Characteristics of the low response:

There is some understanding of the relationship between the playground map and the views that James sees from various places on the lake, but it is tenuous.

At least one of the answers to questions 1, 2, and 4 are within the bounds specified at the beginning of the protorubric.


Clements, Douglas H. and Battista, Michael T. (1992). "Geometry and spatial reasoning" in Grouws, Douglas A (ed.) Handbook of research on mathematics teaching and learning. New York: Macmillan.

deLange, Jan (1987). Mathematics, insight, and meaning. Utrecht: Rijksuniversiteit Utrecht.

Freudenthal, Hans (1983). Didactical phenomenology of mathematical structures. Dordrecht: Reidel.

Paiget, Jean, Inhelder, Barbel, and Szeminska, Alina (1960). The child's conception of geometry. New York: Basic Books.

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