Wednesday, February 14, 2007

Conceptual problem with prisms

My sophomores have taken easily to the volume of a rectangular prism (V=lwh), but other sorts of prisms have given them a lot more trouble. Yesterday seemed to help: I gave a presentation of building a prism by "stacking up" congruent shapes, and pointing out that each piece had the same surface area (a neat connection to volume of solids of rotations, which I'm doing with the calculus class right now-- again, calculus is the geometry of curves!)

What was interesting was this: when I gave them an isometric view, with the instructions to "draw the top, find the area of the top, then mulitply by the height" that got some traction-- but a LOT of students had trouble removing the height from their drawings and calculations of the top. That is, I was continually pointing out that "that number represents how far down below the table your shape is."

Neat bit of discovering misconceptions, anyway.

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