I enjoy mathematics and I am probably more mathematically educated than 95% of the U.S. population. I say this not to brag, but to provide context for what I’m about to say. There are many aspects of K-12 mathematics that I have never considered deeply, despite the many hours I have spent learning and teaching mathematics. Every time I encounter one of these aspects, I feel cheated. How is it that someone who has dedicated years to studying mathematics was never challenged to consider some pretty basic, foundational ideas?
If I have not grappled with these ideas, it is not likely children have either. This is problematic for many reasons. The most important of these reasons (IMO) is that mathematics is fun. When I say mathematics, I don’t mean simple computations, though they can be, but rather trying to understand challenging mathematical ideas is simply fun. People often fail to see mathematics as fun (or useful), probably because it is hard to get excited about repetitious procedures and rote memorization – the unfortunate cornerstones of mathematics education in the U.S. In this blog I will try to uncover some aspects of mathematics that you may have missed in school.
Currently, I am a mathematics educator. Basically, this means I teach people how to teach mathematics and I also research the teaching and learning of mathematics. When I was a teacher I had no idea that a number of people had researched some problems I was encountering in my day-to-day. In fact, many really intelligent people have been studying the teaching and learning of mathematics for a long time. Unfortunately, many of these papers are extremely inaccessible to those outside of academia, both in terms of cost and readability. I am going to try to make some of this work more accessible through this blog. As a former public school teacher, I will try to point out the practical applications of some of this work to help connect these ideas to the people who might actually put the ideas into practice.
So to recap, this blog is about really digging into to some things that will help people become more mathematically educated. I will bring up a number of fun mathematical ideas that I have thought about (and continue to think about) over the years and I will also try to translate research into a more useful format. I welcome feedback, questions, and conversation as you read through my thoughts.