Children's Proportional Judgments: The Importance of "Half"

Abstract

3 experiments are reported, all of which show the crucial importance of the “half” boundary in children's proportional judgments. In the first experiment 4-, 5-, 6-, and 7-year-old children had to judge which of 2 boxes of blue and white bricks was represented in a small picture. The proportion of blue to white bricks was different in the 2 boxes, and the question was whether the children could use these proportions to make their choices. The 6- and 7-year-old children solved the problem much more successfully when the proportions crossed the “half” boundary (e.g., 3/8 blue vs. 5/8 blue). The second experiment showed that discriminations involving half (e.g., 1/2 blue vs. 1/4 blue) are also easier than those that do not cross the “half” boundary for the 6- and 7-year-olds. The third experiment confirmed the results of the first 2 with pictures of different absolute sizes from each other. We conclude that “half” plays a crucial role in children's early proportional reasoning, and that the “half” boundary is to some extent similar to, though not as powerful as, the category boundaries discovered in speech perception.