facing choices about the fourth year in arizona: achieve’s fourth-year capstone course criteria...

Facing Choices about the Fourth Year in Arizona:

Achieve’s Fourth-Year Capstone Course Criteria

October 18, 2008Institute for Mathematics & Education

Tucson, Arizona

Who is Achieve, Inc.?Who is Achieve, Inc.?

Created by the nation’s governors and business leaders, Achieve, Inc., is a bipartisan non-profit organization that helps states raise academic standards, improve assessments and strengthen accountability to prepare all young people for postsecondary education and training, careers, and citizenship.

Presentation OverviewPresentation Overview

History of the American Diploma Project (ADP) Mathematics Graduation Requirements Criteria for High-Quality Capstone Courses Contact Information Questions

History of the History of the American Diploma ProjectAmerican Diploma Project

American Diploma ProjectAmerican Diploma Project

The American Diploma Project (ADP) was created to ensure all graduates leave high school ready for college and careers.

Early research by ADP sought to identify “must-have” knowledge and skills graduates will need to be successful in college and careers.

American Diploma ProjectAmerican Diploma Project

Found a convergence between the skills that high school graduates need to be successful in college and those they need to be successful in a career that supports a family and offers career advancement.

Developed ADP benchmarks that include the core content and skills in mathematics and English all students should have when they graduate high school.

Key findingsKey findings In mathematics, graduates need strong

computation skills, ability to solve challenging problems, reasoning skills, geometry, data analysis, statistics, and advanced algebra.

Essentially, they need the knowledge and skills typically taught in courses such as Algebra I, Algebra II and Geometry, as well as data analysis and statistics.

In English, graduates need strong reading, writing and oral communication skills equal to four years of grade-level coursework, as well as research and logical reasoning skills.

The ADP Benchmarks: The ADP Benchmarks: Challenging content for all Challenging content for all studentsstudents

In Mathematics: A rigorous four-year

course sequence Content* equivalent to

a sequence that includes Algebra I and II, Geometry, and Data Analysis & Statistics

*can be taught via different pathways

In English: Four courses Content equivalent to

four years of grade-level English or higher with a strong focus on oral and written communication skills and considerable research and analysis

To cover the content in the ADP benchmarks, high school graduates need:

Closing the Expectations Gap: Closing the Expectations Gap: ADP Policy AgendaADP Policy Agenda

In 2005, Achieve launched the ADP Network, a group of states committed to taking four college and career readiness action steps: Align high school standards with college and career

expectations. Require all students to take a college- and career-

ready curriculum, aligned with standards, to earn a diploma.

Build “college-ready” measures, aligned with state standards, into high school assessment systems.

Hold high schools accountable for graduating students college- and career-ready, and hold postsecondary institutions accountable for student success.

ADP Network launched at 2005 ADP Network launched at 2005 Summit: 13 states committed to Summit: 13 states committed to improving student preparationimproving student preparation

ADP Network today: thirty-four ADP Network today: thirty-four states now committed to states now committed to improving student preparationimproving student preparation

Mathematics Graduation Mathematics Graduation RequirementsRequirements

An Expectations GapAn Expectations Gap

Historically, we haven’t expected all students to graduate from high school college- and career-ready State standards reflect consensus about

what is desirable, not what is essential Few states required Algebra II or its

equivalent for graduation State tests measure 8th and 9th grade

knowledge and skills High school accountability rarely focuses

on graduation rates or on college- and work-readiness

Arizona MathematicsArizona MathematicsGraduation RequirementGraduation Requirement

The State Board of Education raised the state’s graduation requirements in 2007.

A default diploma was established. The new requirements will affect the

incoming freshman class of 2009-2010 (graduating class of 2013).

“Math courses shall consist of Algebra I, Geometry, Algebra II (or its equivalent) and an additional course with substantial math content as determined by districts or charter schools.”

Minimum Diploma by State Minimum Diploma by State 20052005

LEGENDCollege- & Career- ReadyDiploma

College- & Career- ReadyDiploma w/Opt-Out

General Diploma

Minimum Diploma by State Minimum Diploma by State 20082008

LEGENDCollege- & Career- ReadyDiploma

College- & Career- ReadyDiploma w/Opt-Out

General Diploma

As of October 2008

Minimum Diploma by StateMinimum Diploma by State

Type of Diploma Number of States*

College and Career-Ready Diploma

College and Career-Ready Diploma with Opt-Out

General Diploma 26

No State Requirements 4

* “States” includes the District of Columbia

As of October 2008

State Mathematics State Mathematics Requirements 2005Requirements 2005

Algebra I I GeometryAlgebra I Not Specified

State Mathematics State Mathematics Requirements 2008Requirements 2008

Algebra I I GeometryAlgebra I Not Specified

Mathematics Credits Required Mathematics Credits Required for Graduationfor Graduation

Number of Mathematics Units Required for

Graduation

Number of States*

4 Units 19

3 Units 22

2 Units 6

0 Units/No Statewide Requirements

As of October 2008

Highest Mathematics Courses Highest Mathematics Courses RequiredRequired

Highest Mathematics Course (or its equivalent) Required

for Graduation

Number of States*

Beyond Algebra II 2

Algebra II 19

Geometry 6

Algebra I 6

Not Specified 18

As of October 2008

College students

Students who did not go to college

The Majority of Graduates Would The Majority of Graduates Would Have Taken Harder Courses, Have Taken Harder Courses, Particularly in MathematicsParticularly in Mathematics

Knowing what you know today about the expectations of college/work …

Would have taken more challenging courses in:

Would have taken more challenging courses in at least one area

Science

English

Source: Peter D. Hart Research Associates/Public Opinion Strategies. (2005) Rising to the Challenge: Are High School Graduates Prepared for College and Work? Washington, DC: Achieve.

The Senior Year Is One Step Along The Senior Year Is One Step Along the Education Pipeline, Not an End the Education Pipeline, Not an End PointPoint

Researchers who study learning and cognition describe mathematical learning as a progression in which conceptual understanding builds logically, and expertise is developed gradually.

Students not intending to pursue math-intensive majors should be able to select from a number of fourth year “capstone” courses to maintain and extend their prior mathematical knowledge and connect mathematics instruction with other interests.

Criteria for High-Quality Criteria for High-Quality Capstone CoursesCapstone Courses

Examples of Alternative Capstone Examples of Alternative Capstone Courses (State Curricula)Courses (State Curricula)

Computer Mathematics (AR)

Data Analysis (CA)

Advanced Functions and Modeling (NC)

Discrete Mathematics (IN)

Probability and Statistics (IN)

Modeling and Quantitative Reasoning (OH)

Advanced Mathematical Decision Making (TX)

Computer Mathematics (VA)

Discrete mathematics (VA)

Probability and Statistics (VA)

Examples of Alternative Capstone Examples of Alternative Capstone Courses (National/International Courses (National/International Curricula)Curricula)

International Baccalaureate’s Mathematical Studies Standard Level

Advanced Placement Computer Science A

Advanced Placement Statistics

I. Students should solidify and increase mathematical knowledge and skills at and above the level of Algebra II or its equivalent.

a. The course description indicates that opportunities will be provided for students to reinforce and increase their fluency with arithmetic and algebraic processes.

b. The course description indicates that opportunities will be provided for continued experience with functions that include linear, quadratic, and exponential and possibly extend to some advanced functions, such as logarithmic, trigonometric, higher-degree polynomial, or piecewise-defined functions.

c. The course description offers students new insight into mathematics by including topics from non-traditional areas—such areas might include finite or discrete mathematics, statistical reasoning and inference, computer applications, analytic geometry, non-Euclidean geometry, or geometric probability.

II. Students should deepen and enrich the ways they think about mathematics to elevate its study well beyond rote memorization to a process of analysis and interpretation that enables the learner to grapple with a range of complex questions, topics, and issues.

a. The course description provides opportunities for students to think conceptually, in addition to procedurally, about mathematics.

b. The course description requires students to justify approaches to and results of problems with compelling mathematical arguments and encourages the application of solid reasoning in multiple contexts and across disciplines.

c. The course description provides students with opportunities to deepen their understanding of mathematical reasoning and supports the development of expertise in using the appropriate type of reasoning for a given situation.

d. The course description encourages experimental thinking, inquisitiveness, and evaluation of problem solving processes.

e. The course description includes situations that engage students in the use of abstraction and generalization.

f. The course description includes opportunities to see connections among the branches of mathematics.

g. The course description provides opportunities for the effective use of modern technologies, such as graphing and algebraic calculators or software, data gathering probes, or computer-assisted sampling.

III. Students should develop an appreciation for and experience with a variety of applications of mathematics across disciplines and in practical situations.

a. The course description includes a focus on solving non-routine problems that are of interest to students who do not currently plan to follow a mathematics-intensive postsecondary pathway in college or work.

b. The course description provides opportunities for students to determine the key elements of a problem, translate them into related mathematics, apply relevant mathematical strategies to solve problems, and communicate results using terminology that is understandable, correct, and appropriate for the situation.

c. The course description provides students with problems that can be solved in more than one way and with the opportunity to evaluate the effectiveness and efficiency of particular solution methods.

d. The course description encourages student persistence when solving problems, including those problems that require extended time and/or the gathering of information for their solutions.

e. The course description requires students to visually represent a situation using mathematical diagrams or representations and to apply common sense to evaluate the reasonableness of solutions for practical problems in terms of the context.

The following rating system will be used to judge the quality of a course curriculum:

0 = There is no basis in the course description for evaluation of this criterion.

1 = Criterion is not suggested overtly but is implied in the course description. OR = Criterion is partially suggested in the course description.

2 = Criterion is clearly or strongly suggested by the course description.

In a few cases there may be a need for a higher rating:

3 = Course description requirements satisfy and go beyond the scope of this criterion reference.

Capstone Course RubricCapstone Course Rubric Criteria for High-Quality Capstone Courses Sample

Capstone #1 Course Title Course Title Course Title Course Title

Rating system:

0 = There is no basis in the course description for evaluation of this criterion.1 = Criterion is not suggested overtly but is implied in the course description OR Criterion is partially suggested by the course description

2 = Criterion is clearly or strongly suggested by the course descriptionIn a few cases there may be a need for a higher rating:

3 = Course description requirements satisfy and go beyond the scope of this criterion reference

Directions to an evaluator: Enter the title of the course to be evaluated at the top of the column and the rating for each criterion in the white cells of the column below the title. An average score will be computed automatically in the last cell of each column. An adequate capstone course would rate somewhere around an average score of 1.5 and would ideally approach an average of 2. A course description may rate lower than average for many reasons. Some course descriptions do not provide enough detail to make an evaluation in some areas, and some intentionally have a narrower focus than others. A lower score should not be construed as an indicator of a sub-standard course. Analysis of the scores of individual criterion is needed to make a judgment regarding a course's strengths and weaknesses. It is not the intent of this tool to make a judgment regarding the overall worth of any course but rather to simply provide a system for evaluating and comparing capstone courses relative to these criteria.

A. The course description indicates that opportunities will be provided for students to reinforce and increase their fluency with arithmetic and algebraic processes.

B. The course description indicates that opportunities will be provided for continued experience with functions that include linear, quadratic, and exponential and possibly extend to some advanced functions, such as logarithmic, trigonometric, higher-degree polynomial, or piecewise-defined functions.

C. . The course description offers students new insight into mathematics by including topics from non-traditional areas–such areas might include finite or discrete mathematics, statistical reasoning and inference, computer applications, analytic geometry, non-Euclidean geometry, or geometric probability.

For More Information…For More Information…

www.UTDanaCenter.orgwww.UTDanaCenter.org

Under “More P-16 Projects”

select “Mathematics Benchmarks, Grades K–12”.

Then select “Supporting

Resources”.

www.UTDanaCenter.orgwww.UTDanaCenter.org

For more information on Achieve,please visit Achieve, Inc., on the Web at

http://www.achieve.org

For more information on Fourth Year Capstone Courses,

please visit The Charles A. Dana Center on the Web at

www.UTDanaCenter.org

Contact Achieve: Tracy Halkathalka@achieve.org

More InformationMore Information

Questions???Questions???

facing choices about the fourth year in arizona: achieve’s fourth-year capstone course criteria...

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