For several years now I have taught an Olympic Math interest course at the Grand River Chinese School. This is a weekly, one-hour course on topics in mathematics that students might see on contests, but probably not in their regular curriculum.
I have gradually begun to make available the lesson plans I have used for teaching this course. Indeed, the Number Theory unit is in a state that I am very happy with. I will hopefully soon upload the homework and quizzes for the classes as well to that web page.
During this post, I’d like to reflect on some of the things that I found useful, and some attempts that I found did not work well. Finally, I give a proposed new curriculum that I would love to try out next year.
What Worked Well
- True or false questions. This seems a really minor point, but I have come to believe that this style of question is ideal for students of this age. True or false questions let me ask questions that involve mathematical reasoning, not just computation, without forcing the students to write down their justification. It also develops a student’s intuition.
- Geometry (and measurement). I always start the year off with this unit; it’s very accessible, great for developing intuition, and is also helpful for students who write math contests. Next year I might not start with measurement, but that decision is hard for me to make because of the success this unit has had.
What Didn’t Work Well
- I tried to teach classical logic to the students two years ago or so. It wasn’t a good idea. Students at this age don’t have the experience to understand the rigor involved in classical logic; they need something that is easier to intuit and construct. In the future I’d like to revisit logic, but teach a constructive, intuitionist logic instead.
- Algebra. While a lot of teachers do cover this in their curricula, and many of them succeed, I have never really been able to motivate algebra in a way that students are engaged in. It doesn’t help that this subject is probably going to be covered in school for them soon. Instead, this year I’m taking an approach where I get them used to variables by using them on the homework, lessons, and quizzes.
The Next Step
My goal for next year is to start and teach just one unit for the four months I’ll be here: discrete mathematics. This will include discussion on sets, multisets, pairs, tuples, and other collections; functions and relations; the proposed revision of intuitionist logic; induction and recursion; algorithms and algorithm design; and finally, probability and combinatorics. This might seem like a lot, and indeed it is. But I think this particular way of ordering the subjects will allow me to cover them in the four months.