I'm not a particularly great researcher. You're not going to find a new proof of Fermat's last theorem here I'm afraid. The cult of research is interesting to me. I would have preferred to call this section, "Ideas I have played with" but the first question every mathematician asks every other mathematician is "What is your area of research?" The response is usually a well rehearsed short list in my experience. I have lots of interests and I was always foolishly trying to learn all of math, so I tried to avoid answering this question. For example, I regard The Mistakenator and the computational book I wrote, "Holistic Mathematics", as research involving lot's of math and computer science, but also with an educational objective. Holistic Mathematics involved a lot of investigating integer sequences, a lovely topic at the absolute core of mathematics, and I include some links to the Online Encyclopedia of Integer Sequences (OEIS) below.
In fact, most of my interests have revolved broadly around math, computer science, and education, the areas that I studied in school.
Since I always was, and primarily thought of myself as a teacher, there was always some some blurring of distinction between my teaching activities and my research interests, and this was especially necessary when I taught many classes.
In fact, I finally came to the conclusion that, in retrospect, much of my work could be described as trying to establish the new field of "computational mathematics education". Note, this effort went well beyond merely doing statistics on educational data as this is what many math education researchers do all of the time.
My interest in this is a natural consequence of the confluence of my primary interests, but also, I freely admit, it was an effort to create a counterpoint to the traditional math education narrative in this country which I neither agree with nor understand.
http://oeis.org/A066194 , added a new formula
Holistic Mathematics
The Lightness Distribution in STEM
The Mistakenator