Math is an important tool in life, but the mechanics of math, the way it is often taught, is not actually the way it is typically applied. Probably because our brains aren’t wired like computers.
Here’s an example – you are the cashier at a grocery store. A customer buys $43.37 worth of groceries, and hands you a $50 dollar bill. What do you give them in change?
In math, you would find the difference, $50 – $43.37 = $6.63, then count the change out as $5, $1, 2 quarters, a dime and three pennies.
A real cashier, however, counts up: from $43.37, three pennies makes .40, a dime and 2 quarters makes $44, then $1 and $5 make $50. They don’t need to know the total change amount is $6.63, because the goal is to hand over change, not count it.
Likewise, when solving division problems we don’t tend to do division in our head, we do multiplication. When asked how many nickels make up 45 cents, we don’t think 45/5 = 9. We think what times 5 = 45? It seems that we are programmed to think forward, and that thinking backwards is really difficult to do, and when we do think backwards, we are actually thinking forward in a series of backward steps (like the lagging strand of DNA, if I may be so nerdy).
I think this is really important to recognize. In an earlier post on my approach to problem solving, I talked about the necessity of working backwards from the answer to ensure you know where you are going, and that experienced problem solvers do this without even thinking about it. So when I teach problem solving, I not only try to model this as explicitly as possible for my students, but I also teach the metacognitive side – to get the students thinking about their own thinking process when problem solving. To expose the man behind the curtain, as it were.
Certainly to be good in science one has to have a handle on evidence-based problem solving, both inductive and deductive. I feel that teaching metacognition is a way to help students develop those skills. It also helps me fathom the workings of the teenage brain.