## Memorizing? Or Knowing?

*Published on September 12 2011*

We’ve all heard the phrase “drill and kill.” This refers to the unreasonable and constant emphasis on having students fill out worksheet after worksheet of math problems (and always using the standard algorithm), of insisting on rote recitation/memorization of basic math facts, and, because it’s a “drill,” insisting that it be done in absolute silence. If we want to make learning as difficult and unpleasant as possible, surely, this is the way. It contravenes all we know about how to work effectively with our students. Let’s look at these practices one by one.

**First, worksheets.** Why do we give our students so many worksheets with the same kinds of problems, for example, 25 multiplication problems? Once they’ve completed a couple of these successfully, they’ve shown us that they know how to do them. What’s the point of the next three, four, or half dozen worksheets with the same kinds of problems? Shouldn’t that time be put to a better, more productive use?

**And those basic math facts?** Unquestionably, if our students do not know them, they will get nowhere in math; knowing them is critical. But, did you notice the subtle change of wording? There’s a big difference between ‘memorizing’ and ‘knowing.’ A parrot can memorize basic facts but obviously doesn’t ‘know’ them. We want our students to *know* them, and that means not just memorizing 4 x 6 = 24 but also understanding *why* that is so. When they know the *why*, then the *how* makes more sense and is easier to learn.

**Finally, do we really want our students working in absolute silence?** Well, yes, but only sometimes. Testing, for example, or those occasions when we want to know if students can do the work unassisted. Other than that, our students gain much from working together on a common problem and having a mathematical discussion around that problem. Of course it’s going to be noisy, but it’s what I call “productive noise” - students are on task, talking about their work, learning from each other. This is a much more relaxed atmosphere and far more conducive to learning, rather than memorizing.

Dave Gardner

Mathematician in Residence