Because the difference between six and five can be very damned important

Anyone who’s ever had to fill in this blank understands my pain:

“The real purpose of learning math is _____”

I have a variety of answers, but usually, it’s straight-forward: much of the math you learn is applied to real-life situations, and the ability to do it yourself with no need for a calculator makes sure you’re independent of technological devices to a point. Also, even if it’s not necessarily math you’re using day-to-day, it activates a part of your brain that other subjects aren’t as adept at doing. Problem solving, using the tools in your hypothetical toolbelt, and applying the skills you’ve learned and strategies you’ve acquired to solve the problem leaves you in a better place to create, not simply ingest.

That’s my story and I’m sticking to it. However, the other definitions often laid out for us confuse the hell out of me. Two years ago, for instance, one of the questions read:

“Counselo is grocery shopping and sees that the price of 4 melons is 7$. Write a proportion that Counselo can use to find the price of one melon.”

followed by:

“Use the proportion to find the price of 1 melon.”

At first glance, this seems trivial. However, notice the way it’s phrased. Why does it require that students use a proportion if this problem implicitly requires proportional thinking? For that matter, what’s the purpose of writing a proportion if the student already knows what they need to find and how to find it? Why limit the students’ ability to find their answer by any (valid) means necessary?

Why even taut differentiation if this is the kind of question we’re posing?

I strongly believe in having as many ways of arriving at an answer as possible. Efficiency is key, but so is understanding. If the method that a child chooses is valid, consistent, and useful for the student, then why limit the child to “the way?”

As a test grader, I heard the uproar from teachers who all agreed. Generally, the people who make these tests always have to deal with subjectivity, but more often than not, it’s a question of error and pedagogy. And with the big test coming up soon, I’m in “catch ’em all” mode. I’m seeing how the preparation I’ve given my students has paid off dividends, but I have those few students who have their own methods to their madness, and it’s valid. I’m concerned that their methods won’t be validated, as correct as they are.

Then again, what is the purpose of math? I hope it’s not this.

Mr. Vilson, who’s reviewing percent usage, hoping to remember some of these pieces himself …