Research

My primary research interest is in the area of Mathematics Education. In part because of this I decided to seek a Doctor of Arts degree at the University of Miami. The DA is a terminal doctorate that emphasizes teaching and education rather than traditional mathematics research. It differs from the PhD in that it requires 15 credits in education in place of a fourth qualifying exam and the thesis can either be a treatise covering a purely mathematical topic or can deal with math education rather than pure math.

As an educator, I am motivated to better understand how my students process information and conceptualize ideas. I also want to understand the obstacles that hinder them in these endeavors. My thesis focused on the second matter. I considered two affective variables, mathematics anxiety and learned helplessness and investigated the interplay between them. In following up on this research I have done a set of case studies that further illuminate the relationship between these two variables. These in turn have suggested additional questions. One possible avenue of research that could greatly enhance these studies would be the development of an instrument to measure helplessness in mathematics directly, rather than through its relationship to other factors.

Since I was in elementary school, I’ve been fascinated by U. S. History and elections, especially United States Presidential Elections. In the past few years, that’s led me to an interest in the mathematical field of “Voting Theory.” Voting Theory looks at different ways of conducting elections, the properties of these systems and how using these systems might have affected the outcomes of different historical elections. In the summer of 2009, I worked with Ashley Althouse ’11, one of the students involved in our summer research program. Together we looked at the 2008 Minnesota Senate election and created an application for the MAPLEsoft Application Center. Ashley is following up with an investigation of equivalence classes of Saari Representation Triangles and will be presenting her results at a forthcoming professional conference. I am currently working on a paper about the 2004 U. S. Presidential Election and some property of range voting and evaluative voting.

My other main interest and, for me, one of the most enjoyable parts of teaching mathematics lies in developing materials for students. One recent refereed publication is an activity for Calculus students published through the Wolfram Demonstrations Project. At the University of Miami, a colleague and I developed a series of Mathematica labs for an interdisciplinary course linking calculus and biology. Since then I have created extensive sets of labs using different programs and technology for PreCalculus, Calculus I, II and III and Statistics. In 2003 I developed a series of handouts on cryptography for a Finite Mathematics class at the University of Miami, which allowed me to interweave mathematics with history. These handouts formed the basis for a course in Cryptography that I developed and offer at Elmira College. In Spring Term 2006 I extended the idea of interweaving mathematics and history in a course entitled “A Mathematician Looks at American History.” One of the most important things we can do to motivate students to study mathematics is to demonstrate its usefulness. Developing curricula that link mathematics with other subjects, especially those not traditionally associated with it is an important means of accomplishing this goal.

Some Samples:
A Presidential Election Game: 2016 Edition written with Nguyen and Petkovsek.
            Written in Maple; Download and open in Maple.
Presidential Election Game 2016 Game Data
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Presidential Election Game 2016 Worksheet
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