Transcript Algebra Achievement Predictors

Algebra Achievement Predictors:
A Comparison of English Leaners to
General Population
92nd Annual CERA Conference
Jane Liang, Ed.D.
Education Research and Evaluation Consultant
California Department of Education
Anaheim, CA, December 6, 2013
CALIFORNIA DEPARTMENT OF EDUCATION
Tom Torlakson, State Superintendent of Public Instruction
Overview
TOM TORLAKSON
State Superintendent
of Public Instruction
• Mathematical practices standards in Common
Core State Standards for Mathematics (CCSSM)
• Guiding principles for mathematics programs in
California
• Language demand in thinking and doing
mathematics
• The study of algebra achievement predictors
• Algebra achievement predictors for English
learners
• Recommendations
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Mathematical Practices
Standards1 in CCSSM
TOM TORLAKSON
State Superintendent
of Public Instruction
1.
2.
3.
4.
5.
6.
7.
8.
Make sense of problems and persevere in solving
them
Reason abstractly and quantitatively
Construct viable arguments and critique the
reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated
reasoning
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Mathematical Practices
Standards in CCSSM (Cont.)
TOM TORLAKSON
State Superintendent
of Public Instruction
• Focus on students’ mathematical
reasoning and sense making
• Require mathematical communication
• Involve language and discourse
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Guiding Principles for Mathematics
Programs in California2
TOM TORLAKSON
State Superintendent
of Public Instruction
Guiding Principle 1: Learning
Mathematical ideas should be explored in ways that
stimulate curiosity, create enjoyment of mathematics,
and develop depth of understanding.
• Calls for the balance of mathematics procedures
and conceptual understanding
• Suggests students to be engaged in
– Doing meaningful mathematics
– Discussing mathematical ideas
– Applying mathematics in interesting and thoughtprovoking situations
5
Language Demand in Thinking
and Doing Mathematics
TOM TORLAKSON
State Superintendent
of Public Instruction
The shift from carrying out
procedures to communicating
reasoning makes school
mathematics not a universal
language that students manipulate
with numbers and symbols, but a
language that students express their
thinking.
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The Study of Algebra
Achievement Predictors3
TOM TORLAKSON
State Superintendent
of Public Instruction
• Data:
– Standardized Testing and Reporting
(STAR) student data files, 2006 &
2007, matched files with SSIDs
• Area of interest
– California Standards Test (CST) for
Grade 7 math in 2006, subscores of
reporting clusters
– CST for Algebra I in 2007, 8th graders
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The Study of Algebra
Achievement Predictors (Cont.)
TOM TORLAKSON
State Superintendent
of Public Instruction
Descriptive statistics
Reporting Clusters (CST for Grade 7)
N
Rational numbers
Exponents, powers, and roots
Quantitative relationships and
evaluating expressions
Multistep problems, graphing,
and functions
208043
208043
8.99
5.27
3.123
2.04
14
8
208043
6.49
2.22
10
208043
208043
10.59
7.96
3.03
3.01
15
13
208043
3.46
1.39
5
209364
34.91
11.93
65
Measurement and geometry
Statistics, data analysis, and
probability
CST for Algebra I raw score
Mean
Std Dev Max
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The Study of Algebra
Achievement Predictors (Cont.)
TOM TORLAKSON
State Superintendent
of Public Instruction
• Research questions
– Which reporting cluster is a strong
predictor of 8th grade CST for
Algebra I scores?
• Analysis
– Stepwise regression analysis using
7th grade math CST subscores to
predict 8th grade CST for Algebra I
scores
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The Study of Algebra
Achievement Predictors (Cont.)
TOM TORLAKSON
State Superintendent
of Public Instruction
Model
Yj=β0 + β1x1j + β2x2j + , … , + βix6j + εj
j (number of records) = 1, 2, … 208,043
X1 = Rational numbers
X2 = Exponents, powers, and roots
X3 = Quantitative relationships and evaluating
expressions
X4 = Multistep problems, graphing, and function
X5 = Measurement and geometry
X6 = Statistics and analysis, data analysis, and
probability
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The Study of Algebra
Achievement Predictors3 (Cont.)
TOM TORLAKSON
State Superintendent
of Public Instruction
Step
Independent Variable
R2
B
Beta
t
p
1
Rational numbers
.476
.858
.225
104.34 <.0001
2
Quantitative relationships and .551
evaluating expressions
.958
.179
92.48
<.0001
3
Measurement and geometry
.590
.730
.184
87.22
<.0001
4
Exponents, powers, and roots .609
.963
.165
86.53
<.0001
5
Multistep problems, graphing, .617
and functions
.502
.128
58.57
<.0001
6
Statistics, data analysis, and
probability
.640
.075
42.69
<.0001
.620
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The Study of Algebra
Achievement Predictors (Cont.)
TOM TORLAKSON
State Superintendent
of Public Instruction
Findings:
• Reporting cluster rational numbers is the strongest
predictor of algebra scores (R2=.476, β=.225, t(208,042) =
104.34, p < .0001)
– Accounts for 48% of variance;
– A one-unit standard deviation (SD) increase results in .225
(SD) units’ increase of the CST for Algebra.
• Reporting cluster quantitative relationships and
evaluating expressions is the second strongest predictor
of algebra scores (R2=.075, β=.179, t(208,042) = 92.48, p
< .0001)
– Accounts for 8% of variance;
– A one-unit standard deviation (SD) increase results in .179
(SD) units’ increase of the CST for Algebra.
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Current Study: Investigation
of English Learners (EL)
TOM TORLAKSON
State Superintendent
of Public Instruction
Sample: n = 24,463
Step
Independent Variable
2
R
B
Beta
t
p
1 Multistep problems, graphing, 0.3262 0.44526 0.14863 22.15<.0001
and functions
2 Exponents, powers, and roots
0.4173 0.96674 0.20882 34.75<.0001
3 Rational numbers
0.4527 0.59043 0.17418 27.35<.0001
4 Quantitative relationships and 0.4706 0.64745 0.14674 24.37<.0001
evaluating expressions
5 Measurement and geometry
0.4835 0.49124 0.13332 21.85<.0001
6 Statistics, data analysis, and
probability
0.489 0.60483 0.08996 16.19<.0001
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Current Study: Investigation
of English Learners (Cont.)
TOM TORLAKSON
State Superintendent
of Public Instruction
Findings for EL students:
• Reporting cluster multistep problems, graphing, and
functions is the strongest predictor of algebra scores
(R2=.326, β=.149, t(24,462) = 22.15, p < .0001)
– Accounts for 33% of variance;
– A one-unit standard deviation (SD) increase results in .15
(SD) units’ increase of the CST for Algebra.
• Reporting cluster exponents, powers, and roots is the
second strongest predictor of algebra scores (R2=.091,
β=.209, t(24,462) = 34.75, p < .0001)
– Accounts for 9% of variance;
– A one-unit standard deviation (SD) increase results in .21
(SD) units’ increase of the CST for Algebra.
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Validation of the
Difference of EL Findings
TOM TORLAKSON
State Superintendent
of Public Instruction
Random sampling none EL, N = 24,463
Step
Independent Variable
1 Rational numbers
2 Quantitative relationships and
evaluating expressions
2
R
B
Beta
0.4728 0.8454 0.2219
t
p
35.5<.0001
0.548 0.9359 0.1742 31.04<.0001
3 Measurement and geometry
0.5876 0.7402 0.1861 30.14<.0001
4 Exponents, powers, and roots
0.6076 0.9964 0.1696 30.62<.0001
5 Multistep problems, graphing,
and functions
0.6162 0.5231 0.1325 20.97<.0001
6 Statistics data analysis, and
probability
0.619 0.5965 0.0694 13.58<.0001
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Validation of the Difference
of EL Findings (Cont.)
TOM TORLAKSON
State Superintendent
of Public Instruction
Comparing two samples (N=208,043 &
n=24,463):
•Reporting cluster rational numbers is the
strongest predictor of algebra scores
– (R2=.476, β=.225, t(208,042) = 104.34, p < .0001)
– (R2=.473, β=.222, t(24,462) = 35.5, p < .0001)
•Reporting cluster quantitative relationships and
evaluating expressions is the second strongest
predictor of algebra scores
– (R2=.075, β=.179, t(208,042) = 92.48, p < .0001)
– (R2=.075, β=.174, t(24,462) = 31.04, p < .0001)
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What Do the Data Reveal?
TOM TORLAKSON
State Superintendent
of Public Instruction
• There are different predictors of 8th
grade algebra achievement
between general population and
EL students
• Rational numbers (general
population) vs. multistep
problems, graphing, and
functions (EL)
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EL Predictors
TOM TORLAKSON
State Superintendent
of Public Instruction
• Multi-step problems, graphing,
and functions
• 15 items4, 5 for graphing (7AF3.0),
10 for solving linear equations
(7AF4.0)
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An Example5 of Test
Questions
TOM TORLAKSON
State Superintendent
of Public Instruction
Mr. Ogata drove 276 miles from his house to Los
Angeles at an average speed of 62 miles per
hour. His trip home took 6.5 hours. How did his
speed on the way home compare to his speed on
the way to Los Angeles?
A It was about 2 miles per hour faster.
B It was about 2 miles per hour slower.
C It was about 20 miles per hour faster.
D It was about 20 miles per hour slower.
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An Example5 of Test
Questions (Cont.)
TOM TORLAKSON
State Superintendent
of Public Instruction
Standard tested: CA – 7AF4.2
Grade 7
Algebra and functions
4.0
Students solve simple linear equations
and inequalities over the rational numbers:
4.2
Solve multistep problems involving
rate, average speed, distance, and
time or a direct variation.
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CCSSM Standard
TOM TORLAKSON
State Superintendent
of Public Instruction
7.EE.B.3 (grade 7, expressions and equations)
B. Solve real-life and mathematical problems using
numerical and algebraic expressions and equations.
3. Solve multi-step real-life and mathematical problems posed with
positive and negative rational numbers in any form (whole
numbers, fractions, and decimals), using tools strategically. Apply
properties of operations to calculate with numbers in any form;
convert between forms as appropriate; and assess the
reasonableness of answers using mental computation and
estimation strategies. For example: If a woman making $25 an hour
gets a 10% raise, she will make an additional 1/10 of her salary an
hour, or $2.50, for a new salary of $27.50. If you want to place a
towel bar 9 3/4 inches long in the center of a door that is 27 1/2
inches wide, you will need to place the bar about 9 inches from
each edge; this estimate can be used as a check on the exact
computation.
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Smarter Balanced Sample
Question
TOM TORLAKSON
State Superintendent
of Public Instruction
Claire is filling bags with sand. All the
bags are the same size. Each bag must
weigh less than 50 pounds. One sand bag
weighs 58 pounds, another sand bag
weighs 41 pounds, and another sand bag
weighs 53 pounds. Explain whether Claire
can pour sand between sand bags so that
the weight of each bag is less than 50
pounds.
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Recommendations6
TOM TORLAKSON
State Superintendent
of Public Instruction
• Focus on students’ mathematical
reasoning, not accuracy in using
language
– Uncover, hear, and support students’
mathematics reasoning
– Promote and privilege meaning of all
types of languages
– Move toward accuracy later
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Recommendations (Cont.)
TOM TORLAKSON
State Superintendent
of Public Instruction
• Shift to a focus on mathematical
discourse practices, move away
from simplified views of language
– Words, phrases, vocabulary, or a list
of definition will not be enough.
– Students participate in explaining,
conjecturing, justifying, etc.
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Recommendations (Cont.)
TOM TORLAKSON
State Superintendent
of Public Instruction
• Recognize and support students to engage
with the complexity of language in math
classrooms
– Multiple modes: oral, written, receptive, expressive,
etc.
– Multiple representations: objects, pictures, words,
symbols, tables, graphs, etc.
– Different types of written texts: textbooks, word
problems, student explanations, teacher
explanations, etc.
– Different types of talk: exploratory and expository
– Different audiences: presentations to the teacher, to
peers, by the teacher, by peers, etc.
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Recommendations (Cont.)
TOM TORLAKSON
State Superintendent
of Public Instruction
• Treat everyday language and
experiences as resources, not as
obstacles
– Support students in connecting
everyday and academic language
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Recommendations (Cont.)
TOM TORLAKSON
State Superintendent
of Public Instruction
• Uncover the mathematics in what
students say and do
– Support teachers in learning to
recognize the emerging
mathematical reasoning that learners
are constructing in, through, and with
emerging language
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Endnotes
1.
TOM TORLAKSON
State Superintendent
of Public Instruction
2.
3.
4.
National Governors Association Center for Best Practices
and Council of Chief State School Officers (2010). Common
core state standards for mathematics. Washington, DC:
Author. Retrieved October 22, 2013, from
http://www.corestandards.org/Math
California Department of Education, (2013). Draft
mathematics framework for California public schools.
Sacramento, CA: Author. Retrieved October 22, 2013, from
http://www.cde.ca.gov/ci/ma/cf/draft2mathfwchapters.asp
Liang, J.-H., Heckman, P.E., Abedi, J. (in review). Prior
year’s predictors of eighth-grade algebra achievement.
Journal for Research in Mathematics Education
California Department of Education, (2002). California
Standards Test blueprints. Sacramento, CA: Author.
Retrieved October 24, 2013, from
http://www.cde.ca.gov/ta/tg/sr/blueprints.asp
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Endnotes (Cont.)
TOM TORLAKSON
State Superintendent
of Public Instruction
California Department of Education, (2009). California
Standards Tests released test questions. Sacramento, CA:
Author. Retrieved October 24, 2013, from
http://www.cde.ca.gov/ta/tg/sr/documents/cstrtqmath7.pdf
6. Moschkovich, J. (2013). Mathematics, the Common Core,
and language: Recommendations for mathematics instruction
for ELs aligned with the Common Core. Understanding
Language Conference, Stanford, CA, January 13-14.
5.
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Questions and Answers
TOM TORLAKSON
State Superintendent
of Public Instruction
???
Jane Liang, Ed.D.
Assessment Development and Administration
Division
California Department of Education
[email protected]
916-322-1854
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