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.
So glad you liked my article on http://www.mathforgrownups.com. I couldn’t help responding to your post, because it’s terrific to meet a classroom teacher who embraces the many ways students can arrive at an answer! Yay!
I have come to the sad conclusion that many grownups lost confidence in their math skills partly because they were forced to arrive at the correct answers with only one method. While I understand that algorithms are important tools, over-dependence on them — especially when concepts are being taught — can backfire.
We each think about math differently. Those differences should be celebrated, so that our students leave feeling proud and capable.
Keep spreading the good word!
Laura
I’m not sure where, but somewhere in early math education (honestly Im talking up through the calculus sequence) the idea of encouraging creativity in math was lost. I’m not sure how to handle/fix this but the results are certainly not good. You end up with students who see math as a chore at best who can’t truly think mathematically but only can apply a set of rules. The creativity of finding different approaches or ways of thinking is not only what can make math fun (and bring confidence!) but also what makes someone actually “good at” math so it blows my mind that we as educators at all levels don’t encourage it! It is so cool to see things popping up to help address this! (like your site for instance).