Longitudinal algebra prediction for early versus later takers

References

• Allensworth, E., Nomi, T., Montgomery, N., & Lee, V. E. (2009). College preparatory curriculum for all: Academic consequences of requiring algebra and English I for ninth graders in Chicago. Education Evaluation and Policy Analysis, 31(4), 367–391.
   Web of Science ®Google Scholar
• American Diploma Project (2004). Ready or not: Creating a high school diploma that counts. Washington, DC: Achieve, Inc.
   Google Scholar
• Bailey, D. H., Nguyen, T., Jenkins, J. M., Domina, T., Clements, D. H., & Sarama, J. S. (2016). Fadeout in an early mathematics intervention: Constraining content or preexisting differences? Developmental Psychology, 52(9), 1457. doi: 10.1037/dev0000188
   PubMed Web of Science ®Google Scholar
• Bailey, D. H., Siegler, R. S., & Geary, D. C. (2014). Early predictors of middle school fraction knowledge. Developmental Science, 17(5), 775–785. http://dx.doi.org/10.1111/desc.12155
   PubMed Web of Science ®Google Scholar
• Booth, J. L., & Newton, K. J. (2012). Fractions: Could they really be the gatekeeper’s doorman? Contemporary Educational Psychology, 37(4), 247–253.
   Web of Science ®Google Scholar
• Booth, J., Newton, K., & Twiss-Garrity, L. (2014). The impact of fraction magnitude knowledge on algebra performance and learning. Journal of Experimental Child Psychology, 118, 110–118. doi: 10.1016/j.jecp.2013.09.001
   PubMed Web of Science ®Google Scholar
• Booth, J., & Siegler, R. (2006). Developmental and individual differences in pure numerical estimation. Developmental Psychology, 41(6), 189–201.
   Web of Science ®Google Scholar
• Boyce, R. W. (1964). The prediction of achievement in college algebra. Educational and Psychological Measurement, 24(2), 419–420.
   Web of Science ®Google Scholar
• Brown, G., & Quinn, R. (2006). Algebra students' difficulty with fractions: An error analysis. The Australian Mathematics Teacher, 62(4), 28–40.
   Google Scholar
• Brown, G., & Quinn, R. J. (2007a). Fraction proficiency and success in algebra: What does the research say?. The Australian Mathematics Teacher, 63(3), 23–30.
   Google Scholar
• Brown, G., & Quinn, R. (2007b). Investigating the relationship between fraction proficiency and success in algebra. The Australian Mathematics Teacher, 63(4), 8–15.
   Google Scholar
• Cain, K., Oakhill, J. V., Barnes, M. A., & Bryant, P. E. (2001). Comprehension skill, inference-making ability, and their relation to knowledge. Memory & Cognition, 29(6), 850–859. http://doi.org/10.3758/BF03196414
   PubMed Web of Science ®Google Scholar
• Carraher, D. W., Schliemann, A. D., Brizuela, B. M., & Earnest, D. (2006). Arithmetic and algebra in early mathematics education. Journal for Research in Mathematics Education, 37(2), 87–115.
   Web of Science ®Google Scholar
• Chen, Q., & Li, J. (2014). Association between individual differences in non-symbolic number acuity and math performance: A meta-analysis. Acta Psychologica, 148, 163–172.
   PubMed Web of Science ®Google Scholar
• Cirino, P. T. (2011). The interrelationships of mathematical precursors in kindergarten. Journal of Experimental Child Psychology, 108(4), 713–733.
   PubMed Web of Science ®Google Scholar
• Cirino, P. T., Tolar, T. D., Fuchs, L. S., & Huston-Warren, E. A. (2016). Cognitive and numerosity predictors of mathematical skills in middle school. Journal of Experimental Child Psychology, 145, 95–119.
   Google Scholar
• Clotfelter, C., Ladd, H., & Vigdor, J. (2012). Algebra for 8th graders: Evidence on its effects from 10 North Carolina districts (National Bureau of Economic Research, Working Paper 18649). Retrieved from http://www.nber.org/papers/w18649.
   Google Scholar
• College Board (2000). Equity 2000: A systemic education reform model A summary report, 1990-2000. Washington, DC: Author. Retrieved from http://www.college board.com/prod_downloads/about/association/equity/Equity HistoricalReport.pdf
   Google Scholar
• Conway, A. R. A., Kane, M. J., Bunting, M. F., Hambrick, D. Z., Wilhelm, O., & Engle, R. W. (2005). Working memory span tasks: A methodological review and user's guide. Psychonomic Bulletin & Review, 12(5), 769–786.
   PubMed Web of Science ®Google Scholar
• Crisp, G., Nora, A., & Taggart, A. (2009). Student characteristics, pre-college, college, and environmental factors as predictors of majoring in and earning a STEM degree: An analysis of students attending a Hispanic Serving Institution. American Educational Research Journal, 46(4), 924–942.
   Web of Science ®Google Scholar
• DeWolf, M., Bassok, M., & Holyoak, K. J. (2015). From rational numbers to algebra: Separable contributions of decimal magnitude and relational understanding of fractions. Journal of Experimental Child Psychology, 133, 72–84. http://dx.doi.org/10.1016/j.jecp.2015.01.013
   PubMed Web of Science ®Google Scholar
• Domina, T. (2014). The link between middle school mathematics course placement and achievement. Child Development, 85, 1948–1964.
   PubMed Web of Science ®Google Scholar
• Domina, T., McEachin, A., Penner, A., & Penner, E. (2015). Aiming high and falling short: California’s Eighth-Grade Algebra-for-All effort. Educational Evaluation and Policy Analysis, 37(3), 275–295.
   Web of Science ®Google Scholar
• Dougherty, S. M., Goodman, J. S., Hill, D. V., Litke, E. G., & Page, L. C. (2015). Middle school math acceleration and equitable access to eighth-grade algebra: Evidence from the Wake County public school system. Educational Evaluation and Policy Analysis, 37(1_suppl), 80S–101S.
   Web of Science ®Google Scholar
• Fazio, L., Bailey, D., Thompson, C., & Siegler, R. (2014). Relations of different types of numerical magnitude representations to each other and to mathematics achievement. Journal of Experimental Child Psychology, 123, 53–72. doi:10.1016/j.jecp.2014.01.013
   PubMed Web of Science ®Google Scholar
• Fuchs, L. S., Fuchs, D., Compton, D. L., Powell, S. R., Seethaler, P. M., Capizzi, A. M., … Fletcher, J. M. (2006). The cognitive correlates of third-grade skill in arithmetic, algorithmic computation, and arithmetic word problems. Journal of Educational Psychology, 98(1), 29–43. http://dx.doi.org/10.1037/0022-0663.98.1.29
   Web of Science ®Google Scholar
• Fuchs, L., Fuchs, D., Compton, D., Hamlett, C., & Wang, A. (2015). Is word-problem solving a form of text comprehension? Scientific Studies of Reading: The Official Journal of the Society for the Scientific Study of Reading, 19(3), 204–223.
   PubMed Web of Science ®Google Scholar
• Fuchs, L., Geary, D., Compton, D., Fuchs, D., Hamlett, C., & Bryant, J. (2010). The contributions of numerosity and domain-general abilities to school readiness. Child Development, 81(5), 1520–1533.
   PubMed Web of Science ®Google Scholar
• Fuchs, L. S., Geary, D. C., Compton, D. L., Fuchs, D., Hamlett, C. L., Seethaler, P. M., … Schatschneider, C. (2010). Do different types of school mathematics development depend on different constellations of numerical versus general cognitive abilities? Developmental Psychology, 46(6), 1731–1746.
   PubMed Web of Science ®Google Scholar
• Fuchs, L. S., Schumacher, R. F., Long, J., Namkung, J., Hamlett, C. L., Cirino, P. T., … Changas, P. (2013). Improving at-risk learners’ understanding of fractions. Journal of Educational Psychology, 105(3), 683–700.
   Web of Science ®Google Scholar
• Gaertner, M. N., Kim, J., DesJardins, S. L., & McClarty, K. L. (2014). Preparing students for college and careers: The causal role of Algebra II. Research in Higher Education, 55(2), 143–165. DOI 10.1007/s11162-013-9322-7
   Web of Science ®Google Scholar
• Gamoran, A., & Hannigan, E. C. (2000). Algebra for everyone? Benefits of college-preparatory mathematics for students with diverse abilities in early secondary school. Educational Evaluation and Policy Analysis, 22(3), 241–254.
   Web of Science ®Google Scholar
• Geary, D. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37(1), 4–15.
   PubMed Web of Science ®Google Scholar
• Geary, D. C., Hoard, M. K., Nugent, L., & Rouder, J. N. (2015). Individual differences in algebraic cognition: Relation to the approximate number and semantic memory systems. Journal of Experimental Child Psychology, 140, 211–227.
   PubMed Web of Science ®Google Scholar
• Grover, C. C. (1932). Results of an experiment in predicting first year algebra in two Oakland junior high schools. Journal of Educational Psychology, 23(4), 309–314.
   Google Scholar
• Halberda, J., Mazzocco, M. M. M., & Feigenson, L. (2008). Individual differences in nonverbal number acuity predict Maths achievement. Nature, 455(7213), 665–668.
   PubMed Web of Science ®Google Scholar
• Hanna, G. S., Bligh, H. F., Lenke, J. M., & Orleans, J. B. (1969). Predicting algebra achievement with an algebra prognosis test, IQs, teacher predictions, and mathematics grades. Educational and Psychological Measurement, 29(4), 903–907.
   Web of Science ®Google Scholar
• Hanna, G. S., & Sonnenschein, J. L. (1985). Relative validity of the Orleans-Hanna Algebra Prognosis Test in the prediction of girls’ and boys’ grades in first-year algebra. Educational and Psychological Measurement, 45(2), 361–907.
   Web of Science ®Google Scholar
• Hansen, M. (2014). Characteristics of schools successful in STEM: Evidence from two states’ longitudinal data. The Journal of Educational Research, 107(5), 374–391.
   Web of Science ®Google Scholar
• Hansen, N., Jordan, N. C., Fernandez, E., Siegler, R. S., Fuchs, L., Gersten, R., & Micklos, D. (2015). General and math-specific predictors of sixth-graders’ knowledge of fractions. Cognitive Development, 35, 34–49.
   Web of Science ®Google Scholar
• Hecht, S. A., & Vagi, K. J. (2010). Sources of group and individual differences in emerging fraction skills. Journal of Educational Psychology, 102(4), 843–859. http://dx.doi.org/10.1037/a0019824
   PubMed Web of Science ®Google Scholar
• Heppen, J. B., Walters, K., Clements, M., Faria, A., Tobey, C., Sorensen, N., & Culp, K. (2012). Access to Algebra I: The effects of online mathematics for Grade 8 students (NCEE 2012–4021). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education.
   Google Scholar
• Jordan, N., Hansen, N., Fuchs, L., Siegler, R., Gersten, R., & Micklos, D. (2013). Developmental predictors of fraction concepts and procedures. Journal of Experimental Child Psychology, 116(1), 45–58.
   PubMed Web of Science ®Google Scholar
• Kane, M. J., Hambrick, D. Z., Tuholski, S. W., Wilhelm, O., Payne, T. W., & Engle, R. W. (2004). The generality of working memory capacity: a latent-variable approach to verbal and visuospatial memory span and reasoning. Journal of Experimental Psychology: General, 133(2), 189–217.
   Google Scholar
• Lee, K., Ng, E., & Ng, S. (2009). The contributions of working memory and executive functioning to problem representation and solution generation in algebraic word problems. Journal of Educational Psychology, 101(2), 373–387.
   Web of Science ®Google Scholar
• Lee, K., Ng, S. F., Ng, E. L., & Lim, Z. Y. (2004). Working memory and literacy as predictors of performance on algebraic word problems. Journal of Experimental Child Psychology, 89(2), 140–158.
   PubMed Web of Science ®Google Scholar
• LeFevre, J.-A., Fast, L., Skwarchuk, S.-L., Smith-Chant, B. L., Bisanz, J., Kamawar, D., & Penner-Wilger, M. (2010). Pathways to mathematics: Longitudinal predictors of performance. Child Development, 81(6), 1753–1767.
   PubMed Web of Science ®Google Scholar
• Liang, J.-H., Heckman, P. E., & Abedi, J. (2012). What do the California standards test results reveal about the movement toward eighth-grade Algebra for All? Educational Evaluation and Policy Analysis, 34(3), 328–343.
   Web of Science ®Google Scholar
• Libertus, M., Odic, D., & Halberda, J. (2012). Intuitive sense of number correlates with math scores on college-entrance examination. Acta Psychologica, 141(3), 373–379.
   PubMed Web of Science ®Google Scholar
• Loveless, T. (2008). The misplaced math student lost in eighth-grade algebra (The 2008 Brown Center Report on American Education). Washington, DC: Brookings Institute.
   Google Scholar
• Ma, X., & Wilkins, J. L. M. (2007). Mathematics coursework regulates growth in mathematics achievement. Journal for Research in Mathematics Education, 38(3), 230–257.
   Google Scholar
• Matthews, P. G., Lewis, M. R., & Hubbard, E. M. (2016). Individual differences in nonsymbolic ratio processing predict symbolic math performance. Psychological Science, 27(2), 191–202. DOI: 10.1177/0956797615617799
   PubMed Web of Science ®Google Scholar
• McGrew, K. S., & Woodcock, R. W. (2001). Technical Manual. Woodcock-Johnson III. Itasca, IL: Riverside Publishing.
   Google Scholar
• Misailidou, C., & Williams, J. (2003). Diagnostic assessment of children’s proportional reasoning. The Journal of Mathematical Behavior, 22(3), 335–368. doi:10.1016/S0732-3123(03)00025-7
   Google Scholar
• National Mathematics Advisory Panel (NMAP). (2008). Foundations for success: The Final Report of the National Mathematics Advisory Panel. Washington, DC: U.S. Department of Education.
   Google Scholar
• Nomi, T. (2012). The unintended consequences of an Algebra-for-All policy on high-skill students: The effects on instructional organization and students’ academic outcomes. Educational Evaluation and Policy Analysis, 34(4), 489–505.
   Web of Science ®Google Scholar
• Nomi, T., & Raudenbush, S. W. (2016). Making a success of “Algebra for All”: The impact of extended instructional time and classroom peer skill in Chicago. Educational Evaluation and Policy Analysis, 38(2), 431–451.
   Web of Science ®Google Scholar
• Panamath (2011, October 6). Retrieved December 4, 2014, from http://panamath.org/
   Google Scholar
• Peters, M. (1995). Revised Vandenberg & Kuse mental rotations tests: Forms MRT-A to MRT-D. Guelph, Ontario, Canada: University of Guelph, Department of Psychology.
   Google Scholar
• Rickles, J. H. (2013). Examining heterogeneity in the effect of taking Algebra in eighth grade. The Journal of Educational Research, 106(4), 251–268.
   Web of Science ®Google Scholar
• Rittle-Johnson, B., Star, J. R., & Durkin, K. (2009). The importance of prior knowledge when comparing examples: Influences on conceptual and procedural knowledge of equation solving. Journal of Educational Psychology, 101(4), 836–852. doi:10.1037/a0016026.
   Web of Science ®Google Scholar
• Rose, H., & Betts, J. (2004). The effect of high school courses on earnings. Review of Economics and Statistics, 86(2), 497–513.
   Web of Science ®Google Scholar
• Seagoe, M. V. (1938). Prediction of achievement in elementary algebra. Journal of Applied Psychology, 22(5), 493–503.
   Google Scholar
• Sesma, H. W., Mahone, E. M., Levine, T., Eason, S. H., & Cutting, L. E. (2009). The contribution of executive skills to reading comprehension. Child Neuropsychology, 15(3), 232–246. http://doi.org/10.1080/09297040802220029
   PubMed Web of Science ®Google Scholar
• Siegler, R., & Booth, J. (2004). Development of numerical estimation in young children. Child Development, 75(2), 428–444.
   PubMed Web of Science ®Google Scholar
• Siegler, R. S., Duncan, G. J., Davis-Kean, P. E., Duckworth, K., Claessens, A., Engel, M., … Chen, M. (2012). Early predictors of high school mathematics achievement. Psychological Science, 23(7), 691–697. doi:10.1177/0956797612440101.
   PubMed Web of Science ®Google Scholar
• Siegler, R., & Lortie-Forgues, H. (2014). An integrative theory of numerical development. Child Development Perspectives, 8(3), 144–150.
   Web of Science ®Google Scholar
• Siegler, R., & Opfer, J. (2003). The development of numerical estimation: Evidence for multiple representations of numerical quantity. Psychological Science, 14(3), 237–250. doi:10.1111/1467-9280.02438
   PubMed Web of Science ®Google Scholar
• Siegler, R., Thompson, C., & Schneider, M. (2011). An integrated theory of whole number and fractions development. Cognitive Psychology, 62(4), 273–296.
   PubMed Web of Science ®Google Scholar
• Smith, J. B. (1996). Does an extra year make any difference? The impact of early access to algebra on long-term gains in mathematics attainment. Educational Evaluation and Policy Analysis, 18(2), 141–153. doi: 10.3 102/01623737018002141
   Web of Science ®Google Scholar
• Smith, J. G., & Michael, W. B. (1998). Validity of scores on alternative predictors of success in a college algebra course. Psychological Reports, 82(2), 379–386.
   Web of Science ®Google Scholar
• Star, J. R., Newton, K., Pollack, C., Kokka, K., Rittle-Johnson, B., & Durkin, K. (2015). Student, teacher, and instructional characteristics related to students’ gains in flexibility. Contemporary Educational Psychology, 41, 198–208.
   Web of Science ®Google Scholar
• Stein, M. K., Kaufman, J., Sherman, M., & Hillen, A. (2011). Algebra: A challenge at the crossroads of policy and practice. Review of Educational Research, 81(4), 453–492.
   Web of Science ®Google Scholar
• Swanson, H. L., & Beebe-Frankenberger, M. (2004). The relationship between working memory and mathematical problem solving in children at risk and not at risk for serious math difficulties. Journal of Educational Psychology, 96(3), 471–491.
   Web of Science ®Google Scholar
• Szűcs, D., Devine, A., Soltesz, F., Nobes, A., & Gabriel, F. (2014). Cognitive components of a mathematical processing network in 9-year-old children. Developmental Science, 17(4), 506–524.
   PubMed Web of Science ®Google Scholar
• Taylor, C. L., Brown, F. G., & Michael, W. B. (1976). The validity of cognitive, affective, and demographic variables in the prediction of achievement in high school algebra and geometry: Implications for the definition of mathmetical aptitude. Educational and Psychological Measurement, 36(4), 971–982.
   Web of Science ®Google Scholar
• Tennessee Department of Education. (2002–2005). Tennessee Comprehensive Assessment Program (TCAP) Tests of Achievement. Iowa City, Iowa: Pearson. Retrieved from http://www.tn.gov/education/assessment/achievement.shtml.
   Google Scholar
• Tennessee Department of Education. (2009). Tennessee Mathematics Standards: Algebra I. Retrieved from http://www.tennessee.gov/education/ci/math/2009_10/3102_Algebra_I.pdf
   Google Scholar
• Texas Educational Agency. (2012a). Texas Essential Knowledge and Skills for Mathematics: Subchapter C. High School 111.39. Algebra I. Austin, TX: Texas Education Agency. Retrieved from http://ritter.tea.state.tx.us/rules/tac/chapter111/ch111c.html.
   Google Scholar
• Texas Educational Agency. (2012b). Texas Essential Knowledge and Skills for Mathematics: Subchapter C. High School 111.39. Algebra I. Austin, TX: Texas Education Agency. Retrieved from http://ritter.tea.state.tx.us/rules/tac/chapter111/ch111c.html.
   Google Scholar
• Tolar, T. D., Cirino, P. T., & Fuchs, L. S. (in progress). Delayed effects of early experience in the development of math problem solving.
   Google Scholar
• Tolar, T., Lederberg, A., & Fletcher, J. (2009). A structural model of algebra achievement: Computational fluency and spatial visualisation as mediators of the effect of working memory on algebra achievement. Educational Psychology, 29(2), 239–266. doi:10.1080/01443410802708/903.
   Web of Science ®Google Scholar
• Torbeyns, J., Schneider, M., Xin, Z., & Siegler, R. S. (2015). Bridging the gap: Fraction understanding is central to mathematics achievement in students from three different continents. Learning and Instruction, 37, 5–13.
   Web of Science ®Google Scholar
• U.S. Department of Education, National Center for Education Statistics (2015). The Condition of Education 2015 (NCES 2015-144), High School Coursetaking.
   Google Scholar
• Unsworth, N., Redick, T. S., Heitz, R. P., Broadway, J. M., & Engle, R. W. (2009). Complex working memory span tasks and higher order cognition: A latent-variable analysis of the relationship between processing and storage. Memory, 17(6), 635–654.
   PubMed Web of Science ®Google Scholar
• Vandenberg, S., & Kuse, A. (1978). Mental rotation, a group test of 3-D spatial visualization. Perceptual and Motor Skills, 47(2), 599–604.
   PubMed Web of Science ®Google Scholar
• von Aster, M., & Shalev, R. (2007). Number development and developmental dyscalculia. Developmental Medicine and Child Neurology, 49, 868–873.
   PubMed Web of Science ®Google Scholar
• Vukovic, R., Fuchs, L., Geary, D., Jordan, N., Gersten, R., & Siegler, R. (2014). Sources of individual differences in children's understanding of fractions. Child Development, 85(4), 1461–1476.
   PubMed Web of Science ®Google Scholar
• Vukovic, R. K., & Lesaux, N. K. (2013). The relationship between linguistic skills and arithmetic knowledge. Learning and Individual Differences, 23, 87–91.
   Web of Science ®Google Scholar
• Weaver, B., & Wuensch, K. L. (2013). SPSS and SAS programs for comparing Pearson correlations and OLS regression coefficients. Behavior Research Methods, 45(3), 896–895. DOI 10.3758/s13428-012-028/9-7
   Web of Science ®Google Scholar
• Wechsler, D. (1999). Wechsler Abbreviated Scales of Intelligence: WASI. San Antonio, TX: The Psychological Corporation.
   Google Scholar
• Woodcock, R., McGrew, K., & Mather, N. (2001). Woodcock-Johnson III tests of achievement. Itasca, IL: Riverside Publishing.
   Google Scholar