IES Grant

Title: | National Research and Development Center on Improving Mathematics Instruction for Students with Mathematics Difficulties | ||

Center: | NCSER | Year: | 2010 |

Principal Investigator: | Jordan, Nancy | Awardee: | University of Delaware |

Program: | Special Education Research and Development Centers [Program Details] | ||

Award Amount: | $9,896,532 | ||

Goal: | Multiple Goals | Award Number: | R324C100004 |

Description: |
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.
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.
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.
Publications
Opfer, J.E., & Siegler, R.S. (2012). Development of quantitative thinking. In K. Holyoak & R. Morrison (Eds.), Siegler, R., Fuchs, L., Jordan, N., Gersten, R., and Ochsendorf, R. (2015). The Center for Improving Learning of Fractions: A Progress Report. In S. Chinn (Ed.), Siegler, R.S. (2013). Cognitive Development in Childhood. In E. Diener, and R. Biswas-Diener (Eds.),
Bailey, D. H., Siegler, R. S., & Geary, D. C. (2014). Early predictors of middle school fraction knowledge. Bailey, D. H., Zhou, X., Zhang, Y., Cui, J., Fuchs, L. S., Jordan, N. C., Gersten, R., & Siegler, R. S. (2015). Development of fraction concepts and procedures in U.S. and Chinese children. Fazio, L. K., Bailey, D. H., Thompson, C. A., & Siegler, R. S. (2014). Relations of different types of numerical magnitude representations to each other and to mathematics achievement. Fazio, L., and Siegler, R.S. (2012). Teaching Fractions. Fazio, L. K. & Siegler, R. S. (2013). Microgenetic learning analysis: A distinction without a difference. Commentary on Parnafes and diSessa. Fazio, L.K., DeWolf, M., and Siegler, R.S. (2016). Strategy Use and Strategy Choice in Fraction Magnitude Comparison. Fazio, L.K., Kennedy, C.A., and Siegler, R.S. (2016). Improving Children's Knowledge of Fraction Magnitudes. Fuchs, L.S., Fuchs, D., Compton, D.L., Wehby, J., Schumacher, R.F., Gersten, R., and Jordan, N.C. (2015). Inclusion Versus Specialized Intervention for Very Low-Performing Students: What Does Access Mean in an Era of Academic Challenge?. Fuchs, L.S., Malone, A., Schumacher, R.F., Namkung, J., Hamlett, C.L., Jordan, N.C., Siegler, R.S., Gersten, R., and Changas, P. (2016). Supported Self-Explaining During Fraction Intervention. Fuchs, L.S., Schumacher, R.F., Long, J., Namkung, J., Hamlett, C.L., Cirino, P.T., Jordan, N.C., Siegler, R.S., Gersten, R., and Changas, P. (2013). Improving At-Risk Learners' Understanding of Fractions. Fuchs, L.S., Schumacher, R.F., Long, J., Namkung, J., Malone, A., Hamlett, C.L., Jordan, N.C., Gersten, R., Siegler, R.S., and Changas, P. (2014). Does Working Memory Moderate the Effects of Fraction Intervention? An Aptitude-Treatment Interaction. Fuchs, L.S., Schumacher, R.F., Long, J., Namkung, J., Malone, A., Wang, A., Hamlett, C.L., Jordan, N.C., Siegler, R.S., and Changas, P. (2016). Effects of Intervention to Improve At-Risk Fourth Graders' Understanding, Calculations, and Word Problems With Fractions. Fuchs, L.S., Sterba, S.K., Fuchs D., and Malone, A. (2016). Does Evidence-Based Fractions Intervention Address the Needs of Very Low-Performing Students?. Hansen, N., Jordan, N.C., Fenandez, E., Siegler, R.S., Fuchs, L., Gersten, R., and Micklos, D. (2015). General and Math-Specific Predictors of Sixth-Graders' Knowledge of Fractions. Jordan, N.C., Hansen, N., Fuchs, L.S., Siegler, R.S., Gersten, R., and Micklos, D. (2013). Developmental Predictors of Fraction Concepts and Fraction Procedures. Kurz, A., Elliott, S.N., Kettler, R.J., and Yel, N. (2014). Assessing Students' Opportunity to Learn the Intended Curriculum Using an Online Teacher Log: Initial Validity Evidence. Lortie-Forgues, H., and Siegler, R. S. (2017). Conceptual Knowledge of Decimal Arithmetic. Lortie-Forgues, H., Tian, J., and Siegler, R.S. (2015). Why is Learning Fraction and Decimal Arithmetic so Difficult? Malone, A.S., and Fuchs, L.S. (2014). Comparing the Contribution of Teacher Versus Tutor Ratings of Inattentive Behavior in Predicting Mathematics Achievement. Namkung, J.M., and Fuchs, L.S. (2016). Cognitive Predictors of Calculations and Number Line Estimation With Whole Numbers and Fractions Among At-Risk Students. Resnick, I., Jordan, N.C., Hansen, N., Rajan, V., Rodrigues, J., Siegler, R.S., and Fuchs, L.S. (2016). Developmental Growth Trajectories in Understanding of Fraction Magnitude From Fourth through Sixth Grade. Seethaler, P.M., Fuchs, L.S., Star, J.R., and Bryant, J.R. (2011). The Cognitive Predictors of Computational Skill With Whole Versus Rational Numbers: An Exploratory Study. Siegler, R. S., and Braithwaite, D. W. (2017). Numerical Development. Siegler, R.S. (2016). Magnitude Knowledge: The Common Core of Numerical Development. Siegler, R.S., and Lortie-Forgues, H. (2014). An Integrative Theory of Numerical Development. Siegler, R.S., and Lortie-Forgues, H. (2015). Conceptual Knowledge of Fraction Arithmetic. Siegler, R.S., and Pyke, A.A. (2013). Developmental and Individual Differences in Understanding of Fractions. Siegler, R.S., and Thompson, C.A. (2014). Numerical Landmarks are Useful – Except When They're not. Siegler, R.S., Duncan, G.J., Davis-Kean, P.E., Duckworth, K., Claessens, A., Engel, M., Susperreguy, M.I., and Chen, M. (2012). Early Predictors of High School Mathematics Achievement. Siegler, R.S., Fazio, L.K., Bailey, D.H., and Zhou, X. (2013). Fractions: The New Frontier for Theories of Numerical Development. 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. Tian, J. and Siegler, R.S. (2016). Fractions Learning in Children with Mathematics Difficulties. Vukovic, R.K., Fuchs, L.S., Geary, D.C., Jordan, N.C., Gersten, R., and Siegler, R.S. (2014). Sources of Individual Differences in Children's Understanding of Fractions. Wang, Y., and Siegler, R.S. (2013). Representations of and Translation Between Common Fractions and Decimal Fractions. Watts, T.W., Duncan, G.J., Chen, M., Claessens, A., Davis-Kean, P.E., Duckworth, P., Engle, M., Siegler, R., and Susperreguy, M.I. (2015). The Role of Mediators in the Development of Longitudinal Mathematics Achievement Associations. Watts, T.W., Duncan, G.J., Siegler, R.S., and Davis-Kean, P.E. (2014). What's Past is Prologue: Relations Between Early Mathematics Knowledge and High School Achievement.
Fazio, L., and Siegler, R. (2012). |
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