Moving the Red Queen Forward: Modeling Intersegmental Transition in Math

Terrence WillettDirector of Research

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

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

HS CC A B F H N P W O/X

Total HS % N

A 78% 1% 3% 1% 0% 2% 7% 7% 3% 730

B 0% 87% 1% 2% 0% 0% 2% 6% 6% 1291

F 3% 0% 87% 2% 0% 1% 2% 3% 6% 1262

H 0% 0% 1% 93% 0% 0% 2% 3% 34% 7439

N 3% 2% 4% 9% 38% 1% 35% 9% 1% 164

P 15% 2% 9% 2% 0% 56% 8% 7% 0% 98

W 1% 1% 1% 5% 1% 1% 83% 8% 46% 9907

O/X 4% 13% 2% 52% 0% 3% 18% 9% 4% 859

Total CC % 4% 6% 6% 36% 1% 1% 40% 6%    

N 809 1340 1301 7931 147 187 8773 1262   21750

83% with same ethnicity in high school and community college

First math class attempted in community college Total  

    1 2 3 4 5 6 7 8 % N

Max HS Math

1 3% 46% 38% 0% 9% 2% 2% 0% 100% 213

2 15% 50% 29% 0% 6% 0% 0% 0% 100% 34

3 5% 41% 36% 0% 16% 0% 2% 0% 100% 244

4 2% 36% 29% 0% 24% 3% 6% 0% 100% 280

5 3% 12% 20% 0% 39% 7% 18% 1% 100% 440

6 7% 2% 19% 0% 39% 15% 14% 5% 100% 59

7 4% 8% 12% 0% 30% 8% 25% 12% 100% 953

8 0% 0% 0% 0% 0% 0% 0% 100% 100% 3

  Total 84 448 481 3 602 130 351 127   2226

    Success rate in first math class attempted in community college  

    1 2 3 4 5 6 7 8 Total

Max HS Math

1 67% 71% 60% * 63% * *   65%

2 100% 47% 40%   *       50%

3 77% 56% 46%   55% * 67%   54%

4 83% 75% 66%   65% 57% 75% * 70%

5 80% 87% 83% * 74% 66% 77% * 77%

6 * * 91%   78% 100% 88% * 88%

7 83% 78% 86%   82% 81% 81% 77% 81%

8               * 100%

  Total 82% 71% 69% 67% 75% 77% 79% 76% 74%

0% 20% 40% 60% 80% 100%

Percent earning grade in first college math class

C

B

A

Gra

de

in la

st h

igh

sch

oo

l mat

hF D C B A

0%

10%

20%

30%

40%

50%

60%

70%

11thgrade

Female

12thgrade

Female

11thgradeMale

12thgradeMale

Grade in which last high school math class was passed by gender in relation to math progession in first college math class

At least one levellower

Repeat same level

At least one levelhigher

Variables predicting success rates in college math from High School AR2 = 0.062 Effect Slope Beta

Constant   0.39  

HS to College Transition -0.07 -0.22

Time Lag -0.02 -0.05

High School Grade 0.1 0.15

Variables predicting success rates in college math from High School BR2 = 0.046

Constant 0.45  

HS to College Transition -0.04 -0.17

Time Lag -0.02 -0.04

High School Grade 0.11 0.17

Risk = 0.361

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.

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

New knowledgeStudents will need to learn:how to apply arithmetic properties of the real number system when

simplifying algebraic expressionshow to use the properties to justify each step in the simplification

processto apply arithmetic properties of the real number system when solving

algebraic equations how to use the properties to justify each step in the solution processhow to identify when a property of a subset of the real numbers has

been appliedhow to identify whether or not a property of a subset of the real

number system has been properly appliedthe property of closure

Necessary New Physical Skills

None

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.

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 SkillsState 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 numbersThe set of irrational numbersThe set of rational numbersThe set of positive integers

4( 2) 4 2x x

3( 2) ( 5) 22x x

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.

2x x x

Problem Solving/Application

The sum of three consecutive even integers is –66.

Find the three integers.

Testing the tests

Part 1: The pencil is sharpened

**p < 0.01. Note: Yellow shading indicates weak correlations (r < 0.3) while orange shading indicates stronger correlations (r ≥ 0.3).

2002-2003Correlations with:

CST Math Score

CAHSEE Math Score

CST Science Score

CST Social

Science Score

CST Lang Score

CAHSEE English Score

Arithmetic Grade

r 0.17** 0.17** 0.08 0.10** 0.13** 0.16**

N 1515 931 414 1235 2484 714

Elementary Algebra Grade

r 0.37** 0.30** 0.19** 0.12** 0.25** 0.17**

N 8697 3917 2684 4271 9697 3397

Geometry Grade

r 0.52** 0.49** 0.42** 0.30** 0.47** 0.34**

N 5493 3255 3853 4815 6380 2841

Intermediate Algebra Grade

r 0.53** 0.48** 0.35** 0.34** 0.37** 0.29**

N 4356 1303 1411 1588 4639 1169

Advanced Algebra Grade

r 0.48** 0.53** 0.37** 0.36** 0.41** 0.43**

N 4098 1453 3447 4204 4282 1401

2004-2005Correlations with: CST

Math Score

CST Lang Score

CST Science Score

CST Social

Science Score

Beginning Algebra

r 0.37** 0.20** 0.07 .20**

N 624 621 452 533

Geometry r .57** .46** .40** .24**

N 2741 2738 2190 1808

Remedial English

r .17** .19** .27** 0.08

N 1247 1368 278 242

Regular English

r .35** .44** .35** .38**

N 9351 9941 6033 4927

**p < 0.01. Note: Yellow shading indicates weak correlations (r < 0.3) while orange shading indicates stronger correlations (r ≥ 0.3).

0.00 1.00 2.00 3.00 4.00

Intermediate Algebra Math Grade

200

300

400

500

600

CST Math Score = 275.16 + 21.91 * grmathR-Square = 0.28

0 1 2 3 4

Regular English Grade

200

300

400

500

600

CST Language Score = 289.10 + 17.80 * grenglR-Square = 0.15

8th Grade to High School

0%

20%

40%

60%

80%

100%

Highest High School Math

Passed

Fail (N=676) Succeed (N=2,227)

8th Grade Math Outcome

Calculus

Advanced Algebra

Statistics/Other

Intermediate Algebra

Geometry

Beginning Algebra

Pre-Algebra

Basic Math

1998-2000 Triple Cohort

56%

45%

31% 30%

24%

0%

10%

20%

30%

40%

50%

60%

Asian/PacificIslander

White Hispanic African-American

NativeAmerican

% Meeting UC/CSU Math requirements

1998-2000 Triple Cohort

Overall success rates declined from 65% to 64%

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1998-2002 (N=13,593) 2002-2004 (N=6,034)

Shift in 9th grade math enrollments before and after "Algebra for All" initiative

Advanced Algebra

Intermediate Algebra

Geometry

Beginning Algebra

Pre-Algebra

Basic Math

Next Steps

Thank you!

Terrence Willett

Director of Research

twillett@calpass.org

(831) 277-2690

www.calpass.org