Research

My main research goal is to better understand the communicative aspect of mathematical proofs: how mathematicians present proofs and how students write them, with a particular emphasis on the language of mathematical proofs and how undergraduate students come to understand the conventions of this mathematical language. Some of my recent projects focus on mathematicians' and students' identification of unconventional uses of mathematical language in student-constructed proofs and assembling several corpora of professional and student-constructed mathematical text.  

Current Projects:
  • Investigating the Language of Undergraduate Proof Writing
  • Understanding Mathematical Maturity
  • Understanding Mathematical Metaphors and How They Are Used
  • Investigating How Students Approach Prove-or-Disprove Statements
  • Understanding How Students Leverage Their Understanding of Key Concepts in Their Proof Construction
I have also previously worked on the following projects:
  • Validating Proof Comprehension Tests in Mathematics (NSF TUES #1245625)
  • Proving Styles in University Mathematics (NSF REESE #1008641)
  • Construction and Analysis of Expert and Learner Corpora
  • Perspectives on Proof Presentation in Undergraduate Mathematics
  • How Undergraduate Students Interpret Diagrams in Proof
  • Undergraduate Note-taking in Mathematics
  • How Undergraduate Students Use Informal Representations When Writing Proofs
  • Do Generic Proofs Improve Proof Comprehension?

Refereed Journal Publications:

  • Lew, K., Mejía-Ramos, J.P. (Accepted with revisions). Linguistic conventions of mathematical proof writing at the undergraduate level: Mathematicians' and students' perspectives. Journal for Research in Mathematics Education. 
  • Weber, K., Lew, K., Mejía-Ramos, J.P (Accepted with revisions). Using expectancy value theory to account for students' mathematical justifications. Cognition and Instruction.
  • 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.
  • Weber, K., Fukawa-Connelly, T. P., Mejía-Ramos, J.P., Lew, K. (2016). How to help students understand lectures in advanced mathematics. Notices of the American Mathematical Society, 63(10), 1190-1193.
  • Lew, K., Fukawa-Connelly, T., Mejía-Ramos, J.P., Weber, K. (2016). Lectures in advanced mathematics: Why students might not understand what the professor is trying to convey. Journal for Research in Mathematics Education, 47(2), 162-198.
Conference Proceedings:
  • Lew, K. & Mejía-Ramos, J. P. (2016, February). 'It's not an English class': Is correct grammar an important part of mathematical proof writing at the undergraduate level? Presented at the 19th Annual Conference on Research in Undergraduate Mathematics Education. Pittsburgh, Pennsylvania.
  • Lew, K. & Mejía-Ramos, J. P. (2015, November). Linguistic norms of undergraduate mathematics proof writing as discussed by mathematicians and understood by students. To appear in Proceedings of the 37th Conference of the North American Chapter of the Psychology of Mathematics Education. East Lansing, Michigan: Michigan State University.
  • Lew, K. & Mejía-Ramos, J. P. (2015). Unconventional uses of mathematical language in undergraduate proof writing. In Proceedings of the 18th Annual Conference on Research in Undergraduate Mathematics Education. Pittsburgh, PA.
  • Lew, K., Fukawa-Connelly, T., Mejía-Ramos, J. P., & Weber, K. (2014). How a professor uses diagrams in a mathematics lecture and how students understand them. In P. Liljedahl, C. Nicol, S. Oesterle, & D. Allan (Eds.), Proceedings of the 38th Conference of the International Group for the Psychology of Mathematics Education and the 36th Conference of the North American Chapter of the Psychology of Mathematics Education (Vol. 4, pp. 113-120). Vancouver, Canada: PME.
  • Fukawa-Connelly, T., Lew, K., Mejía-Ramos, J. P., & Weber, K. (2014). Why lectures in advanced mathematics often fail. In P. Liljedahl, C. Nicol, S. Oesterle, & D. Allan (Eds.), Proceedings of the 38th Conference of the International Group for the Psychology of Mathematics Education and the 36th Conference of the North American Chapter of the Psychology of Mathematics Education (Vol. 3, pp. 129-136). Vancouver, Canada: PME.
  • Lew, K., Mejía-Ramos, J. P., & Weber, K. (2013). Students' use of informal representations in proof construction. In M. Martinez & A. Castro Superfine (Eds.), Proceedings of the 35th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (p. 324). Chicago, IL: University of Illinois at Chicago.
  • Fuller, E., Mejía-Ramos, J.P., Weber, K., Samkoff, A., Rhoads, K., Doongaji, D, & Lew, K. (2011). Comprehending Leron's structured proofs. In S. Brown, S. Larsen, K. Marrongelle, & M. Oehrtman (Eds.), Proceedings of the 14th Conference on Research in Undergraduate Mathematics Education (Vol. 1, pp. 84-102). Portland, Oregon.




For more research from the Proof Comprehension Research Group, please visit the following webpage.
http://pcrg.gse.rutgers.edu/