Introducing Differentials with Stock Predictions
The Space Between the Numbers commented on my last post that some people call launch problems like the infection one I did for concavity “Anchor Problems,” the idea being (and I quote from her) “you can keep referring back to the problem to help students latch onto the new learning by remembering this solid, relate-able context.” I think that this describes what I was trying to do perfectly, and I love having new language to talk about my teaching. So, thanks for that!
I wanted to share one more Anchor Problem that I am using in my AP Class tomorrow to introduce Differentials (which I used to what I thought great success in my non-AP class last year). I am relating the idea of making a prediction with differentials/a tangent line to making stock predictions. With charts like this:
… I’m going to have them predict the stocks price in the near and far future using the graph in any way they can. Most students last year figured out to draw a tangent line, use the slope of that tangent line to see how fast it is changing currently and then multiply that by the number of months to get the change in price, and then add that to the original price. It’s an intuitive idea that sounds way more complicated when you try to describe it. I added the “% confidence column” this year to try to get at the idea of a prediction being less and less accurate the further you are from known data.
Eventually, I want us to codify our process into a rough equation like this:
Which we can then use to look at the “equation” for using differentials:
(I think my face is crooked… I always write slopey)
This worked well last year because even when we were solving abstract problems that had nothing to do with stocks, I would ask questions like “well, how fast is your stock changing right now?” and “how many months in the future or past are we predicting?“ which served to connect the abstract to the intuitive situation. I also think it gave students a mental picture of what they are doing.
Hope it works this year too…