During my first ten years as a teacher, I worked in elementary schools. In addition to team teaching my own class (grade 3, then 4, then 5) I was a math specialist for grades K-5. The basic idea was that there was “normal” math (a lot of arithmetic, textbook-based), and there was “enrichment” math. I was in charge of the latter.
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
What do I mean by “curricular”? Rich curricular activities are related to topics that both teachers and students already consider to be part of their job to teach and learn. On the one hand, this makes it possible for teachers to incorporate them with less anxiety, as they do not compete with the perceived need to “cover” material. On the other hand, it helps to get student buy-in, especially since the activities are automatically compared with less inspiring day-to-day drudgery.
A tall order you say? True, but it is not impossible to achieve. Here are some examples of rich curricular activities:
And there are many more throughout 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.