Development of proportional response strategies.

An experimental task modeled after hypothesis-testing probes was devised to examine the hypotheses and strategies children (from grades K, 2, 4, and 6) used when making proportional judgments. Earlier studies of proportional reasoning have been limited by methodological inadequacies and by attempts to obtain a "static" measure of children's understanding of proportion concepts. The task used here was oriented toward determining the maximum level of performance a child was capable of without specific training. However, the children did not change or alter their hypotheses or strategies, even after negative feedback, probably because they did not actually receive a counter (square) of the designated color. Other results showed that choosing the set of elements with a greater proportion of, say, white squares in order to get a white square increased with age and increased when the stimulus squares were randomly displayed. In general, the hypotheses used by children at different grades conformed with a developmental sequence proposed by Piaget and Inhelder (even if the specific ages at which appropriate behaviors were observed did not so conform). Further attempts to describe how children acquire proportion concepts were discussed.