My research interests include inventing and improving upon mathematical pedagogy. For my doctoral dissertation, I wrote a textbook for a basic course linear algebra which uses MATLAB software in self-tutorial exercises. Math education, particularly involving the proper use of instructional technology, was my first academic passion, but these days I've expanded to research in science education in general, and interdisciplinary pedagogy.
A few years ago, I was invited to Montreal to be a session speaker at the 1999 Winter meeting of the Canadian Mathematical Society (Societe Mathematique du Canada). Soon after, I was invited to deliver a one-hour lecture to the general audience of the Ninth International Colloquium on Numerical Analysis and Computer Science with Applications, held last August in Plovdiv, Bulgaria. My related paper was published in its proceedings. Click here for a copy of the paper, in PDF format, which offers an overview of instructional technology usage in teaching linear algebra and numerical analysis, with an admittedly North American bias.
I later took an additional interest in K-12 mathematics education, probably because I now act as Director of UDM's Master of Arts in the Teaching of Mathematics (MATM) program. Nancy Dwyer, Kathy Zhong, Betty Causey-Lee, and I worked on a grant from the Michigan Mathematics Forum (MMF) to revamp UDM's MTH 477 course. Subsequently, Nancy and I have coauthored a paper for the journal "Teaching Mathematics in the Middle School," along with Sharon Laing (an MATM graduate student) and Mark Fratella (a local middle school teacher), a copy of which can be found here in PDF format. I apologize for the poor quality of the scan.
A few years later, with Stokes Baker (UDM Biology) and Deb Hydorn (Mary Washington College, Statistics), I was asked to co-chair the Math/CS/Biology branch of a Project Kaleidoscope initiative, funded jointly my the Mathematical Association of America (MAA) and the National Science Foundation (NSF). It involved a nationwide study to identify the common trends and characteristcs of productive interdisciplinary collaboration between mathematics and biology at two-year colleges and four-year liberal arts and comprehensive universities. Click here for a .PDF file of the paper that came out of it, published in the MAA tradebook Math and BIO 2010: Linking Undergraduate Disciplines.
One of my current projects involves the use of "secret codes" in a middle school setting. These "codes" are simple encryptions using linear congruences. Learning them requires only basic arithmetic operations, yet repeated use of them in game play supplies not only arithmetic drillwork but also foreshadows numerous, more advanced concepts in algebra and number theory. I received a mini-grant for the idea and am looking for a few good undergraduate math education majors and a willing middle school to try it out.