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Measuring Up: Prototypes for Mathematics Assessment
Characteristics of the high response:
The response shows that there is a firm connection between the playground map representation of the situation and the pictures from James' viewpoint.
The dots are all labeled within the limits indicated in the answer key above. (Note that a location for D in which the fort blocks the umbrella is preferable to one in which the merry-go-round blocks the umbrella, because it looks as if the merry-go-round is not tall enough.) The pictures in question 3 are drawn in the correct order, although the individual drawings can be just good enough to be recognizable.
The explanation for question 5 is well reasoned. Ordinarily, in a high response, the child says "No," and explains that if the fort is on the left and the umbrella on the right, then the merry-go-round has to be in front of both of them.
Other high responses will be more inventive: "If the boat is where the view of the merry-go-round is blocked by the fort, then James will see the fort on his left and the umbrella on his right if he stands on his head." An unanticipated response like this shows a mature ability to visualize!
Characteristics of the medium response:
The response shows an overall grasp of the situation; at most, one of the responses to questions 1 through 4 is incorrect.
The response to question 5 is correct, (No), but the explanation is inadequate. For example, "I couldn't find a place where that would happen."