The Postdoctoral Training Program in Mathematical Thinking, Learning, and Instruction focused on math education and provided opportunities for five fellows to focus on a range of scientifically rigorous methods, including data analysis techniques that support causal inference within experimental, quasi-experimental, and observational designs. Fellows worked with faculty on a range of research projects, including ones focused on understanding mathematical cognition by analyzing videos of classroom instruction and learning; exploring mathematical learning opportunities during pre-college engineering courses and through multilevel analyses of school district data and student-level outcomes; understanding student reasoning in mathematical contexts; exploring teachers' use of visual scaffolding, primarily in gesture, in algebra classes and the resultant influence on mathematical learning; and the use of secondary analyses in which hybrid multilevel and structural equation modeling methods are applied to the PISA mathematics literacy data.

Postdoctoral Fellows

Boncoddo, Rebecca
Cooper, Jennifer
Eiland, Michael D. (ORCID)
Lockwood, Elise
Walkington, Candace

As of 2020, Dr. Boncoddo was an associate professor of psychological science at Central Connecticut State University, Dr. Cooper was an assistant professor of psychology at Stonehill College, Dr. Eiland was a senior research associate in the Department of Human and Family Studies at Purdue University, Dr. Lockwood was an associate professor of mathematics at Oregon State University, and Dr. Walkington was an associate professor and a Gerald J. Ford research fellow in the Department of Teaching and Learning at Southern Methodist University.

Products and Publications

Book chapter

Walkington, C., Nathan, M., Wolfgram, M., Alibali, M., and Srisurichan, R. (2014). Bridges and Barriers to Constructing Conceptual Cohesion Across Modalities and Temporalities: Challenges of STEM Integration in the Precollege Engineering Classroom. In J. Strobel, S. Purzer, and M. Cardella (Eds.), Engineering in PreCollege Settings: Synthesizing Research, Policy and Practice (pp. 183–209). West Lafayette, IN: Purdue University Press.

Journal article, monograph, or newsletter

Larsen, S., and Lockwood, E. (2013). A Local Instructional Theory for the Guided Reinvention of the Quotient Group Concept. Journal of Mathematical Behavior, 32(4): 726–742.

Lockwood, E. (2012). Counting Using Sets of Outcomes. Mathematics Teaching in the Middle School, 18(3): 132–135.

Lockwood, E. (2013). A Model of Students' Combinatorial Thinking. Journal of Mathematical Behavior, 32(2): 251–265.

Lockwood, E. (2014). Both Answers Make Sense! Using the Set of Outcomes to Reconcile Differing Answers in Counting Problems. Mathematics Teacher, 108(4): 296–301.

Lockwood, E., Johnson, E.M., and Larsen, S. (2013). Developing Instructor Support Materials for an Inquiry-Oriented Curriculum. Journal of Mathematical Behavior, 32(4): 776–790.

Nathan, M. J., Wolfgram, M., Srisurichan, R., Walkington, C., & Alibali, M. W. (2017). Threading mathematics through symbols, sketches, software, silicon, and wood: Teachers produce and maintain cohesion to support STEM integration. The Journal of Educational Research, 110(3), 272-293.

Walkington, C.A. (2013). Using Adaptive Learning Technologies to Personalize Instruction to Student Interests: The Impact of Relevant Contexts on Performance and Learning Outcomes. Journal of Educational Psychology, 105(4): 932–945.

Walkington, C., Sherman, M., & Howell, E. (2014). Personalized Learning in Algebra. The Mathematics Teacher, 108(4), 272-279.

Walkington, C., Sherman, M., and Petrosino, A. (2012). Playing the Game of Story Problems: Coordinating Situation-Based Reasoning With Algebraic Representation. Journal of Mathematical Behavior, 31(2): 174–195.

Williams-Pierce, C. C., Pier, E. L., Walkington, C., Boncoddo, R., Clinton, V., Alibali, M. W., and Nathan, M. J. (2017). What we say and how we do: Action, gesture, and language in proving. Journal for Research in Mathematics Education, 48(3), 248-260.

Proceeding

Cooper, J., Walkington, C., Williams, C., Akinsiku, O., Kalish, C., Ellis, A., and Knuth, E. (2011). Adolescent Reasoning in Mathematics: Exploring Middle School Students' Strategic Approaches to Empirical-Based Justifications. In Proceedings of the 33rd Annual Conference of the Cognitive Science Society (pp. 2188–2293). Boston: Cognitive Science Society.

Ellis, A.E., Lockwood, E., Williams, C.C.W., Dogan, M.F., and Knuth, E. (2012). Middle School Students' Example Use in Conjecture Exploration and Justification. In Proceedings of the 34th Annual Meeting of the North American Chapter of the Psychology of Mathematics Education (pp. 135–142). Kalamazoo, MI: North American Chapter of the Psychology of Mathematics Education.

Lockwood, E. (2012). A Model of Students' Combinatorial Thinking: The Role of Sets of Outcomes. In Proceedings of the 15th Annual Conference on Research in Undergraduate Mathematics Education (pp. 95–100). Portland, OR: Portland State University.

Lockwood, E. (2012). Students' Uses of Smaller Problems When Counting. In Proceeding of the 34th Annual Meeting of the North American Chapter of the Psychology of Mathematics Education (pp. 267). Kalamazoo, MI: North American Chapter of the Psychology of Mathematics Education.

Lockwood, E. (2013). Developing Facility With Sets of Outcomes by Solving Smaller, Simpler Counting Problems. In Electronic Proceedings for the Sixteenth Special Interest Group of the MAA on Research on Undergraduate Mathematics Education (pp. 172–178). Denver, CO: Northern Colorado University.

Lockwood, E. (2013). The Groups of Students Problem: Insights About Multiplication and Implied Order in Combinatorial Enumeration. In Proceedings of the 35th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 409–406). Chicago: University of Illinois at Chicago.

Lockwood, E., Ellis, A., and Knuth, E. (2013). Mathematicians' Example-Related Activity When Proving Conjectures. In Electronic Proceedings for the Sixteenth Special Interest Group of the MAA on Research on Undergraduate Mathematics Education (pp. 179–186). Denver, CO: Northern Colorado University.

Lockwood, E., Ellis, A.E., Dogan, M.F., Williams, C.C.W., and Knuth, E. (2012). A Framework for Mathematicians' Example-Related Activity When Exploring and Proving Mathematical Conjectures. In Proceedings of the 34th Annual Meeting of the North American Chapter of the Psychology of Mathematics Education (pp. 151–158). Kalamazoo, MI: North American Chapter of the Psychology of Mathematics Education.

Lockwood, E., Ellis, A.E., Knuth, E., Dogan, M.F., and Williams, C.C.W. (2013). How Strategically Chosen Examples Can Lead to Proof Insight: A Case Study of a Mathematician's Proving Process. In Proceedings of the 35th Annual Meeting of the North American Chapter of the Psychology of Mathematics Education (pp. 245–252). Chicago.

Nathan, M., Walkington, C., Srisurichan, R., and Alibali, M. (2011). Modal Engagements in Pre-College Engineering: Tracking Math and Science Concepts Across Symbols, Sketches, Software, Silicon, and Wood. In Proceedings of the 118th American Society of Engineering Education Annual Conference and Exposition (pp. 1–32). Vancouver, BC: American Society of Engineering Education.

Walkington, C., and Maull, K. (2011). Exploring the Assistance Dilemma: The Case of Context Personalization. In Proceedings of the 33rd Annual Conference of the Cognitive Science Society (pp. 90–95). Boston: Cognitive Science Society.

Walkington, C., and Sherman, M. (2012). Using Adaptive Learning Technologies to Personalize Instruction: The Impact of Interest-Based Scenarios on Performance in Algebra. In Proceedings of the 10th International Conference of the Learning Sciences (Vol. 1, pp. 80–87). Sydney, Australia.

Williams, C., Akinsiku, O., Walkington, C., Cooper, J., Ellis, A., Kalish, C., and Knuth, E. (2011). Understanding Students' Similarity and Typicality Judgments in and out of Mathematics. In Proceedings of the 32nd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1180–1189). Reno, NV.