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Comments on Pre-test (January 21, 2004)

Comments on Post-test (February 2, 2004)

The thoughts expressed on the pre-test fall into two general categories:

  1. discussion of the meaning of terms, especially the meaning of "area" and
  2. discussions of the relationship between traingle area and the area of rectangles.

1. About half of the papers made some explicit comments about the meaning of the word "area" or about what "A" refers to. Some examples (these are all quotes):

Five papers talked explicitly about the relationship between the concept of area and the idea of conting the grid squares (or parts of grid squares) inside a figure. Four of these five included diagrams of rectangles or other figures covered by grids. Only two mentioned the need to choose a unit of measurement. The others didn't say anything about how one might know the area of a single grid square.

2. Almost everyone noted that a rectangle can be sliced along a diagonal to yeild two congruent right triangles, each having half the area of the square. There was a lot of variation in the presentnation, but this basic image was pretty consistent: Several papers were even more limited, in that they did not talk about slicing rectangles, but limited the imagery to slicing squares along a diagonal. Only one paper considered the possibility that the triange might not have a right angle.

Some things that few mentioned:

Pre-test page