facing choices about the fourth year in arizona: achieve’s fourth-year capstone course criteria...
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Facing Choices about the Fourth Year in Arizona:
Achieve’s Fourth-Year Capstone Course Criteria
October 18, 2008Institute for Mathematics & Education
Tucson, Arizona
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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.
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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
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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.
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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.
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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.
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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:
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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.
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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
ID
AZ
UT
MT
WY
NM
CO
AL
SC
TN
KY
INOH
NC
SD
KS
NE
MN
WI
IA
IL
MO
AR
MS
OK
ND
OR
CA NV
WA
TX
PA
VA
NY
CT
WV MD
NJ
VTNH
MA
DE
RI
HI
GA
FL
ME
MI
LA
AK
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ADP Network today: thirty-four ADP Network today: thirty-four states now committed to states now committed to improving student preparationimproving student preparation
ID
AZ
UT
MT
WY
NM
CO
AL
SC
TN
KY
INOH
NC
SD
KS
NE
MN
WI
IA
IL
MO
AR
MS
OK
ND
OR
CA NV
WA
TX
PA
VA
NY
CT
WV MD
NJ
VTNH
MA
DE
RI
HI
GA
FL
ME
MI
LA
AK
Mathematics Graduation Mathematics Graduation RequirementsRequirements
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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
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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.”
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Minimum Diploma by State Minimum Diploma by State 20052005
ID
AZ
UT
MT
WY
NM
CO
AL
SC
TN
KY
INOH
NC
SD
KS
NE
MN
WI
IA
IL
MO
AR
MS
OK
ND
OR
CA NV
WA
TX
PA
VA
NY
CT
WV MD
NJ
VTNH
MA
DE
RI
HI
GA
FL
ME
MI
LA
AK
LEGENDCollege- & Career- ReadyDiploma
College- & Career- ReadyDiploma w/Opt-Out
General Diploma
DC
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Minimum Diploma by State Minimum Diploma by State 20082008
ID
AZ
UT
MT
WY
NM
CO
AL
SC
TN
KY
INOH
NC
SD
KS
NE
MN
WI
IA
IL
MO
AR
MS
OK
ND
OR
CA NV
WA
TX
PA
VA
NY
CT
WV MD
NJ
VTNH
MA
DE
RI
HI
GA
FL
ME
MI
LA
AK
LEGENDCollege- & Career- ReadyDiploma
College- & Career- ReadyDiploma w/Opt-Out
General Diploma
DC
As of October 2008
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Minimum Diploma by StateMinimum Diploma by State
Type of Diploma Number of States*
College and Career-Ready Diploma
8
College and Career-Ready Diploma with Opt-Out
13
General Diploma 26
No State Requirements 4
* “States” includes the District of Columbia
As of October 2008
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State Mathematics State Mathematics Requirements 2005Requirements 2005
ID
AZ
UT
MT
WY
NM
CO
AL
SC
TN
KY
INOH
NC
SD
KS
NE
MN
WI
IA
IL
MO
AR
MS
OK
ND
OR
CA NV
WA
TX
PA
VA
NY
CT
WV MD
NJ
VTNH
MA
DE
RI
HI
GA
FL
ME
MI
LA
AK
DC
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1030
2
Algebra I I GeometryAlgebra I Not Specified
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State Mathematics State Mathematics Requirements 2008Requirements 2008
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Algebra I I GeometryAlgebra I Not Specified
ID
AZ
UT
MT
WY
NM
CO
AL
SC
TN
KY
INOH
NC
SD
KS
NE
MN
WI
IA
IL
MO
AR
MS
OK
ND
OR
CA NV
WA
TX
PA
VA
NY
CT
WV MD
NJ
VTNH
MA
DE
RI
HI
GA
FL
ME
MI
LA
AK
DC
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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
4
* “States” includes the District of Columbia
As of October 2008
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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
* “States” includes the District of Columbia
As of October 2008
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72%
48%
41%
38%
62%
29%
34%
32%
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
Math
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.
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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
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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)
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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
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Criteria for High-Quality Criteria for High-Quality Capstone CoursesCapstone Courses
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.
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Criteria for High-Quality Criteria for High-Quality Capstone CoursesCapstone Courses
I. Students should solidify and increase mathematical knowledge and skills at and above the level of Algebra II or its equivalent.
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.
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Criteria for High-Quality Criteria for High-Quality Capstone CoursesCapstone Courses
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.
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Criteria for High-Quality Criteria for High-Quality Capstone CoursesCapstone Courses
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.
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.
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Criteria for High-Quality Criteria for High-Quality Capstone CoursesCapstone Courses
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.
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.
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Criteria for High-Quality Criteria for High-Quality Capstone CoursesCapstone Courses
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.
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.
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Criteria for High-Quality Criteria for High-Quality Capstone CoursesCapstone Courses
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.
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Criteria for High-Quality Criteria for High-Quality Capstone CoursesCapstone Courses
III. Students should develop an appreciation for and experience with a variety of applications of mathematics across disciplines and in practical situations.
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.
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Criteria for High-Quality Criteria for High-Quality Capstone CoursesCapstone Courses
III. Students should develop an appreciation for and experience with a variety of applications of mathematics across disciplines and in practical situations.
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.
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Criteria for High-Quality Criteria for High-Quality Capstone CoursesCapstone Courses
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.
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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.
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.
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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.
2
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.
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For More Information…For More Information…
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www.UTDanaCenter.orgwww.UTDanaCenter.org
Under “More P-16 Projects”
select “Mathematics Benchmarks, Grades K–12”.
Then select “Supporting
Resources”.
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www.UTDanaCenter.orgwww.UTDanaCenter.org
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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 [email protected]
More InformationMore Information
Questions???Questions???