Proof comprehension

research group

Upcoming events

Lidia Gonzalez (York College – CUNY), Eileen Murray, and the PCRG are organizing the 3rd Northeastern Conference on Research in Undergraduate Mathematics Education. The conference will be held on October 5, 2019, in York College – CUNY, NY. Further details about registration and abstract submission can be found here.

Recently published papers


  • Inglis, M. & Mejía-Ramos, J. P. (accepted). Functional explanation in mathematics. Accepted for publication in Synthese.
  • Czocher, J. & Weber, K. (accepted). Proof as a cluster concept. Accepted for publication in Journal for Research in Mathematics Education.
  • Harel, G. & Weber, K. (in press). Deductive reasoning in mathematics education. To appear in S. Lerman (Ed.) Encyclopedia of Mathematics Education. Springer: Dordrecht.
  • Mejía-Ramos, J. P. & Weber, K. (accepted). Mathematics majors’ diagram usage when writing proofs in calculus. Accepted for publication in Journal for Research in Mathematics Education.
  • Wasserman, N., Weber, K., Fukawa-Connelly, T., & McGuffey, W. (in press). Designing advanced mathematics courses to influence secondary teaching: Fostering mathematics teachers’ ‘attention to scope’. To appear in Journal of Mathematics Teacher Education.
  • Weber, K. (in press). The role of syntactic representations in set theory. To appear in Synthese.
  • Weber, K. & Czocher, J. (in press). On mathematicians’ disagreement on what constitutes a proof. To appear in Research in Mathematics Education.
  • Weber, K., Lew, K., & Mejía-Ramos, J. P. (accepted). Using expectancy value theory to account for students' mathematical justifications. Accepted for publication in Cognition and Instruction.


  • Weber, K. & Mejía-Ramos, J.P. (2019). An empirical study on the admissibility of graphical inferences in mathematical proofs. In A. Aberdein & M. Inglis (Eds.) Advances in Experimental Philosophy of Logic and Mathematics. London: Bloomsbury.
  • Lew, K., & Mejía-Ramos, J. P. (2019). Linguistic conventions of mathematical proof writing at the undergraduate level: Mathematicians’ and students’ perspectives. Journal for Research in Mathematics Education, 50(2), 121-155.
  • Mejía-Ramos, J. P., Alcock, L., Lew, K., Rago, P., Sangwin, C., & Inglis, M. (2019). Using corpus linguistics to investigate mathematical explanation. In F. Eugen & C. Mark (Eds.) Methodological Advances in Experimental Philosophy (pp. 239-263). London: Bloomsbury.


  • Byrne, M., Hanusch, S., Moore, R., & Fukawa-Connelly, T. (2018) Student interpretations of written comments on graded proofs. International Journal of Research on Undergraduate Mathematics Education, 4(2), 228-253.
  • Johnson, E., Keller, R., & Fukawa-Connelly, T. (2018). Results from a survey of abstract algebra instructors across the United States: Understanding the choice to (not) lecture. International Journal of Research in Undergraduate Mathematics Education, 4(2), 254-285.
  • Krupnik, V., Weber, K., & Fukawa-Connelly, T. (2018). Students’ epistemological frames and their interpretations of lectures in advanced mathematics. Journal of Mathematical Behavior, 49, 174-183.
  • Miller, D., Infante, N., & Weber, K. (2018). How mathematicians assign points to student proofs. Journal of Mathematical Behavior, 49, 24-34.
  • Paoletti, T., Krupnik, V., Papadopoulos, D., Olsen, J., Fukawa-Connelly, T. & Weber, K. (2018). Teacher questioning and invitations to participate in advanced mathematics lectures. Educational Studies in Mathematics, 98, 1-17.
  • Wasserman, N., Weber, K., Villanueva, M., Mejia-Ramos, J.P. (2018) Mathematics teachers’ views about the limited utility of real analysis: A transport model hypothesis. Journal of Mathematical Behavior, 50, 74-89.
  • Weber, K. (2018). Book review: Dialogue, Argumentation and Education: History, Theory and Practice, by Baruch B. Schwarz & Michael J. Baker. Educational Studies in Mathematics, 97, 111-118.
  • Weber, K. (2018). The role of sourcing in mathematics. In J. Braasch, I Bråten, & M. McCrudden (Eds.) Handbook of Multiple Source Use. New York: Routledge.
  • Weber, K. & Dawkins, P. (2018). Toward an evolving theory of Mathematical Practice informing Pedagogy: What standards for this research paradigm should we adopt? In A. Stylianides & G. Harel (Eds.) Advances in mathematics education research on proof and proving. Springer: Dordrecht.
  • Weber, K. & Moore, K. (2018). The role of abstraction in multiple perspectives on mathematical thinking and reasoning. Invited chapter for V. Thompson & L. Ball (eds.) International Handbook on Thinking and Reasoning. Psychology Press.


  • Dawkins, P., & Weber, K. (2017). Values and norms of proof for mathematicians and students. Educational Studies in Mathematics, 95(2), 123-142. [journal]
  • Fukawa-Connelly, T., Weber, K., & Mejía-Ramos, J. P. (2017). Informal content and student note-taking in advanced mathematics classes. Journal for Research in Mathematics Education, 48(5), 567-579. [preprint] [journal]
  • Mejía-Ramos, J. P., Lew, K., de la Torre, J., & Weber, K. (2017). Developing and validating proof comprehension tests in undergraduate mathematics. Research in Mathematics Education, 19(2), 130-146. [preprint] [journal]
  • Stylianides, G., Stylianides, A. & Weber, K. (2017). Research on the teaching and learning of proof: Taking stock and moving forward. In J. Cai (Ed.) Compendium for Research in Mathematics Education (pp.237-266). National Council of Teachers of Mathematics: Reston, VA. [preprint]
  • Wasserman, N. & Weber, K. (2017). Pedagogical applications from real analysis for secondary mathematics teachers. For the Learning of Mathematics, 37(3), 14-18.

Related sites

  • ULTRA. Upgrading Learning for Teachers in Real Analysis is an NSF-funded collaborative project to design, implement, and assess an innovative real analysis course for pre-service and in-service mathematics teachers. [site]