“Jimmy wants to determine the height of the tree on the corner of his block. He knows that a fence by the tree is 4 feet tall. At 3 pm, he measures the shadow of the fence to be 2.5 feet tall. Then he measures the shadow of the tree to be 11.3 feet. What is the height of the tree?” I hear from the other room. Homework is going on, and from her tone, I can tell my daughter is disgusted by the question being asked of her in geometry. “Ugh!” she says to no one in particular.
I remember this type of word problem as the bane of my existence in high school. “It’s 27.2,” I call to her, omitting the unit (because really, does it matter?). I am fully confident that I am not even close.
“What?” she says, a hopefulness in her tone that indicates she believes I might actually be supplying her with the right answer.
“I said, the answer is 27.2. I just did it in my head. Impressive, isn’t it?” I walk into the living room and smile at her. All three children are staring at me like I have three heads, maybe four. “What?” I look at them innocently. “I made it up. It’s called ‘creative mathematics.’ It’s a new thing I just invented.”
“Oh!” My daughter jumps up, completely on board with the new class I have just discovered. It would be kind of like creative writing, but on a math scale. “Where do I sign up? I could totally get into that class!”
Me too… and probably, many other people I know would also appreciate it. Word problems would be awesome! The question would no longer say, Calculate the height of the tree. It would now ask, How tall do you want the tree to be? Or maybe you could simply decide how tall you need the tree to be to suit your purposes. Of course, you would have to give the reasons to support your answer.
Creative mathematics would have nothing to do with calculations. It would be about problem solving and creating your world with the specifications that you find necessary. Plausible or not, you would be allowed to reimagine your world to suit your needs.
Granted, just like creative writing, creative mathematics would not fit every situation. For example, if you were putting new counters in your kitchen, you would need an accurate measurement rather than simply deciding how big you wanted your counter to be. However, such a mathematical option would allow the creative among us to enjoy math and take a break from the many long years of calculating the right answer and showing the work we did to get there.
In life—even in situations like medicine—there are very few “right” answers. Creative mathematics would honor that fact and encourage effective problem solving. Yes, in mathematical calculation, students would still be expected to find the right answer. But in creative mathematics… the sky’s the limit.
* this post is dedicated to the best math teacher I have never had. Once upon a time, a long time ago, she spent hours in daily telephone tutelage to move my sorry math-challenged self through high school calculus.