The machine analogy gives students something to "hold on to" in terms of understanding functions. The analogy also carries over well when we start inverse functions where now the inverse is working in reverse. If in the original function we put in 1 and got out 3, when we press the reverse button (inverse function) and put in a 3 we should get out a 1.
But when I get to transformation of functions (reflections, dilation, etc.), it gets a little harder to carry on the metaphor.
I initially used the idea of tweaking the machine, and that works a little, but in the end we just work through notes and examples. And that isn't too fun, until... I had a student ask me why we even need to know these transformations, and I found I didn't have any idea. Basically, transformations were just the next thing in the curriculum.
I accept that some math at this level is just going to be theoretical particularly if you are not applying it to a science or if you are not a mathematician, but I was curious. I asked a bunch of my friends who work in S.T.E.M. fields, and I couldn't find anyone who uses transformations of functions, a couple of them even needed a reminder as to what transformations were.
Next, I did an Internet search. I didn't find much, but one of the interesting applications was the use of function transformations in digital animation software. In animation the figure is moved a little bit or even sometimes stretched. Now, I was excited about transformations of functions. I'm sure you can guess what we did next.
First, I showed students this brief animation video from animator, Glen Keane. Then, after copious notes on different types of transformations and a card sort activity, we had some fun with transformations of functions. I gave students flip book pages with graphs pre-printed on them. Students drew a function on the first page. It could be as simple as f(x) = x.
The unit was a win in that students:
- Developed a strong understanding of functions and transformations,
- Saw a real life application of a math concept, and
- Were actively engaged in learning.
Tags: Math Mondays