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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
Type: Training Award Number: R305B130007

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

This training program prepared four researchers to conduct scientifically rigorous math education research. Researchers at the University of Wisconsin-Madison trained four postdoctoral fellows on advanced quantitative methods and 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 conducted studies in natural settings (e.g., classrooms) and collected, analyzed, and interpreted both process and fidelity of implementation data.

University of Wisconsin-Madison researchers used an apprenticeship with project-based learning approach to provide individualized mentoring in an interdisciplinary and collaborative research community. Fellows worked with mentoring committees to identify specific training opportunities dependent on their previous experiences, current interests, and long-term goals. They participated in at least two federally funded grants, led research activities, managed their own research, presented their findings, published manuscripts, audited courses, attended workshops and colloquia, and prepared grant proposals. Fellows worked on grant projects at the University of Wisconsin-Madison and other campuses that covered 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. (ORCID)
Fonger, Nicole (ORCID)
Fyfe, Emily
Gutiérrez, José (ORCID)

As of 2020, Dr. Eiland was at the University of Illinois, Urbana-Champaign, Dr. Fonger was an assistant professor of mathematics and mathematics education at Syracuse University, Dr. Fyfe was an assistant professor of psychological and brain sciences at Indiana University, and Dr. Gutiérrez was an assistant professor in the Department of Education, Culture & Society at the University of Utah.


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. (2019). Mathematical Thinking in Children With Developmental Language Disorder: The Roles of Pattern Skills and Verbal Working Memory. Journal of Communication Disorders, 77, 17-30.

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