Sum of Squares

What if showing your work IS your work?

I teach an elective, counting things, Combinatorics, really some nice enumeration, with a lot of problem solving approach.

I used to give tests, but they got in the way of learning, and wasted class time, and caused needless stress. So I have small homework assignments, and I have bigger assignments. The bigger assignments I call “write-ups” – they are sort of mathematical lab reports, documenting something that was learned in the course of a full period or so, by way of collaborating in a group…

I also give final projects. Big poster, like from a science fair. And a presentation – something between three and five minutes. No matter how complicated or simple the project, the goal for the presentation is that it can be digested by the student’s classmates. Over the years I have done better at assigning the final project, and the quality of the projects has gone up. Some have been quite good.

In the fall of 2018 a then junior, Z, chose a slightly simpler topic – the sum of the squares – and did an absolutely superior job explaining and extending the problem. She knew it. We all did. Everyone understood what they were watching/hearing as the presentation unfolded.

A year and change later, during the pandemic (and without my knowledge – there was no reason for me to know – just mentioning that I wasn’t part of it) she repackaged the project as a video, attempting to channel Vi Hart, and submitted the product to the Museum of Mathematics and won a communication first prize.

I am proud of her. Also a little intimidated – this is the first student who is so quickly advancing to mathematical knowledge beyond mine – she is currently a college sophomore, math major, doing tough work. And also a little personally proud to have given her a push in this direction. Plus, I can see a bit of my style how she clears the fractions in fractions.

So this here is me, sharing Z’s video. It’s just 2 ½ minutes. Please watch it and say nice things