Enhancing learning about elastic collisions with LEDs

What will be the velocities of the elastic balls after collision?

The ball are moving in a straight line and collide head-on. They have the same mass and the left ball has a speed of 3 units and the right ball a speed of 2 units, in the opposite direction.

This is a typical question used in our studies of problem solving and learning with different systems of representations for this domain.

Conventional solution

A typical solution attempt by a physics graduate. The student correctly remembers the laws of the domain, does extensive algebraic manipulations, including spotting an error and back tracking, but he gets the wrong answer because of a conceptual misinterpretation of the formulas near the end.

LED solution

A typical LED correct solution to a slightly more complex problem (unequal masses). The solution was produced by a student in a post-test following one brief session on a computer-based discovery learning environment in which interactive LEDs could be manipulated on screen to model different types of collisions.

He drew the diagram to scale and simply read the answer off the diagram. The post-test was the first time this student had drawn such diagrams by himself.

Students using these diagrams often cross check their answer by substituting the values in to the laws for this domain to ensure that momentum and energy are conserved.