Math Education Professor Dor Abrahamson: Making Math Meaningful (Transcript)

Dor Abrahamson: What is mathematics if you think about it? Mathematics is a way of thinking. It’s a way of solving problems.

I’m Dor Abrahamson. I’m a professor of mathematics education over at U.C. Berkeley. I study the way that kids learn mathematics. I’m also an inventor. I build all kinds of gadgets, using both traditional and cutting-edge technology, to help kids learn and teachers teach.

Usually when people think about math, they think about, you know, X and Y and numbers and doing all these calculations. However, mathematics is about making sense of the world and unless we can sort of ground all of the scribbling in something concrete that we really get, we’ll never understand what we’re doing.

Like adding, you know what adding is. Take one and one and woo! You have two. Or if you think about multiplication, it’s like you take what is five times three? Three and three and three and three. You have a sense of what this thing is. But beyond that, do people have a sense or are they only scribbling around and getting answers but not really understanding what these things are?

My job is to help kids connect between what their brain already knows to do and the math that they are being taught, so that they can do much more than just scribble little numbers and symbols, so that they can really get it. So they can go out into the world and identify those phenomenon, see those patterns, use math in their lives to solve the problems that they care about.

Any researcher of math education can tell you that the big crisis starts when fractions enter the scene. Up to then it’s just been counting numbers: one, two, three, four until you get all these weird kind of relationships where half is bigger than one-third, is bigger than one-quarter is bigger than one-fifth even though the numbers are going up the fractions are getting smaller. Kids flip. Kids suddenly lose a sense of what these things are.

Ratio and proportion are everywhere. Even on my cello. When you take a string, play it, and then you have it, it’s the same note. What we need is to help kids see the world mathematically. So our way of going about solving this problem is to develop what we are calling the “Mathematical Imagery Trainer”. We’ve set this up so that as long as the crosshair on the right is double-height of the crosshair on the left, it’s going to be green. So if I move it this way, it will keep being green. However, if I find a green spot and I keep the distance the same, it will go red. That means we can struggle with the core learning challenge of ratio and proportion even before we introduce a single number.

In our lab we are creating all these sophisticated devices. But we count on teachers to bring these things alive in their classrooms. All you need is to be creative, as all teachers are, in figuring out how to make these ideas come alive. So just like with the Mathematical Imagery Trainer, kids saw how the distances between their hands keep on growing. We can show that just with blocks. We can show the same idea instead of growing up vertically, going horizontally. Imagine you’re leaving home and you’re driving one thing, say a bicycle and your buddy is driving a car. As you’re moving along, you’re each going at a constant rate but the distance between you keeps growing. This guy is moving two units at a time for every one unit this guy is moving. That’s proportion. You can use anything.

It’s those images that they’ll be carrying out through their lives. Not the numbers. They’ll forget the procedures. We want kids to be masters of their mathematical knowledge so that they can solve the problems of the world.