by Mindy Capaldi

Last year I completed my first year here at VU as a visiting professor.  During that time, I worked on revising and submitting a paper on algebraic topology that included topics from my dissertation. This year I have transitioned to a tenure-track position while also moving into the field of  mathematics education research. During this hiatus from topology research I hope to analyze the language and content of abstract algebra textbooks, investigate methods of teaching proofs, and delve into the pedagogy of  inquiry-based learning (IBL).

After developing and teaching an online Finite mathematics course during the early months of summer, I spent much of my time on the textbook study. My current work is still in that area. Research on proof techniques and inquiry-based learning will begin in earnest this spring as I teach abstract algebra. I hope to teach the class with very little lecture and instead many discussions and presentations by the students, much like the way MATH 110 is taught at VU. Also in abstract algebra, I plan to teach and require rigorous proof techniques that I think will help the students as they struggle to understand the process of proof-writing and reasoning. This research will likely not be finished this year, since I will need to compare several  semesters of student assessment and evaluations. In the meantime, I am teaching Finite mathematics as a semi-IBL class and hope to present my method and its success or lack thereof at the Joint Mathematics Meeting in January.

Although this transition to mathematics education research is not easy, I am very excited about it. I believe that it will benefit me both as a scholar and a teacher, and therefore will also be of advantage to my students.