My research interests in mathematics education are in the teaching and learning of undergraduate mathematics. I am currently interested in students' notions of justification in early undergraduate mathematics and implications for teaching proof. I am also interested in equity in undergraduate mathematics  creating equitable learning opportunities for all students at the undergraduate level.
As a graduate student, I assisted on the NSFfunded grant, The Role and Use of Examples in Learning to Prove (Eric Knuth, Amy Ellis, and Orit Zaslavsky, PIs). On this project, I conducted over 30 taskbased interviews with middle school students, high school students, undergraduates, and mathematicians to investigate the roles that examples play in the development and proof of conjectures.
Journal Publications:  Lynch, A. G., & Lockwood, E. (In Press). A comparison between mathematicians' and students' use of examples for conjecturing and proving. Journal of Mathematical Behavior.
 Ellis, A. B, Ozgur, Z, Vinsonhaler, R., Dogan, M. F., Carolan, T., Lockwood, E., Lynch, A. G., Sabouri, P., Knuth, E., & Zaslavsky, O. (In Press). Student thinking with examples: The criteriaaffordancespurposesstrategies framework. Journal of Mathematical Behavior.
 Lockwood, E., Ellis, A. B., & Lynch, A. G. (2016). Mathematicians’ examplerelated activity when exploring and proving conjectures. International Journal of Research in Undergraduate Mathematics Education. 2(2), 165–196.
Refereed Conference Proceedings:
 Lockwood, E., Lynch, A. G., & Ellis, A. B. (2015). Exhaustive example generation: Mathematicians' uses of examples when developing conjectures. In FukawaConnelly, T., Infante, N. I., Keene, K., & Zandieh, M. (Eds.), Proceedings of the Eighteenth Annual Conference on Research in Undergraduate Mathematics Education. pp. 216230. Pittsburgh, PA.
 Lockwood, E., Lynch, A. G., Ellis, A. B., & Knuth, E. (2014). Mathematicians' ExampleRelated Activity in Formulating Conjectures. In Liljedahl, P., Oesterle, S., Nicol, C., & Allan, D. (Eds.), Proceedings of the Joint Meeting of PME 38 and PMENA 36, Vol. 4, pp. 129136. Vancouver, Canada: PME.
Conference Presentations:
 "Mathematicians' Uses of Examples When Developing Conjectures"
 Conference on Research in Undergraduate Mathematics Education, Pittsburgh, PA, February 19, 2015
 "Undergraduates' ExampleRelated Activity in Proving Conjectures"
 Joint Mathematics Meetings, San Antonio, TX, January 10, 2015
 "Mathematicians' ExampleRelated Activity in Formulating Conjectures"

