## Clicking Useless Buttons and Exponential Models

Last fall, when I was teaching my web design students about jQuery events, I included an example page that counted the number of times a button was clicked and displayed the total. As a clear indicator of their strong engagement in what I asked them to do next, my students competed with each other to see who could click the most number of clicks in a given time period. With the popularity of pointless games like Cookie Clicker , I knew there had to be something there to use toward an end that served my teaching.

Shortly afterwards, I made a three-act video activity that used this concept – you can get it yourself here.

This was how I started a new unit on exponential functions with my Math 10 class this week. The previous unit was about polynomials, and had polynomial regression for modeling through Geogebra as a major component. One group went straight to Geogebra to solve this problem to figure out how many clicks. For the rest, the solutions were analog. Here’s a sample:

When we watched the answer video, there was a lot of discouragement about how nobody had the correct answer. I used this as an opportunity to revisit the idea of mathematics as a set of different models. Polynomial models, no matter what we do to them, just don’t account for __everything__ out there in the universe. There was a really neat interchange between two students sitting next to each other, one who added 20 each time, and another who multiplied by 20 each time. Without having to push too much, these students reasoned that the multiplication case resulted in a very different looking set of data.

This activity was a perfect segue into exponential functions, the most uncontrived I think I’ve set up in years. It was based, however, on a useless game with no real world connections or applications aside from other also useless games. No multiplying bacteria or rabbits, no schemes of getting double the number of pennies for a month.

I put this down as another example of how relevance and real world don’t necessarily go hand in hand when it comes to classroom engagement.