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.
- Investigating the Language of Undergraduate Proof Writing
- Understanding Mathematical Maturity
- Investigating How Students Approach Prove-or-Disprove Statements
- Identifying Metaphors Mathematicians Use to Describe Mathematical Practice
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?