In order to succeed, your desire for success should be greater than your fear of failure.
To say I had a desire to succeed with this lesson would be an understatement. I showed the Futurama clip to the parents and got all geeked up about how it would enlighten their children to the power of mathematics!!! In the end, it wasn’t the lesson that fell flat, but the sequencing of several lessons. That’s exactly why I’m blogging – so this gets recorded and I (perhaps some others as well) can make that enlightening lesson, you know, enlighten.
I slotted this as the second day of our Recursion unit. Why? Because that’s exactly where the book had the question: If Lucy puts $2000 in a savings account that accrues 7% interest yearly, how much money will the account have after one year?” It is the Futurama question. So, it seemed like it would be the perfect place for it. The prior day we had discussed what recursive definitions were, how to set up tables for sequences, the difference between an arithmetic sequence and a geometric sequence. However, when I wanted to turn to this lesson, we needed more work with these newfangled recursive formulas, what with their subscripts and all.
After spending the needed time to review those finer points, I went to the Fry lesson, but with just 20ish minutes left in class. The kids liked the clip, of course, but I had provided too much help: they were uninterested in finding the result because they knew they would have to push the button 1000 times. In each class I had one person willing to crank out that work. In one class I had someone trying to adjust the problem to an explicit formula.
In the end, I decided I did not properly set up the problem and gave up actually expecting them to find the answer. I showed them a picture of when I pushed the button 1000 times, talked about exponential growth a bit (without actually referring to exponentiation) and how the more money you invest initially, the faster your account can grow.
I think the right way to do this lesson is to not provide any kind of structure for the kids. Show it before we start recursive formulas, do a better job of establishing group norms, and be willing to sacrifice a day to the lesson. If I let my students try to find an answer on their own – without pushing the recursive method – maybe (probably!) they come up with some interesting methods. Maybe they are all completely wrong. And that would be great! Two days later we revisit Fry and find the correct answer. We can still have the discussion of why recursion can by bad and how it would be great to have a faster way to do this.
While it was a little deflating to be so excited for a lesson only to watch it flounder, I feel like my desire to succeed outweighed my fear of failure. Now the question is, next year, will my fear of failure while sacrificing a day stop me from conducting what could still be an excellent introduction to recursion. Of course it won’t, but it will up the ante that much.