I am building this site, primarily, as a reference for me, and to some extent my students. I like to investigate different mathematical perspectives to develop a particular concept. Doing so deepens my understanding and enables me to teach my students using the mathematics with which they are most comfortable.
Also, through this site, I hope to collaborate and to discuss mathematics and mathematics education with people from around the world.
Hopefully, this site is self-explanatory. Each menu, except one, has a description of its contents and current organization. ‘Recent Posts’ will contain, primarily, my interpretations regarding many issues in mathematics education and interesting math problems or solutions.
The ‘Search’ field will search the entire site including tags.
The platform for generating this site is WordPress.
Most of the mathematical notation in this site is rendered using MathJax.
The interactive information is generated using Mathematica and can be viewed using Wolfram’s Free CDF Player.
It is inevitable that there will be errors in this site. Hopefully, the majority of errors will be typographical in nature. However, I am sure from time to time I will make a serious mathematical error. I am not troubled by this for two reasons. First, I am hopeful that my readers will correct me. Second, Neils Bohr once said, “An expert is someone who has made every possible mistake in a very narrow field.” I think of each of my mistakes and the mistakes of others as one mistake closer to being an expert.
Hi, my name is Robert. I am a mathematics teacher and tutor. Teaching is both personally satisfying and professionally gratifying to me. I cannot seriously imagine being anything else.
After five years at university, and working two jobs for most of those years, I graduated with a double-major in physics and Classics focusing on Latin. In my last year of university I took a job working with underprivileged youth helping them to reach state proficiency standards in mathematics and science. It was during this time that I caught the “teaching bug.” After university graduation I continued to work with the students on a volunteer basis. Over the next two years I enjoyed volunteering more than my paid job. I realized teaching was my vocation.
Initially, I earned certification to teach physics and did so for two years until I changed districts. Hoping to secure another physics position I interviewed with a principal that indelibly changed my teaching trajectory. During the interview, which was going well from my perspective, the principal said, “What I really need is an AP Calculus teacher. Can you teach calculus?” to which I responded, “I’ve never taught calculus but I know it.” I was hired shortly thereafter. In hindsight that was a rather naive statement. What I “knew” at the time was calculus from a physicist’s or engineer’s perspective. I did not truly understand calculus from a mathematician’s perspective.
As I began teaching calculus I was very fortunate to have students that asked some very insightful questions. My students inspired me to begin studying calculus from a mathematician’s point of view. I began to study and learn about the rigorous logical structure of calculus, as well as its historical development. It was fun to learn that some of the very concepts that mathematicians struggled to make precise my students were naively questioning themselves. Finally, as I continued to learn new mathematics I would periodically pause and ask myself “how can this knowledge improve my instruction? Is there another perspective here that might facilitate my students’ learning.” I refer to this as my teaching filter.
I study new mathematics or try to solve unfamiliar problems nearly every day because it is fun and I love learning. I still use my teaching filter for all the new mathematics that I encounter. While it is true that I do not teach most of what I know, that knowledge continues to improve and inform my teaching. This is what makes me different from many math teachers; I like to go home and learn more math because it is fun, and I as I learn more math I ask myself “how can this improve my professional practice.”
What can I say, I like teaching and learning mathematics.