Friday, December 10, 2010

Learning as I Teach

I was reflecting upon how you always learn while you teach. This is especially true the first time you teach something, but also true generally, if you keep working at it over the years.

During the last day of review week for midterms, a Precalc kid asked me for help with a problem from the textbook. The problem describes a worm that is 5 cm on Day 1 and grows 3 cm the next day, and grows 1.8 cm the next day, etc. Each subsequent day, the worm grows 60% from the day before. What's the total length after 2 weeks?

So, I showed the kid how to use the geometric series formula u1(1-r^k)/(1-r) to find the sum of this geometric series. Then, the kid asked me, "But why can't we just use 5(1.6)^(n-1) as our formula, since the worm is growing 60% each day?" Took me a few minutes to think through it, and in the end I felt really silly about it all, because the difference is obvious as daylight.

The worm is not growing 60% everyday. If it were, it'd be growing exponentially faster! Instead, its amount of daily/incremental growth is diminishing at a rate of 0.6 (losing 40%) each day.

It's always so fun teaching something for the first time, because when kids ask me questions, I still have to do a double take on some topics with which I am rusty. :) (And then in real time, try to think of the best way to break it down.) Does this happen to you??

Anyway, MIDTERMS START TODAY!!!