DragginMath: About Representations

When you are learning math, there is a question you must constantly ask yourself:

“Am I learning about math here, or am I learning about a representation of math?”

If this seems like a strange question, perhaps this will help:

Math is about ideas that can be hard to touch, like clouds blowing on the wind. To make math easier to grasp, people think up ways of representing those ideas, and then we learn to work with the representations. There may be several good representations for the same idea. Sometimes, one representation is more useful in one context, while another is more useful in another context. But a representation is not the same as the thing it represents, and that distinction matters. Much of what we learn in a math class is about how to use a representation, and often only a little bit about the math.

Sadly, many people never learn to know the difference, which leaves math looking silly in their eyes.

A computer program’s user interface is a representation. It shows us what is inside the computer and also gives us a way to work with it. The traditional user interface for math is something we learn to read and write on paper. People have made computer programs whose user interface looks like what we write on paper. But this traditional notation is not the only way to represent math. And when working with computers, it may not be the most useful.

A computer screen and keyboard are similar in some ways to paper and pen, but they are not the same. At the top of its screen, DragginMath reads and writes math in a way that is similar to what we traditionally write with paper and pen. Where DragginMath notation differs from traditional math notation, it does so with good reason having to do with these physical differences. The result is easier to read and write in the context of a computer.

Based on what you type at the top of the screen, DragginMath builds interactive pictures of equations. This is yet another representation of math that explicitly shows how the symbols you write are related to each other. When you drag parts of these pictures around in certain ways, algebra happens. And when algebra happens, the result is rewritten at the top of the screen. You can also ask to have it rewritten in traditional math notation, making it easy to relate your work to what you read in books.

Learning to deal with traditional math notation is one of the biggest hurdles in math education. Let’s face it: that stuff is complicated. But when working with DragginMath, the focus is its interactive pictures. This representation is closer to the essential ideas of symbolic algebra, and therefore easier to learn. The student can immediately see: “When I write this, it means that.” And “When I do this, it becomes that.” From there, it is a short leap into traditional notation and mathematical success.