When Students are Better at Math than You

I’ve discovered this week that if you ever want to be humbled, coach a student for the Waterloo Math Contest. I’ve been volunteering at HSC this winter, and one niche I’ve fallen into is running prep for students who want to write the Fermat and Euclid math contests. The Fermat contest is quite challenging, but doable. The Euclid, on the other hand, sometimes seems near impossible. Questions generally fall into 7 categories:

1.     Logarithms and Exponents

2.     Functions and Equations

3.     Analytic Geometry

4.     Trigonometry

5.     Sequences and Series

6.     Circle Geometry

Although it’s not listed as a category, there is also a fair bit on combinatorics, though I suppose that that would fall in as a combination of functions and series. I have personally found having to prepare for these study sessions a great challenge to my knowledge and I would encourage anyone interested to work through some of the prep material (http://www.cemc.uwaterloo.ca/contests/euclid_eWorkshop.html) as part of their own professional development. The hardest one by far is the circle geometry, I still can’t solve some of those problems. Even given the solution, I have difficulty understanding the logic.

In doing this contest prep, not only has my understanding of math (particularly stats) sharpened, but it’s helped me know what to do when I get a student who is smarter than me. One student I help in particular is a true genius. When I give him a problem, he launches immediately into a proof and it takes all my concentration to keep up with his train of thought. Sometimes I think I catch a mistake, but often I’m wrong. It has shown me how to make mistakes as a teacher, but not let that diminish my authority in the subject. I think we sometimes place a burden on ourselves to know everything, and knowing how to cope with mistakes has been a valuable learning experience for me. I’ve also realized, even though this student is much, much smarter than me, I still know more than he does so I don’t have to feel like I have nothing to offer.