1. Moving the Red Queen Forward: Modeling Intersegmental Transition in Math Terrence Willett Director of Research

4. What Kinds of Data are Collected? Student identifier (encrypted) Student file  Demographic information  Attendance Course file  Enrollment information  Course performance Student test file  STAR  HS exit exam Award file  Diplomas, degrees, certificates Optional files  Information collected on interventions Data is anonymous – personal identifier information is removed or encrypted

5. Data Issues  Data sharing is local, not necessarily statewide  Intersegmental matching  Students moving out of consortium area  Students not fitting “typical” model of progression  repeating grade levels  Concurrent enrollments  No K12 summer school  K12 Students with multiple instances of same course in same year  K-6 don’t typically have distinct courses  Categorizing courses between segments to track progression  Technical issues when dealing with large data sets

6. HS  CC  ABFHNPWO/X Total HS %N A78%1%3%1%0%2%7% 3%730 B0%87%1%2%0% 2%6% 1291 F3%0%87%2%0%1%2%3%6%1262 H0% 1%93%0% 2%3%34%7439 N3%2%4%9%38%1%35%9%1%164 P15%2%9%2%0%56%8%7%0%98 W1% 5%1% 83%8%46%9907 O/X4%13%2%52%0%3%18%9%4%859 Total CC % 4%6% 36%1% 40%6% N80913401301793114718787731262 21750 83% with same ethnicity in high school and community college

7. First math class attempted in community collegeTotal 12345678%N Max HS Math 13%46%38%0%9%2% 0% 100% 213 215%50%29%0%6%0% 100% 34 35%41%36%0%16%0%2%0% 100% 244 42%36%29%0%24%3%6%0% 100% 280 53%12%20%0%39%7%18%1% 100% 440 67%2%19%0%39%15%14%5% 100% 59 74%8%12%0%30%8%25%12% 100% 953 80% 100% 3 Total844484813602130351127 2226

8. Success rate in first math class attempted in community college 12345678Total Max HS Math 167%71%60%*63%** 65% 2100%47%40% * 50% 377%56%46% 55%*67% 54% 483%75%66% 65%57%75%*70% 580%87%83%*74%66%77%* 6**91% 78%100%88%* 783%78%86% 82%81% 77%81% 8 *100% Total82%71%69%67%75%77%79%76%74%

11. Variables predicting success rates in college math from High School A R 2 = 0.062 EffectSlopeBeta Constant 0.39 HS to College Transition  -0.07-0.22 Time Lag  -0.02-0.05 High School Grade  0.10.15 Variables predicting success rates in college math from High School B R 2 = 0.046 Constant0.45 HS to College Transition  -0.04-0.17 Time Lag  -0.02-0.04 High School Grade  0.110.17

13. Risk = 0.361

15. Standard Set 1.0 1.0. Students identify and use the arithmetic properties of subsets and integers and rational, irrational, and real numbers, including closure properties for the four basic arithmetic operations where applicable: 1.1 Students use properties of numbers to demonstrate whether assertions are true or false. Deconstructed standard Students identify arithmetic properties of subsets of the real number system including closure for the four basic operations. Students use arithmetic properties of subsets of the real number system including closure for the four basic operations. Students use properties of numbers to demonstrate whether assertions are true or false.

16. Prior knowledge necessary Students should: know the subsets of the real numbers system know how to use the commutative property know how to use the associative property know how to use the distributive property have been introduced to the concept of the addition property of equality have been introduced to the concept of the multiplication property of equality have been introduced to the concept of the additive inverses have been introduced to the concept of the multiplicative inverses

17. New knowledge Students will need to learn: how to apply arithmetic properties of the real number system when simplifying algebraic expressions how to use the properties to justify each step in the simplification process to apply arithmetic properties of the real number system when solving algebraic equations how to use the properties to justify each step in the solution process how to identify when a property of a subset of the real numbers has been applied how to identify whether or not a property of a subset of the real number system has been properly applied the property of closure

18. Necessary New Physical Skills None

19. Products Students Will Create Students will provide examples and counter examples to support or disprove assertion about arithmetic properties of subsets of the real number system. Students will use arithmetic properties of subsets of the real number system to justify simplification of algebraic expressions. Students will use arithmetic properties of subsets of the real number system to justify steps in solving algebraic equations.

20. Standard #1 Model Assessment Items (Much of this standard is embedded in problems that are parts of other standards. Some of the examples below are problems that are from other standards that also include components of this standard.) Computational and Procedural Skills State the error made in the following distribution. Then complete the distribution correctly. Solve the equation state the properties you used in each step. Problem from Los Angeles County Office of Education: Mathematics (National Center to Improve Tools of Education) Which of the following sets of numbers are not closed under addition? The set of real numbers The set of irrational numbers The set of rational numbers The set of positive integers

21. Conceptual Understanding Problem from Mathematics Framework for California Public Schools Prove or give a counter example: The average of two rational numbers is a rational number. Prove of give a counter example to: for all real numbers x.

22. Problem Solving/Application The sum of three consecutive even integers is –66. Find the three integers.

23. Testing the tests Part 1: The pencil is sharpened

24. **p < 0.01. Note: Yellow shading indicates weak correlations (r < 0.3) while orange shading indicates stronger correlations (r ≥ 0.3). 2002-2003 Correlations with: CST Math Score CAHSEE Math Score CST Science Score CST Social Science Score CST Lang Score CAHSEE English Score Arithmetic Grade r0.17** 0.080.10**0.13**0.16** N151593141412352484714 Elementary Algebra Grade r0.37**0.30**0.19**0.12**0.25**0.17** N869739172684427196973397 Geometry Grade r0.52**0.49**0.42**0.30**0.47**0.34** N549332553853481563802841 Intermediat e Algebra Grade r0.53**0.48**0.35**0.34**0.37**0.29** N435613031411158846391169 Advanced Algebra Grade r0.48**0.53**0.37**0.36**0.41**0.43** N409814533447420442821401

25. 2004-2005 Correlations with: CST Math Score CST Lang Score CST Science Score CST Social Science Score Beginning Algebra r0.37**0.20**0.07.20** N624621452533 Geometry r.57**.46**.40**.24** N2741273821901808 Remedial English r.17**.19**.27**0.08 N12471368278242 Regular English r.35**.44**.35**.38** N9351994160334927 **p < 0.01. Note: Yellow shading indicates weak correlations (r < 0.3) while orange shading indicates stronger correlations (r ≥ 0.3).

28. 8 th Grade to High School

29. 1998-2000 Triple Cohort

31. Overall success rates declined from 65% to 64%

32. Next Steps

33. Thank you! Terrence Willett Director of Research twillett@calpass.org (831) 277-2690 www.calpass.org