Musings: A Common Misconception

One of my favorite podcasts to listen to is Pam Harris’s Math Is Figure-Out-Able because she puts so many of my thoughts into words.

For example:

“We have a misconception in math education that we think we need to teach methods so that kids can answer the craziest kind of a particular problem.

“We would be far better served to teach kids to think about the most common kinds of questions WELL, and let the cranky ones go to ChatGPT. Because they’ll recognize the sense of the answer.

“Let technology handle the crankiest, and REASON about the rest of them.”

—Pam Harris,
the Math is Figure-out-able Fractions Challenge

Well, I do think she’s wrong about the AI chatbot, because ChatGPT comes up with the strangest bald-faced nonsense about math problems. Wolfram Alpha is a much more reliable resource.

But Harris’s main point stands. This misconception, this math-education myth, drives much of what happens in our classrooms and home schools today.

The Math Children Need

Children don’t need to know how to solve 3,762 ÷ 58 without a calculator. But they do need to understand how to make sense of 36 divided by 6 and use that to reason about related problems like 36 ÷ 12 or 3600 ÷ 60.

Children don’t need a method for calculating 89/315 of 72 by hand. But they do need to master relationships like one-half of 72 and how that connects to one-fourth, one-eighth, and other fractions, as well as how to use such relationships to make sense of a calculation like 75% of 720.

Our own school math experiences led many of us to think that math is all about memorizing and following specific procedures to get right answers. But that kind of math is obsolete in our modern world.

The math that matters today is our ability to recognize and reason about numbers, shapes, and patterns, and to use the relationships we know to figure out something new.

Don’t Cripple Your Kids

Our children won’t build robust thinking skills if we force them to walk with crutches. When we say, “Use this method, follow these steps,” we teach kids to be mathematical cripples.

Students trained in methods may be able to pass tests, because tests focus only on the answers to problems. But what really matters in math is the reasoning behind an answer.

If your reasoning is, “I followed the teacher’s or textbook’s steps and out popped this answer,” then you’re not doing real math.

Real mathematical thinking says, “I know this and that are both true, and when I put them together, I can figure out this answer.”

That’s the kind of math our kids need to learn.