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Algebra Achievement Predictors: A Comparison of English Leaners to General Population

This study compares algebra achievement predictors between English learners and the general population, analyzing data from standardized tests in California. It delves into mathematical practices, guiding principles for math programs, and the language demand in mathematics, offering recommendations based on the findings.

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Algebra Achievement Predictors: A Comparison of English Leaners to General Population

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  1. Algebra Achievement Predictors: A Comparison of English Leaners to General Population 92nd Annual CERA ConferenceJane Liang, Ed.D.Education Research and Evaluation Consultant California Department of EducationAnaheim, CA, December 6, 2013

  2. Overview • 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

  3. Mathematical Practices Standards1 in CCSSM • 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

  4. Mathematical Practices Standards in CCSSM (Cont.) • Focus on students’ mathematical reasoning and sense making • Require mathematical communication • Involve language and discourse

  5. Guiding Principles for Mathematics Programs in California2 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 thought-provoking situations

  6. Language Demand in Thinking and Doing Mathematics 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.

  7. The Study of Algebra Achievement Predictors3 • 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

  8. The Study of Algebra Achievement Predictors (Cont.) Descriptive statistics

  9. The Study of Algebra Achievement Predictors(Cont.) • 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

  10. The Study of Algebra Achievement Predictors(Cont.) 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

  11. The Study of Algebra Achievement Predictors3 (Cont.)

  12. The Study of Algebra Achievement Predictors(Cont.) 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.

  13. Current Study: Investigation of English Learners (EL) Sample: n = 24,463

  14. Current Study: Investigation of English Learners (Cont.) 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.

  15. Validation of the Difference of EL Findings Random sampling none EL, N = 24,463

  16. Validation of the Difference of EL Findings (Cont.) 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)

  17. What Do the Data Reveal? • 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)

  18. EL Predictors • Multi-step problems, graphing, and functions • 15 items4, 5 for graphing (7AF3.0), 10 for solving linear equations (7AF4.0)

  19. An Example5 of Test Questions 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.

  20. An Example5 of Test Questions (Cont.) 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.

  21. CCSSM Standard 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.

  22. Smarter Balanced Sample Question 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.

  23. Recommendations6 • 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

  24. Recommendations(Cont.) • 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.

  25. Recommendations(Cont.) • 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.

  26. Recommendations(Cont.) • Treat everyday language and experiences as resources, not as obstacles • Support students in connecting everyday and academic language

  27. Recommendations(Cont.) • 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

  28. Endnotes • 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

  29. Endnotes (Cont.) • 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 • 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.

  30. Questions and Answers ??? Jane Liang, Ed.D. Assessment Development and Administration Division California Department of Education JLiang@cde.ca.gov 916-322-1854

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