Hill-Shaped Misconception

Character

Dialogue

Jeremy:

Al, anything else?

Mentor:

 I've gotta run--you two chat, OK? (David leaves)

Teacher:

Thanks Dr. Math. Well... I did have another question, about using elevators instead of clowns in MathWorlds. I have noticed an interesting problem students have thinking about graphs that look like "hills." Students think that if a velocity graph is hill-shaped, then the motion will go up and down.

Jeremy:

Yes, I know that one from the research literature on graphing misconceptions and our own experience with MathWorlds. We've been working on it. We want students to understand that if the velocity graph is always positive, then the motion is always going positive--not positive and then negative.

Teacher:

Could we design a MathWorlds activity to work on that misconception?

Jeremy:

Sure let's go use a simple sketchpad as a design board.

Teacher:

Here is the kind of velocity graph I would like:

Jeremy:

Well we could make that kind of graph in MathWorlds, but I'd recommend that you use an approximation like this
(Jeremy in TAPPED IN, drawing it)

Teacher:

That would be excellent. But I also want the opposite.

Jeremy:

Show me what you mean.

Teacher:

ILike this:


 (click the script to hide and show the graph).