary school” in Question 1.

%

Kindergarten 9.3%

1st 12.9%

2nd 21.9%

3rd 16.5%

4th 20.4%

1a. In what grade is this child

currently enrolled?

5th 19.0%

Overview of Data

194

1b. If answered “Middle school” in Question 1.

%

6th 36.5%

7th 33.5% 1b. In what grade is this child

currently enrolled? 8th 29.9%

1c-1d. If answered “High school” in Question 1.

%

9th 27.7%

10th 30.8%

11th 22.8%

1c. In what grade is this child

currently enrolled?

12th 18.8%

%

All honors or accelerated

classes 32.1%

A few honors classes and

other non- honors classes 40.2%

All non-honors classes 20.1%

Mostly non-honors classes

and a few support classes 6.2%

All support classes .9%

1d. From the list below, please indicate

which selection best describes the type of

classes your child takes at his/her school.

I don't know. .4%

195

2. Thinking about your child's experience with the School District of Clayton, please indicate your level of satisfaction with each of the following...

Very satisfied Very/somewhat

satisfied Neutral

Very/somewhat

dissatisfied

% % % %

2a. Your child's overall educational

experience with the School District

of Clayton

54.7% 90.0% 4.6% 5.4%

2b. Your child's teacher(s) 50.4% 89.4% 5.0% 5.6%

3. Now think specifically about your child's current math program, and indicate your level of satisfaction with each of the following...

Very

satisfied

Very/somewhat

satisfied Neutral

Very/somewhat

dissatisfied

% % % %

3a. The math program in which my

child is currently enrolled 33.3% 64.6% 9.8% 25.6%

3b. My child's math teacher's ability to

teach the math curriculum in a way so

that my child can understand

41.0% 70.0% 11.8% 18.2%

196

4. For each of the following statements, please tell me how strongly you agree or disagree with each...

Agree

Agree/

somewhat

agree

Disagree/

somewhat

disagree

Don't

know

% % % %

4a. My child enjoys learning

mathematics. 55.2% 81.9% 17.8% .3%

4b. My child has a positive attitude

towards math. 56.9% 79.0% 20.2% .7%

4c. I am satisfied with the amount of

help teachers are willing to give my

child outside of math class.

41.8% 65.8% 21.0% 13.2%

4d. I do not feel my child always has

mastered a skill before the teacher

moves on to another math concept.

26.4% 52.7% 38.6% 8.6%

4e. My child was prepared to take

his/her current math class. 60.8% 82.4% 15.6% 1.9%

4f. My child is adequately challenged

in math. 47.8% 71.3% 25.9% 2.8%

4g. There is adequate communication

from my child's teacher about his/her

progress in math.

33.5% 61.6% 36.2% 2.3%

4h. I read the family letters that

accompany each unit. 66.2% 88.5% 10.1% 1.4%

4i. I am satisfied with my child's

computation skills. 44.7% 71.1% 27.4% 1.5%

4j. I have enough information from the

District to assist my child with math

homework.

29.0% 50.8% 39.8% 9.5%

197

5. If answered “Elementary school” in Question 1.

%





More than one hour .0%

I don't know 1.8%

5. How much time does your child spend

each day doing math homework?

Doesn't have math specific

homework

5.7%

%

My child spends more time doing math homework than

he/she does on other subjects. 26.8%

My child spends the same amount of time on math

homework as he/she does on other subjects. 39.0%

My child spends less time on math homework than

he/she does on other subjects. 20.8%

I don't know how much time my child spends on math

homework. 4.0%

6. Which statement most closely

matches the time your child

spends on math homework


Other 9.4%

198

%

All of the time 39.6%

Some of the time 50.2%

Rarely 8.1%

7. My child's homework in

mathematics is useful.

Never 2.1%

%

Yes 62.6%

No 36.9%

8. Do you or does any other family

member provide extra help for your

child specifically in math? I don't know .4%

9. If answered “Yes” in Question 8.

%

My child is doing fine in math and

understands all the concepts, but I want

him/her to excel beyond their current level

18.2%

My child mostly understands the

concepts but needs a little additional

help with some of the math concepts.

47.6%

My child doesn't understand his/her math

homework and needs my help to complete

his/her homework.

11.7%

I think there are gaps in the math curriculum

and my extra help makes up for these gaps.

11.5%

9. Why do you provide extra help

for your child in math? Please

choose which statement most

closely matches your reason.

Other 11.0%

199

10. If answered “No” in Question 8.

%

My child does not need help 60.2%

I am not able to help my child

with their math homework

22.9% 10. Why does your child not

receive extra help?

Other 16.9%

%

Yes, currently 18.9%

Yes, in a previous grade(s) 11.1%

Yes, currently and in a

previous grade(s)

7.1%

No 62.0%

11. Does your child now receive or has

he/she received at anytime in the past

since attending the School District of

Clayton, any form of tutoring or extra

help in math by someone other than a

family member? I don't know .9%

200

11a. If answered “Yes, in a previous grade(s)” in Question 11.

%

1st 21.3%

2nd 24.0%

3rd 33.3%

4th 38.7%

5th 33.3%

6th 25.3%

7th 24.0%

8th 22.7%

9th 30.7%

10th 32.0%

11th 10.7%

11a. In which grade or grades did your

child receive tutoring or extra help in

math by someone other than a family

member?

12th .0%

11b. If answered “Yes, currently and in a previous grade(s)” in Question 11.

%

1st 20.8%

2nd 20.8%

3rd 31.2%

4th 33.3%

5th 39.6%

6th 45.8%

7th 37.5%

8th 31.2%

9th 37.5%

10th 31.2%

11th 16.7%

11b. In which previous grade or grades did

your child receive tutoring or extra help in

math by someone other than a family

member?

12th 10.4%

201

%

My child needs to feel more confident in

math class, and tutoring helps him/her

gain this confidence

8.4%

My child is doing fine in math and

understands all the concepts, but I want

him/her to excel beyond their current

level.

10.4%

My child mostly understands the

concepts but needs a little additional

help with some of the math curriculum.

18.3%

My child doesn't understand his/her

math course work and needs help to

complete his/her homework.

16.3%

I think there are gaps in the math

curriculum, and additional tutoring

makes up for these gaps.

31.5%

12. If yes, why do you use tutoring

for your child in math? Please

choose which statement most

closely matches your reason.

Other 15.1%

%

Kumon 43.4%


Other professional tutoring

service

4.4%


Extra help from a classroom

teacher outside of the classroom

27.9%

13. What type of tutoring/extra help

do you utilize?

Other 13.9%

202

%

Reading 19.3%

Math 87.3%

Writing 10.5%

Science 11.4%

ACT Prep 11.4%

SAT Prep 1.3%

ACT/SAT prep in math only 3.1%

14. Please check ALL of the

following subjects in which your

child receives tutoring.

Other 6.6%

%



5.1%





15. How often does your child

receive tutoring for math?

Other 16.5%

%

none 21.7%

Less than $25 10.8%

$25 to $50 34.1%

$51 to $75 14.1%

$76 to $100 7.2%

More than $100 2.8%

16. Approximately how much do

you spend per hour on tutoring for

math?

I don't know 9.2%

203

17. If answered “High school” in Question 1.

%


College prep Integrated 20.1%

College prep Alternate 20.5%

Informal 3.1%

17. What math "track" is your

child on at Clayton High School

I don't know 1.8%

18. If answered “Middle school” in Question 1.

%

Extension/Challenge

math class

52.4%

Regular math class 42.2%

Regular math class and

Math Strategies class

3.6%

18. What type of math class is your

child in at Wydown Middle School?

I don't know 1.8%

%

My child has only attended the


66.4%

My child attended school in one

other School District before the


14.7%

My child attended school in more

than one School District before the


5.4%

My child attended a

private/parochial school before the


11.0%

19. Choose the statement that

best reflects your child's length

of time with the School District

of Clayton.

Other 2.5%

204

%

0 to 2 years 18.0%

3 to 5 years 20.2%

6 to 10 years 23.6%

11 to 20 years 29.9%

20. How long have you lived in

the School District of Clayton?

More than 20 years 8.3%

%

Male 28.7% 21. Gender

Female 71.3%

205

Appendix E Annotated Bibliography

206

Annotated Bibliography (Not Complete)

Ahuja, O. P. (2006). World class high quality mathematics education for all K-12 American students. The Montana Mathematics Enthusiast, 3(2), 223-248. Allsopp, D., Lovin, L., Green, G., & Savage-Davis, E. (2003, February 14). Why students with special needs have difficulty learning mathematics and what teachers can do to help. Mathematics Teaching in the Middle School, 8(6), 308-314. Retrieved from http://www.nctm.org/‌eresources/‌article_summary.asp?URI=MTMS2003-02-308a

Describes four learning characteristics that make learning and doing mathematics difficult for students with special needs. Discusses instructional strategies that make learning and doing mathematics attainable for these students in the context of a vignette based on real-life experiences.

Alper, L., Fendel, D., Fraser, S., & Resek, D. (1996). Problem-based mathematics - not just for the college bound. Educational Leadership, 53(8), 18-21.

The authors explore differences in the approach and structure of the Interactive Mathematics Program (IMP). The article begins with an example (a unit called “Meadows or Malls?”) from the IMP’s problem-based mathematics curriculum, where students work as if they were city planners deciding how best to use public land. Problems such as these begin units and are often too difficult for students to solve right away; this opens students’ thinking so that they pose questions, look for patters, and make connections to mathematics they already know. The article also addresses parent concerns that Standards-based curricula do not contain enough repetition for students to master skills; it explains that problems encountered in IMP encourage students to discover and construct ideas, rather than merely memorize definitions, for more meaningful learning. To conclude, the authors address the “results” that can be seen from curricula like IMP by looking at studies that follow students’ progress and learning in school and after graduation.

Andrews, D. (2006, July). Departmentalization in the 5th grade classroom: Rethinking the elementary school model. Retrieved from Math in the Middle Institute, University of Nebraska-Lincoln website: http://scimath.unl.edu/‌MIM/‌ar.php Ball, D., Ferrini-Mundy, J., Kilpatrick, J., Schmid, W., Milgram, R., & Schaar, R. (2005). Reaching for common ground in k-12 mathematics education. Notices of the American Mathematical Society, 52(9), 1055-1058.

This article is the result of conversations between mathematicians and mathematics educators around forging areas of common agreement over several, sometimes contentious, issues in K-12 mathematics education. Three fundamental assertions (e.g., proficiency with computational procedures) are detailed and explained, followed by seven areas of agreement. These areas of agreement center around the automatic recall of basic facts, calculator use, algorithms, fractions, “real-world” contexts, instructional methods and teacher knowledge. Readers of this article may be interested in the areas of common ground sometimes overlooked in “math wars” discussions.

207

Ball, D., Hill, H., & Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator, 29(3), 14, 16-17, 20-22, 43-46.

There is general agreement that teachers’ knowledge of the mathematical content to be taught is the cornerstone of effective mathematics instruction. But the actual extent and nature of the mathematical knowledge teachers need remains a matter of controversy. A new program of research into what it means to know mathematics for teaching - and how that knowledge relates to student achievement - may help provide some answers.

Ball, D. L., Hill, H. C., & Bass, H. (2005, Fall). Knowing mathematics for teaching. American Educator, 14-46. Retrieved from http://www.aft.org/‌pubs-reports/‌american_educator/‌issues/‌fall2005/

Mathematical knowledge for teaching. How teachers who are skilled at mathematical teaching increase student achievement, i.e. knowing the mathematical process/‌algorithm is essential, but it’s not enough. Knowing how to explain, listen and examine student work. Knowing which example to show and how. Knowing how to identify and rectify a typical wrong answer (error analysis) - specialized fluency with mathematical language. Teachers with mathematical skill vs. skillful teachers of mathematics

Behrend, J. L. (2003, January). Learning-disabled students make sense of mathematics. Teaching Children Mathematics, 9(5), 269-273.

Five primary-grade students identified as learning-disabled benefited from instruction that focused on making sense of mathematics word problems. Examples of student work demonstrate the students’ ability to solve a variety of problem types and justify their solutions.

Briars, D. (1999, January). Square one: Promoting systemic math reform. The School Administrator, 56(1), 39-43.

Briars addresses systemic mathematics reforms with particular attention to the following eight issues: 1) High stakes assessments must be tied to appropriate instructional targets; 2) Standards-based instruction is more than using manipulative and cooperative learning; 3) Teachers need Standards-based instructional materials; 4) Teachers need substantial, continuing professional development and in-class support; 5) Administrators must recognize and support Standards-based instruction; 6) District policies and practices will have to change; 7) Materials and services are available to support mathematics reform; 8) Reform has a payoff for all students. In addition, Briars includes a short piece on educating parents about mathematics education reform, stressing that parents play an important role in reform efforts.

Budd, K., Carson, E., Garelick, B., Klein, D., Milgram, R. J., Raimi, R. A., . . . Stotsky, S. (2005, May 4). Ten myths about math education and why you shouldn’t believe them. Retrieved from New Your City HOLD and Mathematically Correct website: http://nychold.com/‌myths-050504.html

For almost two decades, mathematics education in K-12 classrooms has been driven by unsupported pedagogical theories constructed in our schools of education and propagated by the National Council of Teachers of Mathematics (NCTM). Their curricular and pedagogical “vision” for mathematics education reform, articulated in the two NCTM standards documents (1989 and 2000), has dominated local, state and federal education decision-making and policies, as well as public discussions, and press coverage. But

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many parents, mathematics experts, and K-12 teachers of mathematics do not share this vision. A well-informed group of education stakeholders rejects the NCTM doctrine and model for mathematics reform. The expertise and viewpoints of this diverse group, comprised of mathematicians and scientists, K-12 teachers of mathematics, educational researchers, and concerned parents across our nation has been regularly eclipsed and marginalized by the dominant voice of mathematics educators in our schools of education and of NCTM officials. This constituency’s expertise is often entirely absent from the decision-making process. We are members of that constituency, and are part of an informal bipartisan grassroots coalition of advocates for authentic reforms in mathematics education. The chart offers our point-by-point refutation of a set of common myths propagated by mathematics educators in our schools of education and NCTM officials that are often presented as fact to policy makers and the general public.

Burns, M. (2007, November). Nine ways to catch kids up. Educational Leadership, 65(3), 16-21. Retrieved from http://www.ascd.org/‌publications/‌educational_leadership/‌nov07/‌vol65/‌num03/‌Nine_Ways_to_Catch_Kids_Up.aspx

Essentials to best instructional practices for math -connections between and among mathematical concepts -connections between new and prior learning -correct answers supported by mathematical reasoning Interventions must be more than drill, additional practice and more of the same.

Byrd Carmichael, S., Wilson, W. S., Finn, Jr., C. E., Winkler, A. M., & Palmieri, S. (2009, October 8). Stars by which to navigate? Scanning national and international education standards in 2009. Retrieved from The Thomas B. Fordham Institute website: http://www.edexcellence.net/‌index.cfm/‌news_stars-by-which-to-navigate-scanning-national-and-international-standards-in-2009

In the Fordham Institute’s latest report--Stars By Which to Navigate? Scanning National and International Education Standards in 2009--expert reviewers appraised the Common Core drafts, which outline college and career readiness standards in reading, writing, speaking and listening, and in math. These draft standards were made public on September 21 by the National Governors Association and the Council of Chief State School Officers. This report goes further however--Fordham’s reviewers also evaluate the reading/‌writing and math frameworks that undergird the National Assessment of Educational Progress (NAEP), the Trends in International Mathematics and Science Study (TIMSS) and the Programme for International Student Achievement (PISA). How strong are these well-known models? This report presents their findings.

Carter, S. (2009, April). Connecting mathematics and writing workshop: It’s kinda like ice skating. The Reading Teacher, 62, 606-610.

Second-grade students struggle with writing about mathematical topics during math class, so the teacher begins to integrate mathematical topics into their Writing Workshop. Content journals are used during math, and students are encouraged to write about personal connections to mathematical situations, as well as incorporate mathematical concepts into stories. As a result, the Writing Workshop is invigorated, and written answers during math class are improved and expanded.

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Cavanagh, S. (2008, March). Panel calls for systematic, basic approach to math. Education Week, pp. 1, 12. Retrieved from http://www.edweek.org/‌ew/‌articles/‌2008/‌03/‌19/‌28math_ep.h27.html

The influence of a federal report calling for a more orderly approach to teaching mathematics in the early grades will hinge largely on whether its message is accepted by the nation’s diverse and often fiercely divided math community, members of the panel that crafted it acknowledge. Released this week, the report of the National Mathematics Advisory Panel Requires Adobe Acrobat Reader recommends that schools present elementary and middle school math in a better-defined manner, in contrast to the jumble of strategies now used in states and school districts.

Cavanagh, S. (2009, June 17). Study puts results on international tests on common metric. Education Week, pp. 12-13. Retrieved from http://www.edweek.org/‌ew/‌articles/‌2009/‌06/‌17/‌35international.h28.html?r=1198122686

International tests known by odd acronyms like PISA and TIMSS have become fixed in the American educational and political vernacular. Newspaper editorial writers and elected officials at all levels hash over U.S. students’ scores on those nation-by-nation exams with a zeal and frequency they once reserved for the release of state and local test results. Now an American researcher has attempted to make those comparisons more meaningful to the public, by comparing the performance of students in U.S. states and cities against that of their foreign peers using a well-understood metric: letter grades.

Chval, K. B., & Keys, R. (2008). Effective use of manipulatives across the elementary grade levels. NCSM Journal of Mathematics Education Leadership, Spring 2008, 3-6.

Using manipulatives in every classroom every year is critical in student growth. Many teachers are reluctant to use manipulatives. The authors describe what should be done when teachers need support to use manipulatives.

College board standards for college success: Mathematics and statistics. (2006). [Brochure]. Retrieved from http://professionals.collegeboard.com/‌k-12/‌standards College board standards for college success: Mathematics and statistics adapted for integrated curricula. (2007). [Brochure]. Retrieved from http://professionals.collegeboard.com/‌k-12/‌standards Cuoco, A., Goldenberg, E., & Mark, J. (1996). Habits of mind: An organizing principle for mathematics curricula. Journal of Mathematical Behavior, 15(4), 375-402.

By emphasizing the ways of thinking that are essential in mathematics, one can design mathematics courses that simultaneously serve the needs of students who will go on to advanced mathematical study and students who will not. The authors address a series of mathematical “habits of mind,” arguing that students should be pattern sniffers, experimenters, describers, tinkerers, inventors, visualizers, conjecturers, and guessers. Using mathematical examples, the authors discuss mathematical approaches to things and how geometers and algebraists approach their world. Materials for teaching and learning provide students with problems and activities to develop these habits of mind and put them into practice.

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Cuoco, A., Goldenberg, E. P., & Mark, J. (1996, December). Habits of mind: An organizing principle for mathematics curriculum. The Journal of Mathematical Behavior, 15(4), 375-402. doi:10.1016/‌S0732-3123(96)90023-1 Dossey, J. A., & Others, A. (1998, June). The name assigned to the document by the author. This field may also contain sub-titles, series names, and report numbers. Mathematics: Are We Measuring Up? The Mathematics Report Card, Executive Summary. Rosedale Road, Princeton, NJ 08541-0001: Publisher name and contact information, as provided by the publisher; updated only if notified by the publisher. National Assessment of Educational Progress, Educational Testing Service.

This executive summary presents key findings from the 1986 National Assessment of Educational Progress (NAEP) in mathematics. It is designed to alert leaders in classrooms, families, and councils of government to the state of mathematics education in the United States. “Why Mathematics Counts” is summarized in the first section. Then, highlights from the assessment are given: the trend in mathematics performance is encouraging, particularly for students at ages 9 and 17 and for Black and Hispanic students. However, the gains have been confined primarily to lower-order skills. Other findings concerning achievement, instructional patterns, technology, course taking, and attitudes are succinctly presented. Next, the assessment procedures are summarized followed by some reflections on the findings. Trends in mathematics proficiency is the concern of the next section, with a graph highlighting overall trends and a chart showing the percentage of students in each age group (9, 13, and 17) in the last three assessments (1978, 1982, and 1986). Implications for instruction are considered in terms of students’ perception of mathematics, patterns of classroom instruction, and the place of mathematics in the curriculum. Finally, a summary stresses the need to teach not only skills, but also higher-order thinking strategies.

Elements of highly effective mathematics programs. (2007). Educational Research Service Informed Educator Series.

There is no single best program for teaching mathematics. Math instruction should build on existing student knowledge. Teaching math needs teachers who have specific characteristics (see note card). Proper, explicit instruction can help low achieving math students catch up with peers. Professional development is essential to improving classroom instruction and increasing student learning.

Foundations for success: the final report of the national mathematics advisory panel. (2008). Retrieved from http://www.ed.gov/‌about/‌bdscomm/‌list/‌mathpanel/‌report/‌final-report.pdf Foundations for success: The final report of the national mathematics advisory panel. (2008, March 13). Retrieved from National Mathematics Advisory Panel, U.S. Department of Education website: http://www.ed.gov/‌about/‌bdscomm/‌list/‌mathpanel/‌index.html

On March 13, 2008, the National Mathematics Advisory Panel presented Foundations for Success: The Final Report of the National Mathematics Advisory Panel to the President of the United States and the Secretary of Education. In response to a Panel recommendation, the U.S. Department of Education, in partnership with the Conference Board of Mathematical Sciences, hosted the first National Math Panel Forum on October 6-7, 2008. The Forum brought together various organizations and other interested parties to use the Panel’s findings and recommendations as a platform for action.

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The mission of the panel created by the President was to rely on the best available scientific evidence and recommend ways to foster greater knowledge of and improved performance in mathematics among American students. The panel reports that America has opportunities for improvements in math education and they lay out actions for their recommendations. There is a clear emphasis on the need for improvement in algebra.

Garden, R. A., Lie, S., Robitaille, D. F., Angell, C., Martin, M. O., Mullis, I. V., . . . Arora, A. (2006). TIMSS advanced 2008 assessment frameworks. Retrieved from http://www.iea.nl/‌latest_publications.html?&tx_ttnews%5Btt_news%5D=118&tx_ttnews%5BbackPid%5D=8&cHash=78f57edece

Developing the TIMSS Advanced 2008 Assessment Frameworks was a collaborative venture involving mathematics and physics experts from around the world. The document contains two frameworks for implementing TIMSS Advanced 2008 - one for advanced mathematics and one for physics. It also contains an overview of the assessment design. The TIMSS Advanced content frameworks specify the mathematics and physics to be covered by the assessment, as follows: * Advanced Mathematics o Algebra o Calculus o Geometry * Physics o Mechanics o Electricity and Magnetism o Heat and Temperature o Atomic and Nuclear Physics Both the advanced mathematics and physics frameworks also have a cognitive dimension—Knowing, Applying, and Reasoning. TIMSS Advanced plans to report student achievement on each subject overall as well as separately by each content and cognitive domain.

Garelick, B. (2006, Fall). Miracle math. Education Next, 6(4). Retrieved from http://educationnext.org/‌miracle-math/‌A successful program from Singapore tests the limits of school reform in the suburbs

A successful program from Singapore tests the limits of school reform in the suburbs Geary, D. C. (2008, October). An evolutionarily informed education science. Educational Psychology, 43(4), 179-195.

In this article Geary discusses the primary and secondary domains of learning and though children are inherently motivated to learn in the primary domain (e.g. learning to talk) this is not true in the secondary domain. The learning of mathematics falls in the secondary domain. In the secondary domain it is important that students understand that learning requires effort and is not an inherent talent or ability. Geary states that “many children will need to have any associated problem-solving steps explicitly organized by instructional materials and extensively practiced for long-term retention.”

Gersten, R., & Clarke, B. S. (2008). Effective strategies for teaching students with difficulties in mathematics. National Council of Teachers of Mathematics, 1-2. Retrieved from http://www.nctm.org/‌news/‌content.aspx?id=8452

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This research brief focuses on evidence-based practices for teaching students with difficulties in mathematics. Most of the summary for this research brief is based on two recently conducted meta-analyses (Baker, Gersten, and Lee 2002; Gersten et al. 2006) as well as complementary work by Kroesbergen and van Luitt (2003). Together, the reviews encompass more than fifty studies, and although this is an emerging and substantial research base, it is far from definitive. As a composite, the studies reviewed present a picture of specific aspects of instruction that are consistently effective in teaching students who experience difficulties with mathematics. The principles that emerged from the research seem appropriate for instruction in a variety of situations and possible settings. Six aspects of instruction have been studied in depth. Table 1 lists each of these along with the average effect size for teaching special education students (Gersten et al. 2006) and other students with difficulties learning mathematics (Baker, Gersten, and Lee 2002). Effect sizes of 0.2 are considered small, 0.4 moderate, and 0.6 or above large. A small effect might raise students’ scores on a standardized test about 8 percentile points; a large effect would raise a score approximately 25 percentile points.

Greeno, J. G., & Collins, A. (2008). Commentary on the final report of the National Mathematics Advisory Panel. Educational Researcher, 37(9), 618-623.

Foundations for Success: The Final Report of the National Mathematics Advisory Panel (2008) excludes the view of students learning the social practices of mathematical reasoning and the use of mathematics in understanding and modeling situations. The authors argue that by filtering research to only “statistically significant individual effects, significant positive mean effect size, or equivalent consistent positive findings.” the report misrepresents the resources that education research affords for improving mathematics education and education in general. The authors argue that only offering research results of statistical comparisons in inappropriately limited. They recall a strategy developed by the National Academy of Education in which researchers and educators collaborate to strengthen educational practice in local settings and to provide analyses and develop resources intended to support travel of their innovations to other sites.

Greeno, J. G., & Collins, A. (2008). Commentary on the final report of the national mathematics advisory panel. Educational Researcher, 37(9), 618-623.

The authors argue that by filtering research to only “statistically significant individual effects, significant positive mean effect size, or equivalent consistent positive findings,” the report misrepresents the resources that education research affords for improving mathematics education and education in general.

Herner, L. M., & Lee, H.-J. (2005). Standards, special education, and access to mathematics curriculum. TEACHING Exceptional Children Plus, 1(6), article 5.

This article explains one elementary teacher’s approach to math education and preparing all students to be successful on standardized tests. Access to the same math curriculum and objectives does not mean that students are taught in the same manner. Details of how she gives all learners access to the curriculum are described. One of the methods described is building math vocabulary. Students keep a notebook with all of the vocabulary, along with drawings and their own thoughts about concepts. The teacher kept a display of the vocabulary as it built throughout the school year. A quote from the article regarding vocabulary is “Mathematics includes some of the most difficult and

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unfamiliar vocabulary for students, and without the proper vocabulary students have difficulties wit the conceptual understanding.” Students were also expected to use math vocabulary in their writing and their conversations regarding mathematics.

Hill, H., & Loewenberg Ball, D. (2009, October). The curious - and crucial - case of mathematical knowledge for teaching. Phi Delta Kappan, (68-69).

In this article the authors attempt to answer the questions “What must teachers know and be able to do?” Studies suggest that a teacher’s mathematical knowledge alone is not sufficient for determining their ability to teach mathematics. It is also important for teachers to be able to explain mathematics and have knowledge of multiple representations. Teachers need to see the math content from another’s perspective and understand their mathematical reasoning. The authors broke down Mathematical Knowledge for Teaching (MKT) into six domains: 1. Common content knowledge (knowing when an answer is wrong, the definition of a concept or object and procedural knowledge) 2. Knowledge at the mathematical horizon (view of the larger mathematical landscape) 3. Specialized content knowledge (able to model mathematics using different representations) 4. Knowledge of content and students 5. Knowledge of content and teaching 6. Knowledge of curriculum

Holloway, J. H. (2004, February). Closing the minority achievement gap in math. Educational Leadership, 61(5), 84-86. Retrieved from http://www.ascd.org/‌publications/‌educational_leadership/‌feb04/‌vol61/‌num05/‌_Closing_the_Minority_Achievement_Gap_in_Math.aspx

The United States has set a national goal of ensuring that each student receives an equitable, high-quality education, and that no child is left behind in this quest. Are we achieving that goal in mathematics education? Not according to the results of the National Assessment of Educational Progress (NAEP). Although all racial/‌ethnic subgroups have shown improvement since 1990, the 2003 NAEP scores show that white students and Asian/‌Pacific Islander students continue to outperform black, Hispanic, and American Indian/‌Alaskan native students at every grade level (National Center for Education Statistics, 2003a). What causes the continuing minority achievement gap in mathematics and other content areas? Barton (2003) has shown that minority students face numerous academic barriers to achievement, both in the classroom and outside of school. One factor that shows up in his research is that minority students as a group experience a less rigorous curriculum. Lower expectations for these students often preclude the opportunity for them to take more rigorous courses because of inadequate prior preparation.

Hood, L. (2009, November/‌December). “Platooning” instruction. Harvard Education Letter, 25(6), 1-3. Retrieved from http://www.hepg.org/‌hel/‌article/‌426

To platoon or not to platoon? That’s the question facing Irving Hamer, Deputy Superintendent of Academic Operations, Technology and Innovation for the Memphis City Schools. This year for the first time, the state’s achievement test, known as TCAP -(Tennessee Comprehensive Assessment Program), will include algebraic concepts on the

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fifth-grade test. Hamer says Memphis “is bracing for a very heavy downturn in student performance on the exams.” Hamer’s office has taken a close look at the district’s 351 fifth-grade teachers and found that not one majored in math. “So what that means to the teaching of algebra at grade five is [that] it will most certainly be done by people who don’t have extensive math preparation,” he says. That doesn’t mean they won’t be able to teach what’s required, he says, but “the thinking on the part of this administration is that maybe one way to get higher-order math in the fifth grade would be to departmentalize the fifth grade and to make sure the math is being taught by the most able math teachers in a fifth-grade configuration.”

Huntley, M. A. (2008, Fall). A framework for analyzing differences across mathematics curricula. NCSM Journal, 10-17. Retrieved from http://www.mathedleadership.org/

This article discusses the mathematics textbooks and how they have a tremendous influence on what and how mathematics is taught.

Improving student achievement in mathematics for students with special needs. (2008, Winter). National Council of Supervisors of Mathematics Improving Student Achievement Series. Retrieved from http://www.mathedleadership.org/‌docs/‌resources/‌.../‌NCSMPositionPaper4.pdf

It is the position of the National Council of Supervisors of Mathematics that in order to improve the achievement of students with special needs, educators must truly believe that all students can learn rigorous mathematics. When this foundational belief is in place, educators can embrace the learning issues of students with special needs in order to provide effective instruction and develop productive lessons. Sustained and frequent collaboration between classroom teachers and special educators must occur in order to create the conditions leading to success in mathematics for all students.

Jerald, C. D. (2008). Benchmarking for success: Ensuring U.S. students receive a world-class education. Retrieved from National Governors Association, Council of Chief State School Officers, Achieve, Inc. website: http://www.nga.org/‌portal/‌site/‌nga/‌menuitem.6c9a8a9ebc6ae07eee28aca9501010a0/‌?vgnextoid=431809a4cbf4e110VgnVCM1000005e00100aRCRD

International governments are increasingly comparing their educational outcomes to the best in the world, not just to see how they rank, but also to identify and learn from top performers and rapid improvers. This process, known as “international benchmarking,” has become an important tool for governments striving to create world-class education systems as nations race to create knowledge-fueled innovation economies. The author maintains that American education has not adequately responded to the challenges of the new education, is loosing its edge in educational attainment and that if state leaders want to ensure that their citizens and their economies remain competitive, they must look beyond America’s borders and benchmark their education systems with the best in the world. The report concludes that it is through benchmarking that countries can understand relative strengths and weaknesses of their respective education systems and identify best practices and ways forward. A table of Countries Participating in International Assessments is appended.

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Jordan, N. C. (2007, October). The need for number sense. Educational Leadership, 65(2), 63-65. Retrieved from http://www.ascd.org/‌publications/‌educational_leadership/‌oct07/‌vol65/‌num02/‌abstract.aspx#The_Need_for_Number_Sense

A signature characteristic of children with math difficulties and disabilities is difficulty quickly solving combinations, such as 9 + 7 or 16 - 9. Nancy Jordan’s research suggests that this lack of computational fluency is rooted in deficiencies in number sense, or the intuitive knowledge of numbers. Children lacking number sense might struggle to add 3 + 2, because they don’t understand its relationship to such combinations as 2 + 3, 3 + 3, and 5 - 3. Jordan’s research group assessed children in kindergarten and again in 1st grade and found that number sense at the beginning of kindergarten is highly correlated with math achievement in 1st grade. Jordan suggests that schools regularly conduct number-sense assessments in kindergarten so that students who are likely to struggle with math get the support they need.

Kanold, T. (Ed.). (2008, Winter). The National Council of Supervisors of Mathematics Improving Student Achievement Series, (No. 4).

The article discusses how to improve student achievement for special needs students. It is stated that to accomplish this goal teachers must believe these students can learn high quality and high order mathematics. Teachers need to deep their understanding of learning issues; create a nurturing classroom environment; use strategic, customized instructional practices and collaborate with special education teachers. The article encourages classroom teachers and special education teachers to co-teach math classes which they believe would foster a broader and deeper understanding of math, develop better questions about math, and expand student’s mathematical thinking. The article also encouraged teachers to use strategic customization of instructional practices and effective use of accommodations specific to the student’s special needs. These could include: adjustment of the pace of the lesson, built-in scaffolds, changes in time or schedule of assessment, use of manipulatives, graphic organizers, changes in test directions, changes in presentation of questions and how student respond to questions.

Kilpatrick, J., & Swafford, J. (Eds.). (2002). Helping children learn mathematics (Eighth ed.). Washington, D.C.: National Academy Press. (Original work published 2002)

The book establishes new goals for mathematics learning and a course of action that should be taken so that all students are mathematically proficient. The book states that “mathematically proficiency involves five intertwined strands: (1) understanding mathematics: (2) computing fluently; (3) applying concepts to solve problems; (4) reasoning logically; and (5) engaging with mathematics, seeing it as sensible, useful, and doable.” The book recommends that instruction support math proficiency, instructional materials integrate the five strands of math proficiency, assessment contributes to the goal, teachers have the needed support, and that efforts to this goal be coordinated, comprehensive, and research based. In order for all students to be math proficient all stakeholders must work together.

Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. Washington, D.C.: National Academy Press.

Adding it Up explores how students in pre-K through 8th grade learn mathematics and recommends how teaching, curricula, and teacher education should change to improve mathematics learning during these critical years. The committee identifies five

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interdependent components of mathematical proficiency and describes how students develop this proficiency. The committee discusses what is known from research about teaching for mathematics proficiency, focusing on the interactions between teachers and students around educational materials and how teachers develop proficiency in teaching mathematics.

Kirschner, P. A., Sweller, J., & Clark, R. E. (2006). Why minimal guidance during instruction does not work: An analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching. Educational Psychologist, 41(2), 75-86.

The article begins with an explanation of the differences between the two approached to learning, the constructivist model (discovery learning) and the direct instruction model. The authors discuss long and short-term memory and how “everything we see, her, and think about is critically dependent on and influenced by our long-term memory.” The article stresses the importance of using direct instruction with novice and intermediate learners. Though emphasis on practical application is a positive it is a mistake to assume that instruction should exclusively focus on application.

Leinwand, S. (2009, January). Moving mathematics out of mediocrity. Education Week, 28(15), 32-33.

In the article the author discusses ways to improve mathematics in the United States. Suggestions include national math standards; best practices being utilized by teachers in the classroom; candid coaching and supervision of teacher’s instruction to strengthen teaching skills; assessments that are problem-oriented with constructed responses -- similar to Singapore and PISA assessments; and structures to allow for collaborative work among teachers, including lessons studies of current teacher practices.

Leinwand, S., & Ginsburg, A. (2009, April). Measuring up: How the highest performing state (Massachusetts) compares to the highest performing country (Hong Kong) in grade 3 mathematics. Retrieved August 21, 2009, from American Institutes for Research website: http://www.air.org/‌news/‌documents/‌AIR%20Measuring%20Up%20Report%20042709.pdf

This paper examines assessments in the early elementary grades, where a strong foundation in basic mathematics concepts and procedures has to be developed, and on which more-advanced mathematics topics can build. It compares Hong Kong’s Grade 3 assessment administered in June with that for Grade 3 in Massachusetts administered in May. The comparison of the content and characteristics of the Massachusetts assessment with those of the Hong Kong assessment suggests areas of difference that may guide Massachusetts and other states to reexamine their mathematics assessments. When examining the test items on the assessments that were more cognitively demanding (most from Hong Kong) the following features showed to increase mathematical rigor: - developing multistep solutions that require students to carry out a series of math procedures rather than a single calculation - solving problems in non-routine situations require students to adapt what they have learned - satisfying multiple problem conditions simultaneously - correctly differentiating among multiple representations of the same concept - finding the most efficient solution strategy among alternative strategies - translating different representations to a common representation before completing the solution - having to manipulate problem elements to obtain the solution - selecting the appropriate information from a set that includes extraneous information

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Loveless, T. (2003, February 6). Trends in math achievement: The importance of basic skills. Address presented at The Secretary of Education’s Mathematics Summit, Washington, D.C.

Tom Loveless, speaking before the Secretary of Education’s Mathematics Summit in Washington, D.C., on February 6, 2003, at the Department of Education’s launch of its Mathematics and Science Initiative

Loveless, T. (2008, October 16). Policy implications of the national mathematics advisory panel final report. Brookings Institution. Retrieved from http://www.brookings.edu/‌interviews/‌2008/‌1016_education_loveless.aspx

Tom Loveless discusses the policy implications of the National Mathematics Advisory Panel’s findings at the federal, state, district, and school levels in a recent interview.

Lubienski, S. T., Lubienski, C., & Crane, C. C. (2008, November). Achievement differences and school type: The role of school climate, teacher certification, and instruction. American Journal of Education, 115.

This study provides “evidence that both teacher certification and some reform-oriented mathematics teaching practices correlate positively with achievement and are more prevalent in public schools than in demographically similar private schools.”

Making math count. (2007, November). Educational Leadership, 65(3). Miller, S. P., & Hudson, P. J. (2006, September/‌October). Helping students with disabilities understand what mathematics means. Teaching Exceptional Children, 28-34.

Designing instruction to develop students’ conceptual understanding of mathematics is an important goal. Helping students with disabilities understand the underlying meaning of mathematics promotes acquisition, retention, and generalization of many mathematics objectives. It also helps them recognize mathematical relationships and connections. Without a focus on teaching conceptual understanding, mathematics instruction becomes memorization of meaningless facts and procedures. Instruction that the teacher plans and implements by using the five evidence-based guidelines (i.e., use various modes of representation, consider appropriate structures for teaching specific concepts, consider the language of mathematics, integrate real-world applications, and provide explicit instruction) supports the acquisition of high level of conceptual understanding. A high level of understanding will serve students well while they progress through the mathematics curriculum within school and when they translate the use of mathematics to environments outside school.

Pehkonen, E. (2007, November 9). Problem solving in mathematics education in Finland. Retrieved August 21, 2009, from University of Helsinki, Finland website: http://www.unige.ch/‌math/‌EnsMath/‌Rome2008/‌WG2/‌Papers/‌PEHKON.pdf

The main content of the paper is to describe problem solving in Finnish school mathematics, since this is the picture of mathematics teaching that is convoyed to teacher students at universities. The description begins with considering Finnish mathematics curricula with the focus on the role of problem solving. Furthermore, different manifestations of problem solving in mathematics textbooks are discussed as well as how Finnish teachers implement problem solving in mathematics lessons. Additionally the way teachers use problem solving in assessment is discussed briefly. At the end of the paper, a new solution for teaching problem solving within the curriculum is dealt with.

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Such a reform is based on the use of problem solving as a teaching method that often is manifested by the use of open problems.

Phillips, G. W. (2009, June). The second derivative: International benchmarks in mathematics for U. S. states and school districts. Retrieved August 21, 2009, from American Institutes for Research website: http://www.air.org/‌news/‌documents/‌AIRInternationalBenchmarks2009.pdf

This report was developed out of an attempt to find a scientifically rigorous way to compare the mathematics performance of U.S. states and school districts against challenging international benchmarks. In order to compare ourselves with the best in the world in mathematics, this report provides a crosswalk between the data provided by the 2007 Trends in International Mathematics and Science Study (TIMSS) and the 2007 National Assessment of Educational Progress (NAEP). The report simplifies these comparisons by grading the countries, states, and school districts with a comparable grading system that is more familiar to policymakers, a grade of A, B, C, D, or BD (below a D). The report assumes that the international benchmark, against which we should calibrate our expectations and monitor our success, is a grade of B. The grade of B was chosen because this report shows it is statistically equivalent to the Proficient level on NAEP that has been recommended by the National Assessment Governing Board (NAGB) and No Child Left Behind (NCLB) as the level of performance we should expect from our students.

Phillips, V. J., Leonard, W. H., Horton, R. M., Wright, R. J., & Stafford, A. K. (2003, October). Can math recovery save children before they fail? Teaching Children Mathematics, 10(2), 107-111. Retrieved from http://www.nctm.org/‌eresources/‌article_summary.asp?URI=TCM2003-10-107a

The article contains experimental and observational results of an early intervention program designed for low-achieving six- and seven-year-olds.

The PISA 2003 assessment framework: Mathematics, reading, science and problem solving knowledge and skills. (2003). Retrieved from Organization for Economic Co-Operation and Development website: http://www.pisa.oecd.org/‌document/‌29/‌0,3343,en_32252351_32236173_33694301_1_1_1_1,00.html

The OECD Programme for International Student Assessment (PISA) is a collaborative effort on the part of the Member countries of the OECD to measure how well students at age 15, and therefore approaching the end of compulsory schooling, are prepared to meet the challenges of today’s societies. The OECD/‌PISA assessment takes a broad approach to assessing knowledge and skills that reflect the current changes in curricula, moving beyond the school based approach towards the use of knowledge in everyday tasks and challenges. These skills reflect the ability of students to continue learning throughout their lives by applying what they learn in school to non-school environments, evaluating their choices and making decisions. The assessment, jointly steered by the participating governments, brings together the policy interest of countries with scientific expertise at the national and international levels.

Provasnik, S., & Gonzales, P. (n.d.). U.S. performance across international assessments of student achievement (Monograph No. 2009-083).

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Special analysis from recent international studies that U.S. students have participated in: PIRLS, PISA, TIMSS. Specifically addresses how our students compare with peers in other countries, and describes the reliability, validity, and comparability of international assessments.

Provasnik, S., Gonzales, P., & Miller, D. (2009, August). U.S. performance across international assessments of student achievement: Special supplement to the condition of education 2009. Retrieved from National Center for Education Statistics, U.S. Department of Education website: http://nces.ed.gov/‌PUBSEARCH/‌pubsinfo.asp?pubid=2009083

This Special Supplement to The Condition of Education 2009 looks closely at information gathered from recent international studies that U.S. students have participated in: the Progress in International Reading Literacy Study (PIRLS), the Program for International Student Assessment (PISA), and the Trends in International Mathematics and Science Study (TIMSS). It examines the performance of U.S. students in reading, mathematics, and science compared with the performance of their peers in other countries that participated in PIRLS, PISA, and TIMSS. It identifies which of these countries have outperformed the United States, in terms of students’ average scores and the percentage of students reaching internationally benchmarked performance levels, and which countries have done so consistently. When possible, it examines trends in U.S. student performance.

Schmidt, W. (2004, February). A Vision for Mathematics. Educational Leadership, February 2004, 6-11.

Schmidt contends that a coherent curriculum is critical for improving mathematics achievement. The United States must create common curricular standards and this curriculum must effectively implemented. Teachers must have the mathematical training in order to implement this cohesive curriculum. Teachers in the United States have significant less training than teachers in countries that score at the top of international testing.

Schneider, M. (2009, June 2). International benchmarking. Retrieved August 21, 2009, from https://edsurveys.rti.org/‌PISA/‌documents/‌schneiderNCES_International_Benchmarking_final.pdf

Despite a growing fascination with international comparisons of student performance and the feedback they provide on how young Americans are doing compared with their age-mates in other countries, current international assessments cannot generate a great deal of reliable policy advice. Indeed, many of the policy conclusions drawn from these assessments seem to be motivated as much by existing ideas as by strong evidence. The latest wrinkle in the nation’s interest in these international assessments is the drumbeat for state-level participation in the Organization for Economic Co-operation and Development’s (OECD’s) Programme for International Student Assessment (PISA), with a somewhat weaker chorus asking for state-level participation in the Trends in International Mathematics and Science Study (TIMSS)...... While TIMSS has its partisans and several states have actually chosen to participate in it, momentum is behind PISA. If we do implement state PISA, what should states expect? First, states would get a PISA score that would allow them to compare themselves to other PISA participants. In some cases, this would provide bragging rights (“Our students scored better than those in Korea”). In most states, disappointing results would provide reform-minded governors with ammunition to push for policy changes. But along with the PISA scale score would

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come all of the OECD’s policy advice, which might make it harder for governors to choose the policy options they prefer. Caveat emptor.

Schoen, H. L., & Hirsch, C. R. (2003). Responding to calls for change in high school mathematics: Implications for collegiate mathematics. American Mathematical Monthly, February 2003, 109-123.

The main goal of the curriculum is to improve students’ understanding of mathematical concepts and processes and their ability to use mathematics effectively in realistic problem solving. The authors discuss calls for change in high school mathematics and the relationship to mathematics instruction in college.

Schoenfeld, A. H. (2004, January). The math wars. Educational Policy, 18(1), 253-286. Retrieved from http://epx.sagepub.com/‌cgi/‌content/‌abstract/‌18/‌1/‌253

During the 1990s, the teaching of mathematics became the subject of heated controversies known as the math wars. The immediate origins of the conflicts can be traced to the “reform” stimulated by the National Council of Teachers of Mathematics’ Curriculum and Evaluation Standards for School Mathematics. Traditionalists fear that reform-oriented, “standards-based” curricula are superficial and undermine classical mathematical values; reformers claim that such curricula reflect a deeper, richer view of mathematics than the traditional curriculum. An historical perspective reveals that the underlying issues being contested—Is mathematics for the elite or for the masses? Are there tensions between “excellence” and “equity”? Should mathematics be seen as a democratizing force or as a vehicle for maintaining the status quo?—are more than a century old. This article describes the context and history, provides details on the current state, and offers suggestions regarding ways to find a productive middle ground.

Schoenfeld, A. H. (2006, March). What doesn’t work: The challenge and failure of the what works clearinghouse to conduct meaningful reviews of studies of mathematics curricula. Educational Researcher, 35(2), 13-21. Retrieved from http://edr.sagepub.com/‌cgi/‌content/‌abstract/‌35/‌2/‌13

An early version of this article, discussing curricular interventions in mathematics, was written for the What Works Clearinghouse (WWC). The Institute of Education Sciences (IES), which funds WWC, instructed WWC not to publish it. An expanded version, written at WWC’s invitation for a special issue of an independent electronic journal and a book to be published by WWC, argued that methodological problems rendered some WWC mathematics reports potentially misleading and/‌or unable to interpret. IES instructed WWC staff not to publish their chapters—thus canceling the publication of the special issue and the book. Those actions, chronicled here, raise important issues concerning the role of federal agencies and their contracting organizations in suppressing scientific research that casts doubt on current or intended federal policy.

Slavin, R. E., & Lake, C. (2007, February). Effective Programs in Elementary Mathematics: A Best-Evidence Synthesis. Abstract retrieved from http://www.bestevidence.org/‌math/‌elem/‌summary.htm

This article reviews research on the achievement outcomes of three types of approaches to improving elementary mathematics: Mathematics curricula, computer-assisted instruction (CAI), and instructional process programs. Study inclusion requirements included use of a randomized or matched control group, a study duration of 12 weeks, and achievement measures not inherent to the experimental treatment. Eighty-seven

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studies met these criteria, of which 36 used random assignment to treatments. There was limited evidence supporting differential effects of various mathematics textbooks. Effects of CAI were moderate. The strongest positive effects were found for instructional process approaches such as forms of cooperative learning, classroom management and motivation programs, and supplemental tutoring programs. The review concludes that programs designed to change daily teaching practices appear to have more promise than those that deal primarily with curriculum or technology alone.

Slavin, R. E., Lake, C., & Groff, C. (2008, October). Effective Programs in Middle and High School Mathematics: A Best-Evidence Synthesis. Abstract retrieved from http://www.bestevidence.org/‌math/‌mhs/‌summary.htm

This article reviews research on the achievement outcomes of mathematics programs for middle and high schools. Study inclusion requirements included use of a randomized or matched control group, a study duration of at least twelve weeks, and equality at pretest. There were 102 qualifying studies, 28 of which used random assignment to treatments. Effect sizes were very small (weighted mean ES=+0.03 in 40 studies) for mathematics curricula, and for computer-assisted instruction (ES=+0.08 in 40 studies). They were larger (weighted mean ES=+0.18 in 22 studies) for instructional process programs, especially cooperative learning (weighted mean ES=+0.42 in 9 studies). Consistent with an earlier review of elementary programs, this article concludes that programs that affect daily teaching practices and student interactions have larger impacts on achievement measures than those emphasizing textbooks or technology alone.

Stein, M. K. (n.d.). Selecting the right curriculum [Review of the math curriculum Math curriculum review process]. National Council Teachers of Mathematics. Retrieved from http://www.nctm.org/‌news/‌content.aspx?id=12320

“One of the most critical decisions educational leaders make is the selection of a mathematics curriculum.” The three main components that need to be evaluated when selecting the right curriculum is the curriculum materials, the pedagogical approach, and the professional development required. When looking at content coverage it is important that the decision makers are “clear regarding what they value in the way of student outcomes and the to select a review that reflects their values as closely as possible.” The true can also be said with regard to how content is presented. Decision makers will also need to determine the learning demand placed on teachers when selecting curriculum. Research in the area of effectiveness for standards-based math and conventional math is limited. “Most curricula (standards-based and conventional) intend for students to learn concepts, skills, applications, problem solving, and efficient procedures. They differ, however, with regard to the order and manner in which these elements are presented, the balance that is struck among different elements, and organizational style. Conventional curricula tend to rely on direct explication of the to-be-learned material as well as careful sequencing and the accumulation of lower-level skills before presenting students with the opportunity to engage in higher-order thinking, reasoning, and problem solving with those skills. Standards-based materials rarely explicate concepts for students; rather , they rely on students’ engagement with well-explored by students, the curriculum and teacher step in to apply definitions, standard labels, and standard procedural techniques.” Research suggests that “students taught using conventional curricula can be expected to master computational and symbolic manipulation better, whereas students taught using

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standards-based curricula can be expected to perform better on problems that demand problem solving, thinking, and reasoning.”

Stewart, V. (2009, November). China and U.S. can swap ideas about math and science. Phi Delta Kappan, 91(3), (94-95).

The article discusses how to improve student achievement for special needs students. It is stated that to accomplish this goal teachers must believe these students can learn high quality and high order mathematics. Teachers need to deep their understanding of learning issues; create a nurturing classroom environment; use strategic, customized instructional practices and collaborate with special education teachers. The article encourages classroom teachers and special education teachers to co-teach math classes which they believe would foster a broader and deeper understanding of math, develop better questions about math, and expand student’s mathematical thinking. The article also encouraged teachers to use strategic customization of instructional practices and effective use of accommodations specific to the student’s special needs. These could include: adjustment of the pace of the lesson, built-in scaffolds, changes in time or schedule of assessment, use of manipulatives, graphic organizers, changes in test directions, changes in presentation of questions and how student respond to questions.

Stylianides, A. J., & Stylianides, G. J. (2007). Learning mathematics with understanding: a critical consideration of the learning principle in the Principles and Standards for School Mathematics. The Montana Mathematics Enthusiast, 4(1), 103-114.

In this article the authors discuss both the strengths and shortcomings of the Principle Learning section of the Principles and Standards for School Mathematics from the National Council Teachers of Mathematics. The authors agree with the Learning Principle that supports the claim that learning with understanding is necessary in math education. In the Learning Principle section it states that rote learning of facts and/‌or procedures often result in “fragile learning.” NCTM discusses the three major components of proficiency are conceptual understanding, factual knowledge and procedural facility. The learning principle emphasized the need for ideas to be well connected and conceptually grounded and believe that students working with problems are the source of making meaning. The author recommends that NCTM discuss the idea of desirable learning outcome. They suggest that understanding is not always the goal of the math lesson and drill can be an important method for learning when the idea is already understood and the goal is to increase proficiency. The authors also take issue with the Learning Principle not discussing when learning from one situation to another does not transfer. There are many articles discussing situated cognition where the methods taught in the classroom are not transferred to real-life situations. The authors also take issue with the Learning Principle discussing the importance of previous knowledge in assisting in mathematics learning. NCTM does not discuss when the previous knowledge has misconceptions about a mathematical concept/‌process and how teachers need to assist students in their thinking. The last recommendation was the important role that cultural context plays in the learning environment. The authors encourage the Learning Principle address the importance culture can play in a student’s understanding of mathematics when there is a diverse student population in a classroom.

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Tan, J., Keys, R., Keys, B., Chavez, O., Shih, J., & Osterlind, S. (2008). The impact of middle-grades mathematics curricula and the classroom-learning environment on student achievement. National Council of Teachers of Mathematics, 39(May 2008), 247-280.

Six researchers set out to compare and contrast 1) the systemic effects of adopted textbooks 2) teacher practices and 3) standards-based learning environments on student achievement in mathematics.

Viadero, D. (2009, March 4). Study gives edge to 2 math programs. Education Week, pp. 1, 13. Retrieved from http://www.edweek.org/‌ew/‌articles/‌2009/‌03/‌04/‌23math-2.h28.html

Two programs for teaching mathematics in the early grades—Math Expressions and Saxon Math—emerge as winners in early findings released last week from a large-scale federal experiment that pits four popular, and philosophically distinct, math curricula against one another. But the results don’t promise to end the so-called “math wars” anytime soon, according to experts. That’s because the two most successful programs embody different approaches to teaching math in grades K-2.

Walker, E. N. (2007, November). Why aren’t more minorities taking advanced math? Educational Leadership, 65(3), 48-53. Retrieved from http://www.ascd.org/‌publications/‌educational_leadership/‌nov07/‌vol65/‌num03/‌Why_Aren’t_More_Minorities_Taking_Advanced_Math%C2%A2.aspx

Black and Latino students are still underrepresented in upper-level math classes in the United States, a fact that has serious implications for their academic achievement and futures. Walker provides six suggestions for how educators can encourage more black and Latino students to successfully take higher level math courses: (1) Expand our thinking about who can do mathematics; too often educators assume that minority students don’t have the ability or interest to do higher level math. (2) Build on underrepresented students’ existing academic communities. Walker’s research reveals that minority students doing well in math often draw on networks of family and peers that support this achievement. (3) Learn from institutions that promote math excellence, such as historically black colleges and universities that graduate many minorities with math-related degrees. (4) Expand the options in school math courses. (5) Expand enrichment opportunities by providing more out-of-classroom mathematics experiences. (6) Make minority students less isolated in advanced mathematics courses.

Wang-Iverson, P., Meyers, P., & Lim W.K., E. (2009-2010, Winter). Beyond Singapore’s mathematics textbooks. American Educator, 28-38.

With America’s strong interest in Singapore’s mathematics textbooks, these researchers caution against thinking that Singapore’s high achievement comes from its books alone. In particular, they explore the preparation and support of mathematics teachers who, unlike their counterparts in the United States, are guided by a coherent national curriculum; benefit from comprehensive preparation programs that emphasize subject-matter knowledge, pedagogy, and classroom based learning; and have several options to grow as educators.

Watanabe, T. (2007). In pursuit of a focused and coherent school mathematics curriculum. The Mathematics Educator, 17(1), (2-6).

In the article the author discusses what makes a curriculum coherent. Main features of a coherent math curriculum are that the contents are sequenced in a way that new ideas are

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built on previously developed ideas; the text itself makes clear the potential learning paths that teachers follow during instruction; and the math curriculum should show how one part of the curriculum relates to another. A consistent use of the same or similar items across related math ideas is not limited to problem contexts but also representations. The author discusses why it is so difficult to have focused curriculum. One reason is that textbooks and teachers are reluctant to remove any topic from the existing curriculum for fear that the wrong topic is being removed. Another culprit is the replacement unit. Originally it was intended to supplement a less effective unit in a book but allowed for an entire year to get rearranged to the point that the intent and flow of the content is lost. The author suggests using the Japanese model of lesson study to form a cohesive math curriculum. Where teachers work collaboratively to answer the following questions: o Why is the topic taught at this particular point in the curriculum? o What previously learned materials are related to the current topic? o How are students expected to use what they have learned previously to make sense of the

current topic? o How will the current topic be used in the future topics? o Is the sequence of topics presented in the textbooks the most optimal one for their students?

During the process teachers read research and invite researchers to participate as consultants. The lesson study often includes researchers, university-based math educators, district math supervisors and even officials from the Ministry of Education.

What the United States can learn from Singapore’s world-class mathematics system (and what Singapore can learn from the United States): An exploratory study (Monograph No. 20007-3835). (2005, January). American Institutes for Research.

This study compares key features of the Singapore and US mathematics systems. The article addresses the topics of curriculum framework, textbooks, assessments, and teachers. Singapore’s national framework is a carefully sequenced and has fewer topic than the U.S. There is an emphasis on computation skills along with more conceptual and strategic thinking. Singapore follows a spiral organization in which topics are presented at one grade level and again in a later grade, but only at a more advanced level. Their textbooks are problem-based and the illustrations feature a concrete to pictorial to abstract approach. Singapore assessments stress the importance of constructed response questions allowing students to demonstrate a higher-level cognitive ability. Teachers in Singapore are highly trained and continue once in the classroom with 100 hours of required annual professional training. The U.S. is strong in its emphasis on applied mathematics and developing 21st Century skills such as representation, reasoning, making connections and communication.

Wood, T., Williams, G., & McNeal, B. (2006, May). Children’s mathematical thinking in different classroom cultures. Journal for Research in Mathematics Education, 37(3), 222-255.

The relationship between normative patterns of social interaction and children’s mathematical thinking was investigated in 5 classes (4 reform and 1 conventional) of 7- to 8-year-olds. In earlier studies, lessons from these classes had been analyzed for the nature of interaction broadly defined; the results indicated the existence of 4 types of classroom cultures (conventional textbook, conventional problem solving, strategy reporting, and inquiry/‌argument). In the current study, 42 lessons from this data resource were analyzed for children’s mathematical thinking as verbalized in class discussions and

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for interaction patterns. These analyses were then combined to explore the relationship between interaction types and expressed mathematical thinking. The results suggest that increased complexity in children’s expressed mathematical thinking was closely related to the types of interaction patterns that differentiated class discussions among the 4 classroom cultures.

Wu, H. H. (2009, Fall). What’s sophisticated about elementary mathematics? American Educator, 4-14. Retrieved from http://www.aft.org/‌pubs-reports/‌american_educator/‌issues/‌fall2009/‌index.htm

Improving mathematics instruction is a priority in the United States, but there’s little agreement on how to do it. Here’s an idea that is rarely discussed: starting no later than fourth grade, math should be taught by math teachers (who teach only math). Teaching elementary math in a way that prepares students for algebra is more challenging than many people realize. Given the deep content knowledge that teaching math requires—not to mention the expertise that teaching reading demands—it’s time to reconsider the generalist elementary teacher’s role.

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Appendix F PISA Data

Expect to receive PISA data by the end of December

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Appendix G TIMSS Data on High Achieving Countries

Grades 4 and 8

228

4th grade Singapore Massachusetts Hong Kong

Average achievement in the mathematics content and cognitive domains number

geometric shapes and measure data and display number

geometric shapes and measure data and display number

geometric shapes and measure data and display

average scale scores for mathematics content domains 611 570 583 571 564 571 606 599 585

knowing applying reasoning knowing applying reasoning knowing applying reasoningaverage scale scores for mathematics cognitive

domains 620 590 578 581 566 565 617 599 589Index of time students spend doing mathematics homework in a normal school week % students

average achievement % students


average achievement

high 34% 607 16% 573 185% 599medium 52% 603 75% 574 78% 613

low 15% 581 9% 569 4% 562Index of teachers' emphasis on mathematics homework with trends % students



average achievement

high 32% 590 17% 583 26% 610medium 47% 610 71% 569 63% 611

low 21% 590 12% 577 11% 576Percentage of students whose teachers always or almost always

monitor whether or not the homework was completed 85% 96% 82%

correct assignments and then give feedback to students 80% 26% 77%

have students correct their own homework in class 26% 59% 18%

use the homework as a basis for class discussion 28% 51% 24%

use the homework to contribute towards student's grades/marks 20% 80% 29%

Percentage of students taught by teachers reporting textbook use

use textbook to teach mathematics - primary basis 75% 48% 84%

use textbook to teach mathematics - supplementary resource 24% 34% 15%

do not use textbook to teach mathematics 1% 18% 2%

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Percentage of time in mathematics lessons students spend on various activities in a typical week

reviewing homework 14% 8% 8%listening to lecture style presentations 19% 15% 38%

working problems with teacher's guidance 18% 30% 16%working problems on their own without

teacher's guidance 175% 20% 13%listening to teacher re-teach and clarify content

procedures 11% 12% 9%taking tests or quizzes 8% 7% 6%

participating classroom management tasks not related to the lesson's content/purpose 6% 4% 4%

other student activities 6% 5% 5%

Calculator use in mathematics class with trendsnational curriculum contains policies/

statements about the use of calculators no yes yespercents of students whose teachers reported

that calculators are not permitted 2% 92% 48%percentage of students whose teachers

reported on calculator use about half of the lessons or more 81% 59% 58%

Percentage of students by their teachers' educational level

post - graduate degree

completed university but

not post - graduate

completed post secondary

education but not university

completed upper

secondary school


completed university but not post - graduate



completed upper

secondary school



not post - graduate



completed upper

secondary school

4% 55% 38% 3% 82% 18% - - 12% 71% 16% 1%Percentage of students by their teachers' major area of study in their post-secondary educationprimary / elementary education with a major or

specialization in mathematics 51% 9% 51%

primary / elementary education with a major or specialization in science but not mathematics 6% 4% 2%

mathematics or science major or specialization with a major in primary / elementary education 13% 4% 13%

primary / elementary education without a major or specialization in mathematics or science 15% 70% 26%

other 15% 13% 8%

230

Percentage of students by their teachers' participation in professional development in mathematics in the past 2 years content pedagogy curriculum content pedagogy curriculum content pedagogy curriculum

59% 70% 50% 77% 77% 77% 74% 82% 70%

integrating technology

improving critical thinking or

problem solving skills assessment





improving critical thinking

or problem solving skills assessment

51% 66% 52% 44% 65% 64% 49% 72%Percentage of students by their teachers' frequency of collaboration with other teachers

never or almost never

2 or 3 times per moth at least weekly





percentage : average achievement 9% : 621 77% : 600 14% : 583 10% : 565 56% : 575 34% : 573 4% : 593 87% : 609 9% : 602Percentage of students whose teachers report feeling very well prepared to teach the TIMSS mathematics project 85% 95% 57%

overall average class size 38 21 35

Number of TIMSS mathematics topics intended to be taught up to and including eighth grade

topics for all or almost all

topics for only the more able

not included in curriculum

through grade 4topics for all or

almost alltopics for only the more able


through grade 4topics for all or almost all



through grade 4all mathematics (39 topics) 27 0 8 32 0 3 25 1 9

Schools with few (0-10%) economically disadvantaged students 60% 46% 26%Schools with 11-25% economically disadvantaged students 30% 23% 23%Schools with 25-50% economically disadvantaged students 9% 14% 30%

percent avg achievement percent avg achievement percentavg

achievementSchools with more than 90% of students having the language of the test as native language 3% 620 71% 578 96% 606Schools with 50-90% of students having the language of the test as native language 22% 624 22% 568 3% 629

Weekly intended and implemented instructional time for mathematics with trends hours

% of total instructional

time hours% of total

instructional time hours


timeintended hours 25 22% 25 na 23 13%

implemented hours 26 21% 28 21% 27 15%Percentage of time in mathematics class devoted to TIMSS content domains during the school year number

geometric shapes and measure data and display other number

geometric shapes and measure data and display other number

geometric shapes and measure data and display other

55% 27% 14% 5% 51% 22% 20% 6% 53% 29% 15% 3%

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8th grade Singapore Massachusetts Hong Kong

Emphasis on sources to monitor students' progress in mathematics p. 309

major emphasis some emphasis

little or no emphasis major emphasis some emphasis

little or no emphasis

major emphasis some emphasis

little or no emphasis

teacher's own professional judgment 23 58 18 39 50 11 34 46 19classroom tests 77 21 2 71 26 3 81 18 1

national or regional achievement tests 37 24 39 17 36 47 6 21 74

Percentage of students whose teachers give a mathematics test or exam

every 2 weeks or

moreabout once a

montha few times a year or less

every 2 weeks or more

about once a month

a few times a year or less

every 2 weeks or more

about once a month

a few times a year or less

35 47 18 60 38 2 56 38 2Percentage of students by types of questions on mathematics tests given by their teachers

always or almost always sometimes






questions based on recall of facts and procedures 37 56 8 56 41 4 39 51 10

questions involving application of mathematical procedures 75 25 0 79 21 0 68 32 0

questions involving searching for patterns and relationships 12 81 7 27 69 5 12 65 23

questions requiring explanations or justifications 8 70 22 41 59 0 21 69 11

Average achievement in the mathematics content and cognitive domains number algebra geometry

data and chance number algebra geometry


data and chance

average scale scores for mathematics content domains 597 579 578 574 548 538 519 569 567 565 570 549

knowing applying reasoning knowing applying reasoning knowing applying reasoningaverage scale scores for mathematics

cognitive domains 581 593 579 546 542 543 574 569 557Item formats used by teachers in mathematics tests or exams with trends % of students % of students % of students

only or mostly constructed-response 83% 57% 65%about half constructed-response and half

multiple-choice 3% 30% 34%only or mostly multiple-choice 14% 13% 0%

Index of time students spend doing mathematics homework in a normal school week % students



average achievement

high 42% 616 31% 564 34% 589medium 43% 595 63% 546 48% 576

low 16% 547 6% 500 18% 555

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Index of teachers' emphasis on mathematics homework with trends % students



average achievement

high 43% 612 32% 576 31% 586medium 39% 595 59% 537 52% 582

low 18% 542 9% 494 17% 532Percentage of students whose teachers always or almost always

monitor whether or not the homework was completed 85% 96% 82%

correct assignments and then give feedback to students 80% 26% 77%

have students correct their own homework in class 26% 59% 18%

use the homework as a basis for class discussion 28% 51% 24%

use the homework to contribute towards student's grades/marks 20% 80% 29%

Percentage of students by types of homework assigned by their teachers




doing problem/question sets 75% 21% 81% 17% 64% 34%gathering data and reporting 0% 49% 1% 54% 0% 40%

Percentage of students taught by teachers reporting textbook use

use textbook to teach mathematics - primary basis 51% 57% 76%

use textbook to teach mathematics - supplementary resource 39% 42% 24%

do not use textbook to teach mathematics 9% 1% 1%Percentage of time in mathematics lessons students spend on various activities in a typical week

reviewing homework 12% 13% 11%listening to lecture style presentations 26% 16% 35%

working problems with teacher's guidance 19% 22% 16%working problems on their own without

teacher's guidance 13% 18% 13%listening to teacher re-teach and clarify

content procedures 10% 12% 10%taking tests or quizzes 8% 10% 8%

participating classroom management tasks not related to the lesson's content/purpose 8% 4% 4%

other student activities 5% 4% 3%

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Calculator use in mathematics class with trends

national curriculum contains policies/ statements about the use of calculators yes yes yes

percents of students whose teachers reported that calculators are not permitted 100% 98% 99%

percentage of students whose teachers reported on calculator use about half of the

lessons or more 54% 57% 42%

Percentage of students by their teachers' educational level



not post - graduate



completed upper

secondary school


completed university but not post - graduate



completed upper

secondary school



not post - graduate



completed upper

secondary school

6% 89% 4% 0% 64% 36% - - 26% 62% 12% 1%Percentage of students by their teachers' major area of study in their post-secondary education

education-math 49% 26% 58%mathematics 69% 43% 62%

education-science 18% 3% 19%science 46% 13% 30%

education-general 34% 57% 36%other 50% 39% 40%

Percentage of students by their teachers' participation in professional development in mathematics in the past 2 years content pedagogy curriculum content pedagogy curriculum content pedagogy curriculum

81% 88% 65% 94% 91% 75% 78% 71% 72%










74% 63% 61% 64% 65% 61% 63% 60% 56%Percentage of students by their teachers' frequency of collaboration with other teachers







percentage : average achievement 14% : 561 74% : 595 12%: 620 24% : 554 60% : 544 14% : 542 17% : 604 72% : 564 11% : 581Percentage of students whose teachers report feeling very well prepared to teach the TIMSS mathematics project 82% 96% 67%

overall average class size 38 22 37

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Number of TIMSS mathematics topics intended to be taught up to and including eighth grade

topics for all or almost all



through grade 8topics for all or

almost alltopics for only the more able


through grade 8topics for all or almost all



through grade 8all mathematics (39 topics) 38 1 - 38 0 1 35 1 3

schools with few (0-10%) economically disadvantaged students 52% : 614 32% : 577 12% : 627

schools with 11-25% economically disadvantaged students 30% : 572 37% : 558 24% : 602

schools with 25-50% economically disadvantaged students 9% : 556 12% : 513 24% : 553

percentavg

achievement percent avg achievement percentavg

achievementSchools with more than 90% of students having the language of the test as native language 7% 649 76% 561 89% 576

Schools with 50-90% of students having the language of the test as native language 18% 623 16% 516 9% 540Weekly intended and implemented instructional time for mathematics with trends hours


time hours% of total

instructional time hours


timeintended hours 23 13% 28 np 27 13%

implemented hours 29 13% 29 15% 28 14%Percentage of time in mathematics class devoted to TIMSS content domains during the school year number algebra geometry



data and chance

16% 40% 21% 13% 19% 50% 14% 13% 18% 34% 31% 12%other other other0% 3% 4%

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Appendix H Memo to Board of Education – Core Plus

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MEMO To: Board of Education From: Dottie Barbeau Date: November 14, 2010 Re: Clayton High School Math Program Recommendation As a follow up to the Board of Education discussion following the meeting Wednesday evening, I’d like to provide to you a statement on our recommendation for mathematics curriculum changes at Clayton High School. We recognize the need for addressing the challenges we currently face at the high school. Since our curriculum review goal is to provide the best possible curriculum and instruction for all of our students in a seamless and coherent manner, we also recognize the need to immediately start taking action steps so that we are prepared for curricular changes and registration for courses in the coming school year at Clayton High School. Our first action step is to recommend not bringing forward the Core Plus Integrated Math series for adoption in our new curriculum review cycle. Our Clayton High School mathematics faculty has had numerous discussions with Heidi Shepard regarding this recommendation and are in agreement that it will be in the general best interest for our high school to phase out the integrated mathematics program. Below are listed a few of the challenges that support this decision:

• Having multiple sequences reduces the number of sections for any one course making it more difficult to do scheduling for students.

• Having multiple sequences causes an excessive number of courses within one department which in turn creates a large number of singletons.

• Singletons do not allow for collaborative study among math teachers. Lesson Study, as we well know from our research on math instruction in Japan, has been proven to improve instruction, thus student achievement.

• Moving to one sequence for the college prep students will provide more flexibility for students in their schedules.

• Multiple tracks at the college prep level often causes angst for freshman parents who are making placement decisions.

• We feel a significant portion of our community, through our parent survey, indicated they were not in support of our integrated math sequence.

While we have made the decision not to move forward with Core Plus, we have not yet evaluated new texts as a replacement. That process will take place in January and we will provide ample opportunities for our community to provide input into our decision.

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school district of clayton mathematics program review · 2010-12-15 · school district of clayton...

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