No tricks, just truth.

What does Kentucky Fried Chicken have to do with dividing fractions? There's a math "trick" out there called KCF which stands for Keep, Change, Flip, if you can remember that. We used to mistake it for KFC. Which is exactly the problem. The "trick" wasn't actually that easy to remember, which defeats the purpose all together.

I saw this problem the other day:

2/5 ÷ 1/5 = ?

In other words, how many fifths are in 2/5?

A little math genius could easily answer that question. Two!

A little math genius could prove it with a drawing. Or even apply their understanding of how multiplication of fractions works. If 2/5 x 1/5 is (2x1)/(5x5), then 2/5 ÷ 1/5 would be (2/1)/(5/5), which is 2/1, or 2.

Instead of letting these ideas flow, we worry that the concept is too confusing, so we teach tricks like KCF before giving students a chance to make sense on their own, using ideas they already know and understand.

If we use KCF to solve 2/5 ÷ 1/5, it adds a lot of steps and makes less sense:

Keep 2/5. Change ÷ to x. Flip 1/5 to 5/1. So, 2/5 x 5/1 = 10/5 = 2. It's fine, if you remember when and how to do it, but it's unnecessary for this problem.

I hear from little math geniuses all the time who tell me that we "can't" do something that way or we "have to" do it this way. When I ask why, the answer is always because a grown up told them so.

😢

There is a great article from NCTM by Karen S. Karp, Sarah B. Bush, and Barbara J. Dougherty about "13 Rules that Expire." Go and Google that if you've never read it.

The problem is, adults tell children all sorts of things about math that turn out not to be true. As a result, math becomes mysterious and confusing for students because the rules they learned don't apply anymore. It also erodes their trust in the adults who teach them.

Instead of tricks, let's teach truth. Instead of rules, let's make it real so it makes sense.

What do you think?