Moving the Red Queen Forward: Modeling Intersegmental Transition in Math

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

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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 dont typically have distinct courses
• Categorizing courses between segments to track
  progression
• Technical issues when dealing with large data
  sets

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HS Ü CC è 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
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First math class attempted in community college First math class attempted in community college First math class attempted in community college First math class attempted in community college First math class attempted in community college First math class attempted in community college First math class attempted in 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
Max HS Math 2 15 50 29 0 6 0 0 0 100 34
Max HS Math 3 5 41 36 0 16 0 2 0 100 244
Max HS Math 4 2 36 29 0 24 3 6 0 100 280
Max HS Math 5 3 12 20 0 39 7 18 1 100 440
Max HS Math 6 7 2 19 0 39 15 14 5 100 59
Max HS Math 7 4 8 12 0 30 8 25 12 100 953
Max HS Math 8 0 0 0 0 0 0 0 100 100 3
  Total 84 448 481 3 602 130 351 127   2226
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    Success rate in first math class attempted in community college Success rate in first math class attempted in community college Success rate in first math class attempted in community college Success rate in first math class attempted in community college Success rate in first math class attempted in community college Success rate in first math class attempted in community college Success rate in first math class attempted in community college 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
Max HS Math 2 100 47 40         50
Max HS Math 3 77 56 46   55 67   54
Max HS Math 4 83 75 66   65 57 75 70
Max HS Math 5 80 87 83 74 66 77 77
Max HS Math 6 91   78 100 88 88
Max HS Math 7 83 78 86   82 81 81 77 81
Max HS Math 8               100
  Total 82 71 69 67 75 77 79 76 74
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Variables predicting success rates in college math from High School A R2 0.062 Effect Slope Beta
Constant   0.39  
HS to College Transition ê -0.07 -0.22
Time Lag ê -0.02 -0.05
High School Grade é 0.1 0.15

Variables predicting success rates in college math from High School B R2 0.046
Constant 0.45  
HS to College Transition ê -0.04 -0.17
Time Lag ê -0.02 -0.04
High School Grade é 0.11 0.17
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Risk 0.361
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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.

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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

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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

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Necessary New Physical Skills

• None

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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.

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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

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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.

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Problem Solving/Application

• The sum of three consecutive even integers is
  66.
• Find the three integers.

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Testing the tests

• Part 1 The pencil is sharpened

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2002-2003 Correlations with 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 r 0.17 0.17 0.08 0.10 0.13 0.16
Arithmetic Grade N 1515 931 414 1235 2484 714
Elementary Algebra Grade r 0.37 0.30 0.19 0.12 0.25 0.17
Elementary Algebra Grade N 8697 3917 2684 4271 9697 3397
Geometry Grade r 0.52 0.49 0.42 0.30 0.47 0.34
Geometry Grade N 5493 3255 3853 4815 6380 2841
Intermediate Algebra Grade r 0.53 0.48 0.35 0.34 0.37 0.29
Intermediate Algebra Grade N 4356 1303 1411 1588 4639 1169
Advanced Algebra Grade r 0.48 0.53 0.37 0.36 0.41 0.43
Advanced Algebra Grade N 4098 1453 3447 4204 4282 1401
p lt 0.01. Note Yellow shading indicates weak
correlations (r lt 0.3) while orange shading
indicates stronger correlations (r 0.3).
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2004-2005 Correlations with 2004-2005 Correlations with CST Math Score CST Lang Score CST Science Score CST Social Science Score
Beginning Algebra r 0.37 0.20 0.07 .20
Beginning Algebra N 624 621 452 533
Geometry r .57 .46 .40 .24
Geometry N 2741 2738 2190 1808
Remedial English r .17 .19 .27 0.08
Remedial English N 1247 1368 278 242
Regular English r .35 .44 .35 .38
Regular English N 9351 9941 6033 4927
p lt 0.01. Note Yellow shading indicates weak
correlations (r lt 0.3) while orange shading
indicates stronger correlations (r 0.3).
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8th Grade to High School
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1998-2000 Triple Cohort
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1998-2000 Triple Cohort
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Overall success rates declined from 65 to 64
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Next Steps
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Thank you!

• Terrence Willett
• Director of Research
• twillett_at_calpass.org
• [phone]
• www.calpass.org