One of my most interesting students spent his free-period chatting about math education with me today. He’s very willing to tell me exactly what he doesn’t like about math books, math class and certain students approaches to mathematics.
Today we discussed another student who he thought had a silly approach to math. She tries to memorize everything and doesn’t understand a lot. “Why would you want to do that?” he asks. I’m in total agreement with him but I offer that some kids just prefer thinking on the memorization level of Bloom’s taxonomy because it is easier than synthesis and analysis. I’m glad that at least Perry thinks that understanding why math works is a noble pursuit. I think that is why he likes me as a teacher enough to spend so much time sharing his thoughts about math education.
Then we started discussing volumes of revolution which he told me a few days earlier that he didn’t understand. The lack of understanding centered on the issue of not understanding that f(x) represented the distance between the x-axis and the function. Students tend to see it as a coordinate of point rather than a distance and I’m not exactly sure why. We’d been over this before when the class had bombed a similar question on a test but it was my mistake to assume that it made sense to everyone. It’s amazing how much in Calculus on understanding f(x) is a representation of a distance on a graph. Yeah analytic geometry! Thank you Descartes.
Then we started discussing textbooks and he mentioned a problem that he’d been particularly annoyed by. The problem was: Find the volume formed by revolving the following region around the x-axis:
y=x, y=0, x=0, x=4.
“Look at this problem. It takes at least two inches to write. It’s so mushed together. It took me a minute to recover from the fact that it had so many letters right in a row and then I had to rewrite it spaced out and finally I understood I just needed to graph everything separately. Why don’t authors lay things out in a visually appealing way? Couldn’t we put really well-written, high quality examples in a book a 4th the size and put all the problems online in a visually appealing manner? I know we are not at the point where we are going to be carrying tablet PC’s to school but eventually couldn’t wee take notes on a computer and keep them all stored in files so we can access our Algebra notes when we are struggling with something in Calculus?”
“I’m really interested in what you have to say. I want to make this a life goal. Wouldn’t it be cool if math books had links like Wikipedia does? When you were confused about a word you could click on it to get an explanation” I almost tell him that I’m going to graduate school but I know if I can’t keep it a secret he’s not going to be able to.
We then discussed how he hadn’t understood the key point of rotation around axis and that that point should have been highlighted in the book. I wonder if the lack of ability to attend to small details is a result of short, bold and provocative advertising. It takes time to really sit and contemplate a black and white drawing and all of it’s details. Kids don’t want to do that. He then advised that when I said something fundamental like that I erase the entire board, draw only one picture and point it out. I thought that was good advice.
Lastly, he takes offense at a problem that is a paragraph long as has part a) b) c) d) and e). “Last year in my Pre-Calculus book some problems went up to n! I would think I had only 37 left to go but really it was 37-45. It’s a shock to see that many parts and totally shuts me down.
I don’t think of math books like this. Perry will tell me exactly when he doesn’t want to do something and why. And it’s pretty fascinating. Then I asked “Should it be the textbook authors job to make this all palatable or the students job to interpret?”
The discussion continues….