ProvocaTeach on Nostr: The more I teach math, the more I realize that *understanding* a concept is only the ...

The more I teach math, the more I realize that *understanding* a concept is only the start of learning. True mastery is forged in the fires of *practice*.

Think about the area of a rectangle. I could teach you that area is just the number of 1×1 (“unit”) squares in a shape. Then we could look at a few shapes made of unit squares, and count their area together.

Sounds simple, right?

Well, no. Counting unit squares won’t work on a 1024×768 rectangle. That’s where teachers step in. We help you figure out that, in small rectangles (3×5, 2×4, etc.) you can find area more quickly by multiplying the length and width. Eventually, you realize this applies to all rectangles, and you write down a formula: area = length × width.

Now that you know the formula, you’ve learned it, right?

Well, no. Once you receive the problems, unexpected difficulties arise. Maybe you forgot what 9×9 is. Maybe some problems ask for “perimeter”; do you multiply length × width for that as well? Maybe one of the rectangles has a side length that’s a fraction, or a decimal, or a variable. All of this needs to be addressed before we can say you’ve truly mastered area.

Teachers must provide plenty of chances for practice and feedback. Unfortunately, in the Common Core era, practice often gets short shrift in favor of conceptual exploration. I still have 10th graders who find area by hand-counting the squares in a rectangle. And I just wonder, “Why didn’t you receive the practice you needed?” 😣