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.