mathematics in depth study

In-Depth Study

An In-Depth Study in Mathematics by Holy Cross School150 Emmet Street

Santa Cruz, CA 95060

Continuous School Improvement Focused On High Achievement Of All Students2013

Preface

Administration and faculty of Holy Cross School met in the fall of 2011 to discuss

possible curriculum areas for the focus of our in-depth study. Previous discussions about our

math curriculum and student performance in math on standardized tests and in the classroom led

us to a consensus that an in-depth analysis of this area would have the greatest impact on student

learning.

In the last several years, we have noted that math computation skills are weak across

grade levels. This is evidenced by student performance on assignments and classroom

assessments, as well as by standardized test results. The math computation subtest of the ITBS

has consistently been our lowest scoring area. In an attempt to understand the reasons for this

trend, our teachers investigated current research about primary level math instruction. In an

article titled “Closing the Achievement Gap: Best Practices in Teaching Mathematics” published

by the Education Alliance, Spring 2006, the authors address the consistent low performance in

math in U.S. schools and cite the need “to build the foundations necessary for understanding

higher level math...These foundations can only be built with a mathematics program that teaches

concepts and skills, and problem solving (Daro, 2006.)”

As a result of this research, the primary grade teachers selected a new math curriculum,

Math Expressions by Houghton Mifflin. This curriculum is based on a ten-year research study of

the ways children understand mathematical concepts, approach problem solving, and learn

computation. It also reflects research regarding children’s developmental stages when mastering

concepts to help determine the order of concept introduction and the sequence of topics. The

kindergarten and first grade classes are in their third year of using this curriculum, and second

grade is in their first. The increase in 2010-2012 second grade computation scores on the ITBS

shown in the graph below suggests that the switch the Math Expressions program is helping

students to better acquire the conceptual understanding necessary for success in performing basic

math operations. We will continue to track assessment results to see if this trend continues,

particularly in light of the new Common Core State Standards.

WCEA ISL 2010 Holy Cross School

TASK 1 – ANALYZING CURRICULUM ASSESSMENT DATAHoly Cross School uses educationally sound assessment processes to collect data. The

school disaggregates and analyzes student performance data and uses the analysis as a basis for

instructional and curricular improvement.

The national, norm-referenced, assessment data collected and analyzed for this study is

from the Iowa Test of Basic Skills/Iowa Assessment. Holy Cross administers this test each

September to students in grades 2-8. An analysis of the assessment data below provides evidence

that students are making steady progress over time in math in grades 3-8. The graphs below chart

the growth of single groups of students over the last 2-5 years.

The analysis of data led us to identify two class groups that score lower over time than

other groups. These are the current 3rd and 7th grade classes. We believe this lower performance

can be attributed at least in part to the fact that both of these classes have higher percentages of

students with learning challenges, as evidenced by their participation in Learning Lab, and after

school tutoring programs and through outside testing. In addition, 21% of the students in the 7th


grade class transferred in to our school after 5th grade and therefore did not receive the

continuity of learning provided by our primary and intermediate grade level math programs.

When analyzing the test score data by gender, we did not find any significant trends or

differences in performance. No other sub groups where identified in our student populations.


The analysis of test score data by subtest in the graphs below shows that computation is

our lowest area across all grade levels except for grade 8. Problem solving is our highest area.


Breaking down the computation subtest into its component areas, we find that at most

grade levels, operations with fractions and decimals is lowest. Faculty met to discuss these

results in light of our current math programs and instructional practices, and have concluded that

more of our instructional time should be allocated to the teaching of math facts, operations of

partials, fractions, and decimals.

The analysis of math subtest data shows our strongest areas are problem solving and

concepts and estimation. Looking back over three years (2009-2011), students in grades 2-8

consistently score the highest on these two subtests.

Our ability to more fully disaggregate and analyze the test data has been hampered by a

lack of time allotted for this process. More time would allow teachers to analyze the data in


depth, focus on areas for improvement, identify students’ individual learning needs and adjust

curriculum accordingly.

In the past, teachers have been asked to review the standardized test results for their own

classes, and to use this information in their curriculum planning for the year. However, because

this process did not address performance schoolwide, we were not able to use the data to address

areas that were low across grade levels. We believe a more systematic analysis of testing data

would greatly benefit our ability to support our students’ learning and mastery of the math

standards. We also believe it would be useful to correlate curriculum standards with subtest

topics in areas where our students are underperforming. This information would be instrumental

in planning curriculum and instruction that specifically addresses needs in these areas as well as

addressing the new Common Core State Standards.

Our review of the math assessment data shows that Holy Cross students are making

consistent progress over time in all areas. Our highest areas continue to be problem solving and

concepts and estimation. These findings are supported by strong student performance in the

classroom in conceptual areas of math. The data also confirms that student performance in

computation skills is an area that needs to be addressed schoolwide. Again, this reinforces what

teachers have concluded from assessment of student performance in the classroom.

The data below shows that more Holy Cross students score in the top quartile in total

math than the Diocesan average, with the exception of the two low performing classes identified

above.


Significant Accomplishments:

Adoption of new math curriculum in primary grades to address low computation scores.

Goal:

Develop a schoolwide, systematic plan for analysis and retention of year-to-year

assessment data from the Iowa Assessment with a specific focus in math.


TASK 2 – USING CURRICULUM STANDARDSThe school provides a challenging, comprehensive and relevant curriculum for each student that results in achievement of the Schoolwide Learning Expectations, Arch/diocesan curriculum standards (local curriculum standards where Arch/diocesan standards don’t exist), and other institutional and/or governing authority expectations. All students make acceptable progress toward clearly defined and measurable Schoolwide Learning Expectations, Arch/diocesan curriculum standards (local curriculum standards where Arch/diocesan standards don’t exist), and/or other governing authority expectations.

At Holy Cross School, Diocesan and state standards are the framework for the

development of curriculum and course content. Teachers have cross-referenced California State

Standards with the Common Core State Standards in their lesson planning this year. We will

transition fully to the Common Core State Standards in the 2013-2014 academic year. The

standards guide curriculum planning, instructional practices, and methods of assessment used in

the classroom. Math curriculum at all grade levels is aligned with the California state standards,

and supplemental materials used by teachers are selected to support mastery of the standards as

well.

Teachers meet periodically in grade level clusters to determine the key standards to be

addressed in each grade. This ensures that we are providing a comprehensive continuum of

learning that leaves no gaps in essential areas.

Weekly math lesson plans are required at every grade level, and must specify standards

covered as well as Student Learning Expectations addressed. Explicitly stating teaching goals is

a researched based strategy that has a high probability of impacts student learning (The Art and

Science of Teaching, Robert Marzano, 2007). Teachers are consistently aware of the standards

they are teaching and student progress toward mastery of the standards. Administration is able to

track what standards are being covered as well as how they are being taught.

Math curriculum maps are revised and updated on an as-needed basis, for example, with

the introduction of new curriculum materials, the addition of new faculty, or to incorporate newly

learned instructional methodologies. Our most current math maps were updated schoolwide in

the spring of 2012. Since that time, our school has added three new math teachers who are

updating their curriculum maps this year. We will update all math maps schoolwide this spring to


reflect integration of the Common Core State Standards and the Diocesan Initiative, Catapult

Learning.

Significant accomplishment:

The inclusion of curriculum standards and SLEs in weekly lesson plans.

Goal:

Create a schoolwide curriculum math map utilizing our existing grade level maps with a

specific focus on continuum of skills.


TASK 3 – INSTRUCTIONAL METHODOLOGYTeachers at Holy Cross independently investigate and implement best practice strategies

in their classrooms on an ongoing basis. They share information with colleagues both formally at

grade level cluster meetings and full faculty meetings and informally through peer mentoring and

in faculty room discussions. Some of these practices are shown in the table below:

K-2 3-5 6-8

peer tutoring cooperative learning group problem solving

hands on exploration academic vocabulary development

ability to share and challenge

math talk, math writing math writing use of math journals

interdisciplinary connections interdisciplinary connections interdisciplinary connections

use of interactive technology use of interactive technology use of interactive technology

Within the last three years, the principal and three members of our faculty participated in

a School Leadership Team Training program centered around The Art and Science of Teaching

by Dr. Robert Marzano. The faculty members, representing grade level clusters, learned how to

use research-based instructional strategies that have a high probability of effectiveness. Each

teacher who participated conducted an action-based research project using pre- and post-tests and

control and experimental groups to determine if the targeted strategy was truly a key to student

success. Results were turned in to the Marzano Research Laboratory for further evaluation of

effectiveness. The teachers who participated in the workshop shared their research results with

the rest of the faculty. Built into the model of these workshops was the expectation that the

leadership team would return to the school site and train the rest of the faculty on the different

strategies and assessment they had learned. Unfortunately, follow-up on this goal was very

limited, as time was not allocated for it. Looking forward, we would like to train more faculty

and design a model for schoolwide implementation.


Teachers who use these best practice strategies note their relative effectiveness and use

this information to modify their teaching practice, but to date, we have not implemented a formal

process for analyzing their impact on student learning.

This process of examining our math instructional practices confirms our choice of math

as an important focus for in-depth study. We find this to be the area of our curriculum that would

most benefit from review and ongoing development. While the faculty at Holy Cross

independently pursues and utilizes current best teaching practices, we believe a formal process

for choosing, implementing, and assessing the effectiveness of specific strategies will provide a

more cohesive school-wide math program.

Accomplishments:

A standards-aligned curriculum in all grade levels.

Goal:

To increase time and resources allocated for professional development in the area of math

to ensure program fidelity and cohesion throughout the grades.


TASK 4 – SUMMARY OF FINDINGSThree significant accomplishments in our school in the area of math that have had a

positive impact on student learning are the adoption of Math Expressions in K-2, the inclusion of

curriculum standards and SLEs in weekly math lesson plans, and the infusion of research-based

methodologies (Marzano) into teaching practice. After identifying the need for stronger

conceptual understanding in the primary grades, the implementation of the Math Expressions

curriculum seems to suggest a strengthening in this area over the past three years by those

students who have had the benefit of the program. Grades 3-5 math texts are aligned with this

program, ensuring continuity and smooth transitions between grades. In addition, through weekly

lesson plan submission, administration has the ability to see the progression of skills across the

grades and monitor progress. The ability to see our math instruction as a whole allows for

meaningful oversight and informed discussions. Incorporating the strategies teachers have

learned and shared from the Marzano training into their instructional practice had added

increased emphasis on the skills being taught and the goals of each lesson. The cohesion of texts,

focus areas, and teaching methodologies creates unity across the grades and will lead to program

fidelity in all areas.

The goal that would have the greatest positive impact on student learning would be the

allocation of more time and resources for data analysis, articulation, and professional

development in the area of math. Through the process of analyzing our test data and faculty

articulation around these findings, we have identified the need for program fidelity, common

vocabulary, and increased time for faculty to discuss their math practice. This additional time

would allow faculty to share and enhance curriculum maps, differentiate instruction to include all

learners, and continue to expand and incorporate the breadth of technology we have at our

fingertips. Furthermore, after identifying the two grades in need of increased support, we can

strategize and implement ways to support them through the grades.


Task 5 – Action Plan

Goal: Allocate time and resources for data analysis, articulation, and professional development

in the area of math.

Rationale for this Goal: The process of analyzing our test data and faculty articulation will lead

to program fidelity, common vocabulary, and will enhance the continuum of learning necessary

to support the high achievement of all students.

Alignment with mission, philosophy, SLEs:• Mission: Holy Cross Catholic School, a ministry of Holy Cross Parish, educates and

guides children in their spiritual, intellectual and moral development. • Philosophy: We integrate high academic standards with experiences that develop the

values, attitudes, and habits necessary for our students to become intelligent, articulate,

and socially responsible citizens who contribute to their family, faith and world

communities.• SLE: life-long learners who possess a solid foundation in all academic areas.

Strategy #1 Schedule monthly faculty meetings to facilitate the math articulation process for math teachers

Activities 1. Review Common Core Standards2. Review and Revise Math Maps3. Articulate and plan strategies

Cost or Resources & Sources

$0

Person(s) Responsible For Implementation

Principal and Leadership Team

Process For Monitoring Meeting Agendas and MinutesBaseline Assessment Teachers’ time spent in informal articulationOngoing Assessment 1. Meeting Minutes

2. Teacher Feedback3. Student Assessments

TimelineStart/Stop

2013-2014/On-going

Process forCommunicatingto Shareholders

• Faculty Bulletins• Agendas/Calendars


Strategy #2 Provide professional development to support articulation and collaboration

Activities 1. Prioritize Program/Curriculum Needs2. Research Development Resources3. Secure Funding

Cost or Resources & Sources

Unknown

Person(s) Responsible For Implementation

Principal/Teachers

Process For Monitoring Agendas and Meeting MinutesWorkshop/Resource Documentation

Baseline Assessment 1. Records of Previous Professional Development 2. Student Assessment3. Teacher Evaluation by Principal

Ongoing Assessment Agendas and Minutes Tracking Attendance

TimelineStart/Stop

2013-2014/Ongoing

Process forCommunicatingto Shareholders

• Faculty Bulletins• Agendas/Notes• Calendar/ Website


mathematics in depth study

Documents

new math curriculum

math computation skills

math computation subtest

math expressions program

higher level math

basic math operations

holy cross school page

faculty of holy cross