Journal Articles/ Conference Proposals
The incubation effect: How mathematicians recover from proving impasses
(2015) The Journal of Mathematical Behavior
This article is a large part of my dissertation as well as one of the main reasons why I research on creativity in mathematics education. The results include many actions mathematicians do when they are "stuck" or in a proving impasse. Many mathematicians had a particular action that they used frequently when overcoming impasses. A pre-print is located below.
Examining the Proving Differences Between a Mathematician and a Graduate Student Using a Problem-Solving Framework
(2015) Journal of Humanistic Mathematics
This is an extension of the RUME long paper of the 2013 conference. In this paper, I use the Multidimensional Problem-Solving Framework produced by Carlson and Bloom (2005) to examine the proving process of two participants, a mathematician and a Ph.D student in mathematics. I come to conclude that the mathematician is deliberate with his actions, re-evaluating his mistakes on both a local level (correcting "typos") and on a global level (understanding the need for an identity in the semigroup). On the other hand, the graduate student mostly monitored his proving locally. There were parts of the framework itself that could not be used easily in the proving process, prompting the suggestion of a multidimensional proving-process framework.
Conference Presentations/Invited Talks
AMS Sectional Meeting
October 24th-25th, 2015 (Fullerton, CA)
Gulden Karakok and I presented to the American Mathematical Society sectional meeting about our rubric, and how students have taken to using it.
Inquiry-Based Learning (R.L. Moore Legacy) Conference
June 24th-28th, 2015 (Austin, TX)
At the IBL conference, I presented an interactive poster on the CPR on Proving.
Research in Undergraduate Mathematics Education Conference
February 19th-21st, 2015 (Pittsburgh, PA)
In this conference I presented twice, once on the creativity rubric our group created, and about a video game created for optimization in calculus. I was co-author on three other presentations. All five are located below. I was a busy person!
Joint Mathematics Meetings
January 10th-13th, 2015 (San Antonio, TX)
I presented a talk on how to teach calculus II using inquiry-based learning, and was part of a talk with colleagues about transfer of ideas from groups to rings.