Being in charge of enrichment was tremendously fun, as it allowed me to bring all sorts of unexpected math into the classroom. I did some preview of integer arithmetic with the Zero Monster in first grade. I told stories about finding a strange talking clock on the beach to introduce modular arithmetic to 4th graders. We had a weekly "math lab" where kids throughout the school mostly solved geometric puzzles. And so on.
Later, when I started to teach high school, I found that there was essentially no time for "enrichment". If I wanted students to do fun math, it seemed like the only option was to do it by way of a math club. That's all well and good, but by definition that leaves most students out. In the following decades, I put most of my efforts as a curriculum developer into instilling an enrichment feel to mainstream secondary school topics such as algebra and geometry, by creating rich curricular activities.
What do I mean by "rich activities"?
- They carry significant mathematical content -- as opposed to easily forgotten microskills
- They are accessible (low threshold): the question is easy to understand, and every student can get started
- They are challenging (high ceiling): there are opportunities to go deep and far -- the question is of interest to the teacher as well as to the student
- They are engaging: they trigger student curiosity, while offering avenues for exploration
- They are student-centered: while the teacher structures and guides the activity, students do the work
- There are many paths through them -- that helps to reduce damaging competitiveness
- There are interesting partial results -- that helps to increase helpful competitiveness
- They are "group-worthy" -- students can work collaboratively, and discourse is enhanced
A tall order you say? True, but it is not impossible to achieve. Here are some examples of rich curricular activities:
my Web site.
That said, I did not totally abandon "enrichment", as I reserved a bit of time and energy for nonstandard topics, which I was forced to put into elective classes. I also enjoyed helping George Hart with the Zome Geometry book. But that does not take away from my main belief: "normal math" can be "fun math", for just about all students, if the curriculum is designed with a puzzle constructor's sensibility.