Cognitive Development and the Structuring of Geometric Content
From a pool of secondary students (n = 161), 20 students were chosen who had high (formal operations) scores and 20 who had low (concrete operations) scores on two paper-and-pencil measures of Piagetian formal reasoning (the Test of Logical Thinking and the Longeot Test). The students made similarity judgments among all possible concept pairs from 13 geometric concepts and 10 mathematical expressions from a unit on ratio, proportion, and similarity. Multidimensional scaling procedures showed that despite idiosyncrasies in individual structures, clear prototypical maps could be derived for both the formal and concrete groups. In addition, formal operational students structured subject matter content significantly more like subject matter experts than concrete operational students did.