# Research

My research focuses on the teaching and learning of undergraduate mathematics. Much of my recent work has focused on the role of examples in conjecturing and proof. I am also interested in support structures in mathematics for first-year undergraduate students (as alternatives to developmental math) and creating equitable learning opportunities for all students at the undergraduate level.

## Journal Articles

Lynch, A.G., Lockwood, E., & Ellis, A.B. (2022). Comprehensive example generation: mathematicians' uses of examples when developing conjectures. Research in Mathematics Education

Goyer, A., Lynch, A. G., & Wand, J. (2021). A Redesign of Precalculus at California State University, Monterey Bay. PRIMUS, 31(3-5), 492-503.

Vinsonhaler, R., & Lynch, A.G. (2020). Students' understanding of counterexamples. Mathematics Teacher: Learning and Teaching PK-12, 113(3).

Lynch, A. G., & Lockwood, E. (2019). A comparison between mathematicians' and students' use of examples for conjecturing and proving. Journal of Mathematical Behavior, 53, 323-338.

Ellis, A. B, Ozgur, Z, Vinsonhaler, R., Dogan, M. F., Carolan, T., Lockwood, E., Lynch, A. G., Sabouri, P., Knuth, E., & Zaslavsky, O. (2019). Student thinking with examples: The criteria-affordances-purposes-strategies framework. Journal of Mathematical Behavior, 53, 263-283.

Lockwood, E., Ellis, A. B., & Lynch, A. G. (2016). Mathematicians’ example-related activity when exploring and proving conjectures. International Journal of Research in Undergraduate Mathematics Education, 2(2), 165–196.

Lynch, A. G. (2015). Cauchy Pairs and Cauchy Matrices. Linear Algebra and its Applications, 471, 320-345.

Bleak, C., Bowman, H., Lynch, A. G., Graham, G., Hughes, J., Matucci, F., & Sapir, J. (2013). Centralizers in R. Thompson's group V_n. Groups, Geometry, and Dynamics, 7(4), 821-865.

## Refereed Conference Proceedings:

Ellis, A. B., Lockwood, E., & Lynch, A. G. (2020). Empirical Re-Conceptualization: Bridging from Empirical Patterns to Insight and Understanding. In Karunakaran, S. S., Reed, Z., & Higgins, A. (Eds.), Proceedings of the 23rd Annual Conference on Research in Undergraduate Mathematics Education. pp. 159-167. Boston, MA.

Lynch, A.G., & Pugh, R. (2018). Early Undergraduates’ Emerging Conceptions of Proof and Conviction. In Weinberg, A., Rasmussen, C., Rabin, J., Wawro, M., & Brown, S. (Eds.), Proceedings of the Twenty-first Annual Conference on Research in Undergraduate Mathematics Education. pp. 917-923. San Diego, CA.

Lockwood, E., Lynch, A. G., & Ellis, A. B. (2015). Exhaustive example generation: Mathematicians' uses of examples when developing conjectures. In Fukawa-Connelly, T., Infante, N. I., Keene, K., & Zandieh, M. (Eds.), Proceedings of the Eighteenth Annual Conference on Research in Undergraduate Mathematics Education. pp. 216-230. Pittsburgh, PA.

Lockwood, E., Lynch, A. G., Ellis, A. B., & Knuth, E. (2014). Mathematicians' Example-Related Activity in Formulating Conjectures. In Liljedahl, P., Oesterle, S., Nicol, C., & Allan, D. (Eds.), Proceedings of the Joint Meeting of PME 38 and PME-NA 36, Vol. 4, pp. 129-136. Vancouver, Canada: PME.