Topic: Cognition and Mathematics Instruction

Purpose: The purpose of the National Center on Mathematics Instruction for Students with Mathematics Difficulties is to increase knowledge of how children acquire and fail to acquire an understanding of rational numbers (i.e., fractions) and how children with math difficulties can be taught to understand and operate fluently with rational numbers.

The new center will conduct exploratory research including both small-scale experimental and longitudinal studies to examine the cognitive processes, such as working memory and inhibition, that impede understanding and operating with fractions. Findings from these studies will be used to inform the design of an intervention package intended to improve fraction skills in students with math difficulties.

Established through a five-year, $9.9 million grant from the Institute of Education Sciences (IES) of the U.S. Department of Education, the center is staffed with nationally-recognized experts in math education and instruction, cognitive psychology, mathematics difficulties, and research evaluation and methodology.

Projects

Exploratory Studies

The experimental and longitudinal studies will establish the conceptual and procedural knowledge that is critical for understanding and operating with fractions as well as identify the key cognitive processes, including working memory for numbers, attentional control, and inhibitory control, that underlie this understanding. Individual differences in the emergence and development of fractions skills will also be explored in order to identify early predictors of difficulty in understanding and operating with fractions. Findings from the exploratory studies will be used to inform the development of an intervention package.

Intervention Development

An intervention component will be developed each year. At the completion of the project, the research team will have developed an intervention package intended to promote a solid foundation of conceptual understanding of fractions by addressing concepts and procedures in an integrated manner. Each intervention component will incorporate instructional principles considered effective for students with math difficulties across academic domains (e.g., explicit instruction, embed systematic cumulative practice) and designed to compensate for the cognitive deficits these students experience (e.g., minimize cognitive load, promote attentive behavior, incorporate metacognitive strategies). The research team will use an iterative process to develop each component as well as develop a rubric to measure fidelity. The intervention components will focus on division, multiplicative relations, and fractions and ratios within word problems. The intervention will be designed to be implemented in small groups. During the development process, the research team will collect data on (1) instructional effectiveness; (2) appropriate use of instructional vocabulary; (3) ease of implementation; (4) quality of student engagement; and (5) quality of student work.

Key Personnel: Nancy Jordan, Robert Siegler, Lynn Fuchs, Russell Gersten

Center Website: www.udel.edu/soe/fractions

IES Program Contact: Rob Ochsendorf
Email: robert.ochsendorf@ed.gov
Phone: 202-219-2234

Publications from this project:

Seethaler, P. M., Fuchs, L. S., Star, J. R., & Bryant, J. R. (2011). The cognitive predictors of computational skill with whole versus rational numbers: An exploratory study. Learning and Individual Differences, 21 (5), 536–542. doi: 10.1016/j.lindif.2011.05.002.

Fazio, L., & Siegler, R.S. (2012). Teaching Fractions. Vol 22 of Educational Practice Series. Geneva: International Academy of Education-International Bureau of Education.

Siegler, R.S., Duncan, G.J., Davis-Kean, P.E., Duckworth, K., Claessens, A., Engel, M., Susperreguy, M.I. & Chen, M. (2012). Early predictors of high school mathematics achievement. Psychological Science, 23 (7), 691–697. doi: 10.1177/0956797612440101.

Fuchs, L. S., Schumacher, R. F., Long, J., Namkung, J., Hamlett, C. L., Cirino, P. T., Jordan, N. C., Siegler, R. S., Gersten, R., & Changas, P. (2013). Improving at-risk learners' understanding of fractions. Journal of Educational Psychology, 105, 683–700.

Jordan, N. C., Hansen, N., Fuchs, L. S., Siegler, R. S., Gersten, R., & Micklos, D. (2013). Developmental predictors of fraction concepts and fraction procedures. Journal of Experimental Child Psychology. doi:dx.doi.org/10.1016/j.jecp.2013.02.001

Siegler, R. S., Fazio, L. K., Bailey, D. H., & Zhou, X. (2013). Fractions: The new frontier for theories of numerical development. Trends in Cognitive Science, 17, 13–19.

Fuchs, L.S., Schumacher, R.F., Sterba, S.K., Long, J., Namkung, J., Malone, A., Hamlett, C.L., Jordan, N.C., Gersten, R., Siegler, R.S., & Changas, P. (2014). Does working memory moderate the effects of fraction intervention? An aptitude-treatment interaction. Journal of Educational Psychology, 106, 499–514. (online version available 9/9/2013. doi: 10.1037/a0034341)

Fuchs, L.S., Fuchs, D., Compton, D.L., Wehby, J., Schumacher, R.F., Gersten, R., & Jordan, N.C. (in press). Inclusion versus specialized intervention for very low-performing students: What does access mean in an era of academic challenge? Exceptional Children.

Opfer, J.E., & Siegler, R.S. (in press). Development of quantitative thinking. In K. Holyoak & R. Morrison (Eds.), Oxford Handbook of Thinking and Reasoning. Cambridge, UK: Oxford University Press.

Siegler, R. S., & Pyke, A. A. (in press). Developmental and individual differences in understanding of fractions.Developmental Psychology.

Vukovic, R.K., Fuchs, L.S., Geary, D.C., Jordan, N.C., Gersten, R., & Siegler, R.S. (in press). Sources of individual differences in children's understanding of fractions. Child Development. Published online 2014: onlinelibrary.wiley.com/doi/10.1111/cdev.12218/abstract