North American math education fails at what great problem solvers do: explore better solutions while believing in yourself. Here's a way to improve school math.
Great article! I always thought the intuitive, commonsense approach you suggested was “cheating”. In fact my math teachers made us show our calculations to confirm we’d gotten the answer the “right” way—only then was the answer “right”.
Yeah, I had some math teachers who did the same thing, and that annoyed me to no end. On the one hand I'd think: if I got all the answers right, who cares how I got them?
That being said, there's value in "showing your work" if others can benefit from seeing other approaches to the same problem. But that was never the intent of most math teachers I had.
I forgot if school or my Mom told me this, but I was told to solve it a different way in order to check. But I really like this idea that the goal is to solve in different ways instead of the goal bring to solve the problem.
What if instead of a problem set being solve 10 problems, it's to find different solutions? The first way you're incentivizing powering through while the second way is a more creative exercise. One thing I actually like about math is how it fits together, how taking different paths can get you to the same place.
Sometimes when I drive I do some pretty simple math like figuring out how long it will take to get somewhere driving different speeds or stupid things like that and I always a get a thrill when the math works out using two different ways.
I love all these suggestions, Chris. I don't know if it's just me, but I feel like "creativity" and "math" aren't usually spoken in the same sentence. For too many of my formative years, math was always just about getting to an answer fast using "the one way."
I was also told to try different approaches to check the answer to a math problem. It was considered good practice. But that was never actively encouraged. And I suspect most people didn't do that (me included).
Maybe this all speaks to the unfortunate way our society views math. Exploring different approaches to solving a math problem would bring an element of creativity that might actually make math more fun for more people. Especially the creative types.
Great article! I always thought the intuitive, commonsense approach you suggested was “cheating”. In fact my math teachers made us show our calculations to confirm we’d gotten the answer the “right” way—only then was the answer “right”.
Yeah, I had some math teachers who did the same thing, and that annoyed me to no end. On the one hand I'd think: if I got all the answers right, who cares how I got them?
That being said, there's value in "showing your work" if others can benefit from seeing other approaches to the same problem. But that was never the intent of most math teachers I had.
I forgot if school or my Mom told me this, but I was told to solve it a different way in order to check. But I really like this idea that the goal is to solve in different ways instead of the goal bring to solve the problem.
What if instead of a problem set being solve 10 problems, it's to find different solutions? The first way you're incentivizing powering through while the second way is a more creative exercise. One thing I actually like about math is how it fits together, how taking different paths can get you to the same place.
Sometimes when I drive I do some pretty simple math like figuring out how long it will take to get somewhere driving different speeds or stupid things like that and I always a get a thrill when the math works out using two different ways.
I love all these suggestions, Chris. I don't know if it's just me, but I feel like "creativity" and "math" aren't usually spoken in the same sentence. For too many of my formative years, math was always just about getting to an answer fast using "the one way."
I was also told to try different approaches to check the answer to a math problem. It was considered good practice. But that was never actively encouraged. And I suspect most people didn't do that (me included).
Maybe this all speaks to the unfortunate way our society views math. Exploring different approaches to solving a math problem would bring an element of creativity that might actually make math more fun for more people. Especially the creative types.