Yesterday, I ran across a great article on Math for Grown Ups about different ways of attacking math problems. While this article talks about day to day math, I was wondering how many people really think about this for more advanced topics like algebra or calculus.
I have a habit of giving my students a problem and asking them to find *at least* a couple of ways to find an answer. (In fact, I did one of these as a calculus problem of the week recently). A lot of time, I find that the students are worried they will get confused if they know more than one way – they are simply too focused on just getting an answer! Talking about this always leads to a great discussion which I tend to start off with these two questions:
How do you know what method makes the most sense to you until you have seen several different methods?
How can you be sure you really understand something until you can look at it from a different perspective?
If you have found yourself able to “go through the motions” of math without much understanding then this is a great exercise to try. In fact, this is something that anyone who is trying to understand something better should try! Stop focusing on just getting the answer and start trying to see how things work together. There are patterns hidden all throughout math waiting to be noticed. It’s these patterns that can help you get a deeper understanding and get better at finding fast or efficient ways to “problem solve”.
Try finding another way to do the problem, or change the problem a little and see how the answer changes – basically I say, let yourself explore the topic. Use the textbook problems as a starting point (thats really what they are) and go from there – all you need is paper! Remember, math isn’t about just finding the answer, but instead about problem solving skills.