# Accomplishments of the Prior Fellowship

*What has the experience been like for former fellows in the UW postdoctoral program?*

**Comments from previous postdoctoral fellows (2010-2013) about the Postdoctoral Training Program in Mathematical Thinking, Learning, and Instruction at the University of Wisconsin-Madison.**

“This training program has afforded me the opportunity to learn the nuances of mathematics education research through a variety of research projects, courses, colloquia and collaborations with current mathematics education researchers.”

“I have had an incredibly positive experience in my time as a postdoc through the IES’s training program at UW. Not only have I gained valuable interdisciplinary experiences, but also I have grown as a mathematics education researcher, forged meaningful collaborations, furthered my own research agenda, and gotten my ideal tenure-track position. I owe these successes to this program”

“The numerous available resources coupled with strong interdisciplinary working relationships makes this program truly unique and an amazing opportunity for fostering the development of future mathematics education researchers.”

** “**In my experience, UW – Madison is unique in the extensive amount of ollaboration among faculty,
postdoctoral fellows, and students. The collaborative atmosphere is conducive to high quality research
and open communication of ideas; it is a pleasant and productive working environment. The
collaboration is as extensive in practice as it is portrayed on paper. Having this degree of collaboration
and department support across various education and psychology specialties is an important strength of UW-Madison’s application.”

** “**Put simply, the mentorship I am receiving … is absolutely invaluable, and I am certain that my relationships with them (and things I have learned from them) will continue to have a positive impact on my career for many, many years.”

# Here are many of the intellectual products and activities from prior postdoctoral fellows.

## Cooper, J. (2010-2012)

Degree: Rutgers (PhD. Psych)

### **Fellowship Projects **

National Center for Cognition and Math Instruction (NCCMI, IES funded)

Understanding and cultivating the connections between students’ natural ways of reasoning and mathematical ways of reasoning (IDIOM, NSF funded)

**Current Position**

Research Associate, Wisconsin Center for Education Research, U. Wisconsin-Madison

**Select Fellowship Publications**

**Cooper, J. L.**, & Dogan, M. F., Young, A. G., & Kalish, C. W. (2012). Stronger arguments within inductive generalization in middle school mathematics. *Proceedings of the annual meeting of Psychology of Mathematics Education, North American Chapter.*

**Cooper, J. L.**, & Alibali, M. W. (2012). Visual representations in mathematics problem-solving: Effects of diagrams and illustrations. *Proceedings of the annual meeting of Psychology of Mathematics Education, North American Chapter.*

Walkington, C., **Cooper, J.,** Kalish, C., & Akinsiku, O. (2012). How middle school students reason differently in everyday and mathematical contexts: Typicality and example choice in mathematical justification. *Proceedings of the annual meeting of Psychology of Mathematics Education, North American Chapter.*

**Cooper, J. L.**, Walkington, C.A., Williams, C. C., Akinsiku, O. A., Kalish, C. W., Ellis, A. B., & Knuth, E. J. (2011). Adolescent reasoning in mathematics: Exploring middle school students’ strategic approaches in empirical justifications. *Proceedings of the 33rd Annual Conference of the Cognitive Science Society, *Boston, MA.

Williams, C., Akinsiku, O., Walkington, C., **Cooper, J.**, Ellis, A., Kalish, C., Knuth, E. (2011). Understanding students’ similarity and typicality judgments in and out of mathematics. *Proceedings of the 32nd annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education,* Reno, NV.

## Walkington, C. (2010-2012

Degree: U. Texas-Austin (PhD. Curriculum & Instruction)

**Current Position**

Asst. Prof. Dept. of Teaching & Learning, Simmons School of Education & Human Development, Southern Methodist University

**Fellowship Projects**

Tangibility for Teaching, Learning and Communicating Mathematics

Understanding and cultivating the connections between students’ natural ways of reasoning and mathematical ways of reasoning (IDIOM)

Supporting Robust Learning by Personalizing Instruction in Algebra to Students’ Out-of-School Interests
(PI): Institute of Educational Sciences, 2013-2017. (Submitted)

Personalizing Algebra Instruction to Students’ Interests (PI): Pittsburgh Science of Learning Center, 2012-2014. (Funded)

**Select Fellowship Publications**

Cooper, J., **Walkington, C.**, Williams, C., Akinsiku, O., Kalish, C., Ellis, A., & Knuth, E. (2011). Adolescent reasoning in mathematics: Exploring middle school students’ strategic approaches to empirical-based justifications. In L. Carlson, C. Hölscher, & T. Shipley (Eds.), *Proceedings of the 33rd Annual Conference of the Cognitive Science Society *(pp. 2188-2293). Boston, MA: Cognitive Science Society.

Nathan, M., Alibali, M., Wolfgram, M., Srisurchan, R., Felton, M., & **Walkington, C. **(2011). Threading mathematics through symbols, sketches, software, silicone, and wood: Tailoring high school STEM instruction. Paper presentation at 2011 American Education Research Association Annual Meeting, New Orleans, LA.

Nathan, M., Srisurchan, R., **Walkington, C.**, Wolfgram, M., Williams, C., & Alibali, M. (in press). Cohesion as a Mechanism of STEM Integration. *Journal of Engineering Education*.

Nathan, M., **Walkington, C.**, Srisurichan, R., & 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*. Vancouver, CA.

**Walkington, C.** (2012). Context Personalization in Algebra: Supporting Connections between Relevant Stories and Symbolic Representations. Paper presentation at 2012 Annual Meeting of the American Educational Research Association. Vancouver, Canada.** **

**Walkington, C.**, Cooper, J., Kalish, C., & Akinsiku, O. (in press). How middle school students reason differently in everyday and mathematical contexts: Typicality and example choice in mathematical justification. To appear in *Proceedings of the 33rd annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education*. Kalamazoo, MI.

**
Walkington, C.**, & Maull, K. (2011). Exploring the assistance dilemma: The case of context personalization. In L. Carlson, C. Hölscher, & T. Shipley (Eds.),

*Proceedings of the 33rd Annual Conference of the Cognitive Science Society*(pp. 90-95). Boston, MA: Cognitive Science Society.

**, Nathan, M., Wolfgram, M., Alibali, M., & Srisurichan, R. (in press). Bridges and barriers to constructing conceptual cohesion across modalities and temporalities: Challenges of STEM integration in the precollege engineering classroom. Chapter in**

Walkington, C.

Walkington, C.

*Engineering in PreCollege Settings: Research into Practice.*Johannes Strobel, Senay Purzer, Monica Cardella, (Eds.), Sense Publishers.

**, Petrosino, A., & Sherman, M. (in press). Supporting algebraic reasoning through personalized story scenarios: How situational understanding mediates performance and strategies.**

Walkington, C.

Walkington, C.

*Mathematical Thinking and Learning*.

**Walkington C**., Petrosino, A., & Sherman, M. (2011). The impact of personalization on problem-solving in algebra. Paper presentation at 2011 American Education Research Association Annual Meeting, New Orleans, LA.

**Walkington, C.**, & Sherman, M. (2012). Using adaptive learning technologies to personalize instruction: The impact of interest-based scenarios on performance in algebra. In van Aalst, J., Thompson, K., Jacobson, M., & Reimann, P. (Eds.), *Proceedings of the 10th International Conference of the Learning Sciences*. Sydney, NSW, Australia.

**Walkington, C**., Sherman, M., & Petrosino, A. (2012). ‘Playing the game’ of story problems: Coordinating situation-based reasoning with algebraic representation. *Journal of Mathematical Behavior*, *31*(2), 174-195.

**Walkington, C.**, Srisurichan, R., Nathan, M., Williams, C., & Alibali, M. (2012). Grounding Geometry Justifications in Concrete Embodied Experience: The Link between Action and Cognition. Paper presentation at 2012 Annual Meeting of the American Educational Research Association. Vancouver, Canada.

Williams, C., Akinsiku, O., **Walkington, C**., Cooper, J., Ellis, A., Kalish, C., 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*. Reno, NV.

Williams, C., **Walkington, C.**, Boncoddo, R., Srisurichan, R., Pier, L., Nathan, M., & Alibali, M. (in press). Invisible proof: The role of gestures and action in proof. To appear in *Proceedings of the 33rd annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education*. Kalamazoo, MI

## Boncoddo, R. (2011-2013)

Degree: U Conn-Storrs (PhD, Psych)

### Current Position

Assistant Professor of Psychological Science, Central Connecticut State University

**Fellowship Projects**

Tangibility for Teaching, Learning and Communicating Mathematics

Promoting Discriminative and Generative Learning: Transfer in Arithmetic Problem Solving

**Select Fellowship Publications**

Williams, C. C., Walkington C., **Boncoddo, R. A**, Srisurichan, R., Pier, E., Nathan, M. & Alibali, M. (2012). Invisible proof: The role of gestures and actions in proof. *Proceedings of the 33rd annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education*. Kalamazoo, MI.

## Lockwood, E. (2011-2013)

Degree: Portland State University (PhD., Mathematics & Statistics)

**Current Position**

Assistant Professor, Dept. of Mathematics, Oregon State University

**Fellowship Projects**

Understanding and cultivating the connections between students’ natural ways of reasoning and mathematical ways of reasoning (IDIOM)

How Do Instructional Gestures Support Students' Mathematics Learning? (HIGHLITE)

**Select Fellowship Publications**

**Lockwood, E.** (2012). Both answers make sense! Using the set of outcomes to reconcile differing answers in counting problems. *Mathematics Teacher*.

**Lockwood, E.** (2012). Counting using sets of outcomes: Do I really have to list all of the possibilities? *Mathematics Teaching in the Middle School*.

**Lockwood, E.** (2012). A Model of Students’ Combinatorial Thinking. In the *Electronic Proceedings for the Fifteenth Special Interest Group of the MAA on Research on Undergraduate Mathematics Education*. Portland, OR: Portland State University. February 23-25, 2012.

**Lockwood, E**. (2012). Students’ uses of smaller problems when counting. *Proceedings of the 34th Annual Meeting of the North American Chapter of the Psychology of Mathematics Education* (Kalamazoo, MI).

**Lockwood, E.**, Ellis, A. E., Dogan, M. F., Williams, C. C. W., & Knuth, E. (2012). A framework for mathematicians’ example-related activity when exploring and proving mathematical conjectures. *Proceedings of the 34th Annual Meeting of the North American Chapter of the Psychology of Mathematics Education* (Kalamazoo, MI).

Ellis, A. E., **Lockwood, E.,** Williams, C. C. W., Dogan, M. F., & Knuth, E. (2012). Middle school students’ example use in conjecture exploration and justification. *Proceedings of the 34th Annual Meeting of the North American Chapter of the Psychology of Mathematics Education* (Kalamazoo, MI).

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