Moving the Red Queen Forward-Modeling
Download
Report
Transcript Moving the Red Queen Forward-Modeling
Moving the Red Queen Forward:
Modeling Intersegmental Transition in Math
Terrence Willett
Director 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
A
B
F
H
N
P
W
O/X
Total
HS
%
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%
Total CC %
4%
6%
6%
36%
1%
1%
40%
6%
N
809
1340 1301 7931
147
187
8773 1262
HS CC
N
859
21750
83% with same ethnicity in high school and community college
First math class attempted in community college
Max
HS
Math
Total
1
2
3
4
5
6
7
8
%
N
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
Max
HS
Math
1
2
3
4
5
6
7
1
67%
71%
60%
*
63%
*
*
2
100%
47%
40%
*
3
77%
56%
46%
55%
*
67%
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%
*
100%
76%
74%
*
82%
71%
69%
67%
75%
Total
65%
50%
8
Total
8
77%
79%
54%
Grade in last high school math
F
D
C
B
A
A
B
C
0%
20%
40%
60%
80%
Percent earning grade in first college math class
100%
Grade in which last high school math class was passed by gender
in relation to math progession in first college math class
70%
60%
50%
At least one level
lower
Repeat same level
40%
30%
20%
At least one level
higher
10%
0%
11th
grade
Female
12th
grade
Female
11th
grade
Male
12th
grade
Male
Variables predicting success rates in
college math from High School A
R2 = 0.062
Effect
Constant
Slope
Beta
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 B
R2 = 0.046
0.45
Constant
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 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
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 Skills
State the error made in the following distribution. Then complete the
distribution correctly. 4( x 2) 4 x 2
Solve the equation state the properties you used in each step.
3( x 2) ( x 5) 22
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
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.
2
Prove of give a counter example to:
xx x
for all real numbers 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
2002-2003
Correlations
with:
CST
Social
Science
Score
CST
Lang
Score
CAHSEE
CST
Math
Score
CAHSEE
Math
Score
CST
Science
Score
r
0.17**
0.17**
0.08
0.10**
0.13**
0.16**
N
1515
931
414
1235
2484
714
Elementary r
Algebra
Grade
N
0.37**
0.30**
0.19**
0.12**
0.25**
0.17**
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
Intermediat r
e Algebra
Grade
N
0.53**
0.48**
0.35**
0.34**
0.37**
0.29**
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
Arithmetic
Grade
English
Score
**p < 0.01. Note: Yellow shading indicates weak correlations (r < 0.3) while
orange shading indicates stronger correlations (r ≥ 0.3).
2004-2005
Correlations with:
Beginning
Algebra
Geometry
Remedial
English
Regular
English
CST
CST
Social
Science Science
Score
Score
CST
Math
Score
CST
Lang
Score
r
0.37**
0.20**
0.07
.20**
N
624
621
452
533
r
.57**
.46**
.40**
.24**
N
2741
2738
2190
1808
r
.17**
.19**
.27**
0.08
N
1247
1368
278
242
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).
600
500
C S T M ath S c ore
400
300
200
CST Ma th S c ore = 2 7 5.1 6 + 2 1.9 1 * grma th
R-S qua re = 0 .28
0.00
1.00
2.00
3.00
Intermediate Algebra Math Grade
4.00
600
CST Langua ge S c ore = 2 89 .1 0 + 17 .8 0 * gre ngl
R-S qua re = 0 .15
C S T La ngu ag e S co re
500
400
300
200
0
1
2
Regular English Grade
3
4
8th Grade to High School
100%
80%
Calculus
Advanced Algebra
Highest High
School Math
Passed
60%
Statistics/Other
Intermediate Algebra
40%
Geometry
Beginning Algebra
20%
Pre-Algebra
Basic Math
0%
Fail (N=676)
Succeed (N=2,227)
8th Grade Math Outcom e
1998-2000 Triple Cohort
% M eeting UC/CSU M ath requirements
60%
56%
45%
50%
40%
31%
30%
24%
30%
20%
10%
0%
Asian/Pacific
Islander
White
Hispanic
AfricanAmerican
1998-2000 Triple Cohort
Native
American
Shift in 9th grade math enrollments before and
after "Algebra for All" initiative
100%
90%
80%
Advanced Algebra
70%
Intermediate Algebra
60%
Geometry
50%
Beginning Algebra
40%
Pre-Algebra
30%
Basic Math
20%
10%
0%
1998-2002 (N=13,593)
2002-2004 (N=6,034)
Overall success rates declined from 65% to 64%
Next Steps
Thank you!
Terrence Willett
Director of Research
[email protected]
(831) 277-2690
www.calpass.org