In and out of fashion is the [term] “discovery math.” Usually, when people talk about discovery math, it’s with anger. They think something is wrong with all these people who are making kids discover math. And I think it’s fair to say that, really, nobody is making kids discover math, and it’s probably a misnomer.

What we really mean is that rather than just telling students a whole bunch of stuff that doesn’t mean anything to them anyway, what we do is we set a problem that we think is within their grasp, and we let them mess around with it a little bit to try to figure some stuff out on their own to see if they can see what’s going on—and remember, we’ve set a problem that we think they could use tools they already have to solve—but we [also] probe, and we scaffold, and we suggest, and we talk about it. So, kids do some stuff, but then we discuss it all, and we make sure that when we’re talking about the idea that we really wanted students to see, they’ve had a little bit of experience now to make sense of the things that we’re going to talk about in the discussion. But we also make sure they walk away with that idea in mind.

So, here’s an example. At one point in the curriculum, we usually want kids to learn that the sum of the angles in a triangle is 180°. So, a teacher could just stand there and say [that] it is, and I guess that’s fine. There will be some kids who will forget it tomorrow, and there will be other kids who remember it. But it doesn’t mean anything—it’s just somebody said you’re supposed to know that the sum of the angles is 180°.

It’s so much richer to give kids a bunch of triangles, let them cut out the corners of the angles, put them together, and see what happens. And they will find out when they put the three corners together, they will always fit together and make a half-circle every single time. A half-circle, by the way, is 180°.

And then when we start talking about “What did you notice?” the kids are going to notice that we made a half-circle. “Well, what were the angles? Let’s measure them and talk about them.” And when you actually go back and measure the angles and see that the sum is 180°, it actually means something to you now. And for the rest of the year, if not your life, you can remember, “Oh yeah, that’s the day we tore up the angles and put them together.” And then it sticks with you.

So, a lot of this is to make sure that when we talk to kids, it sticks with them because it means something.