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IES Grant

Title: Postdoctoral Training Program in Mathematical Thinking, Learning, and Instruction
Center: NCER Year: 2013
Principal Investigator: Nathan, Mitchell Awardee: University of Wisconsin, Madison
Program: Postdoctoral Research Training Program in the Education Sciences      [Program Details]
Award Period: 3 years (8/01/2013-7/31/2016) Award Amount: $643,562
Goal: Training Award Number: R305B130007

Co-Principal Investigators: Martha W. Alibali, Amy Ellis, Charles Kalish, Eric Knuth, Peter Steiner

The focus of this training program is to develop researchers who are prepared to conduct scientifically rigorous math education research. Researchers will train four postdoctoral fellows on advanced quantitative methods and in data analysis techniques that support causal inference within experimental, quasi-experimental, and observational designs (e.g., structural equation modeling, multilevel models, propensity score matching). In addition, the fellows will learn how to conduct studies in natural settings (e.g., classrooms) including ways to collect, analyze, and interpret both process data and fidelity of implementation data.

Using an apprenticeship with project-based learning approach, the trainers will provide individualized mentoring in an interdisciplinary and collaborative research community. During their training, fellows will work with mentoring committees to determine which specific training opportunities they should participate in (e.g., research methods courses to audit, colloquia to attend) dependent on their previous experience, current interests, and long-term goals. They will participate in at least two federally funded grants, lead research activities, manage their own research, present their findings, submit manuscripts for publication, audit courses, attend workshops and colloquia, and prepare grant proposals. They will work on current grant projects at the University of Wisconsin-Madison and other campuses that cover a wide range of research methods and analytic strategies, including large-scale randomized control trials, experimental design, think aloud studies, eye tracking, curriculum analysis, and iterative curriculum redesign.

Postdoctoral Fellows

Eiland, Michael D.
Fonger, Nicole
Fyfe, Emily
Gutiérrez, José


Journal article, monograph, or newsletter

Baroody, A.J., Purpura, D.J., Eiland, M.D., and Reid, E.E. (2015). The Impact of Highly and Minimally Guided Discovery Instruction on Promoting the Learning of Reasoning Strategies for Basic Add-1 and Doubles Combinations. Early Childhood Research Quarterly, 30: 93–105. doi:10.1016/j.ecresq.2014.09.003 Full text

Baroody, A.J., Purpura, D.J., Eiland, M.D., Reid, E.E., and Paliwal, V. (2016). Does Fostering Reasoning Strategies for Relatively Difficult Basic Combinations. Journal of Educational Psychology, 108(4), 576.

Davis, J.D., and Fonger, N.L. (2015). An Analytical Framework for Categorizing the Use of CAS Symbolic Manipulation in Textbooks. Educational Studies in Mathematics, 88(2): 239–258. doi:10.1007/s10649–014–9581–z

Fonger, N. L., Davis, J. D., and Rohwer, M. L. (2018). Instructional Supports for Representational Fluency in Solving Linear Equations With Computer Algebra Systems and Paper-and-Pencil. School Science and Mathematics, 118(1–2), 30–42.

Fonger, N. L., Stephens, A., Blanton, M., Isler, I., Knuth, E., and Gardiner, A. M. (2018). Developing a Learning Progression for Curriculum, Instruction, and Student Learning: An Example from Mathematics Education. Cognition and Instruction, 36(1), 30–55.

Fyfe, E. R. (2016). Providing Feedback on Computer-Based Algebra Homework in Middle-School Classrooms. Computers in Human Behavior, 63, 568–574. Full text

Fyfe, E. R., Evans, J. L., Matz, L. E., Hunt, K. M., and Alibali, M. W. (2017). Relations Between Patterning Skill and Differing Aspects of Early Mathematics Knowledge. Cognitive Development, 44, 1–11.

Fyfe, E. R., and Rittle-Johnson, B. (2016). The Benefits of Computer-Generated Feedback for Mathematics Problem Solving. Journal of Experimental Child Psychology, 147, 140–151. Full text

Fyfe, E. R., Matthews, P. G., Amsel, E., McEldoon, K. L., and McNeil, N. M. (2018). Assessing Formal Knowledge of Math Equivalence Among Algebra and Pre-Algebra Students. Journal of Educational Psychology, 110(1), 87.

Fyfe, E. R., Matz, L. E., Hunt, K. M., and Alibali, M. W. (in press). Mathematical Thinking in Children With Developmental Language Disorder: The Roles of Pattern Skills and Verbal Working Memory. Journal of Communication Disorders.

Fyfe, E. R., and Nathan, M. J. (2018). Making “Concreteness Fading” More Concrete as a Theory of Instruction for Promoting Transfer. Educational Review, 1–20.

Gutiérrez, J. F., Brown, S. A., and Alibali, M. W. (2018). Relational Equity and Mathematics Learning: Mutual Construction During Collaborative Problem Solving. Journal of Numerical Cognition, 4(1), 159–187.

Purpura, D.J., Baroody, A.J., Eiland, M.D., and Reid, E.E. (2016). Fostering First-Graders' Reasoning Strategies With Basic Sums: The Value of Guided-Instruction. Elementary School Journal, 117(1), 72–100.

Purpura, D.J., Reid, E.E., Eiland, M.D., and Baroody, A.J. (2015). Using a Brief Preschool Early Numeracy Skills Screener to Identify Young Children With Mathematics Difficulties. School Psychology Review, 44(1): 41–59. doi:10.17105/SPR44–1.41–59 Full text

Rittle-Johnson, B., Fyfe, E. R., Hofer, K. G., and Farran, D. C. (2017). Early Math Trajectories: Low-Income Children's Mathematics Knowledge From Ages 4 to 11. Child development, 88(5), 1727–1742. Full text


Fonger, N. L., Ellis, A., and Dogan, M. F. (2016). Students' Conceptions Supporting Their Symbolization and Meaning of Function Rules. In Proceedings of the 38th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Tucson, AZ: University of Arizona. Full text

Fonger, N.L., Stephens, A., Blanton, M., and Knuth, E. (2015). A Learning Progressions Approach to Early Algebra Research and Practice. In Proceedings of the 37th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 201–204). East Lansing, MI: Michigan State University. Full text