*Guest blog by Dr. Jeremy Roschelle, Digital Promise, @roschelle63*

**Summary: **When integrated with curriculum and pedagogy, visual representations that change in time can improve students’ conceptual understanding of mathematics.

**To understand mathematics, students need to connect ideas. **

For example, the slope of a line is often given as a number — the *m* in y = mx + b. We can measure the slope with triangles of “rise over run” drawn anywhere and at any size along a straight line in a graph. Why does the measure of rise over run always come out the same?

A student can measure rise over run at any pair of points along a line.

The ratio—the slope—will always come out the same. Why?

Fundamentally, slope is connected to concepts of geometric similarity and ratio — *m* always comes out the same because it is a measure of the ratio of the sides of

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