Everyone is familiar with the concept that the cube and octahedron, dodecahedron and icosahedron are dual pairs, with the tetrahedron being self-dual. On the face of it, the concept seems straightforward; however, in all but the most symmetrical cases it is far from clear. By using the computer and three-dimensional graphics programs, it is…

This paper presents a generally applicable method for characterizing subjects' hypothesis-testing behaviour based on a synthesis that extends on previous work. Beginning with a transcript of subjects' speech and videotape of their actions, a Reasoning Map is created that depicts the flow of their hypotheses, tests, predictions, results, and…

A test was given to 322 secondary students to develop a profile of mathematical ability based on four components: computation, pattern recognition, logical reasoning, and symbolic manipulation. These profiles were compared to mathematics test scores; the results verified hypotheses about individual differences in mental processes and knowledge…

Examines Japanese and American children's styles of processing computerized geometric matrices. Hypothesizes cultural differences for response latencies. Finds no difference in accuracy between the two groups but significant differences in response times for second- and fifth-graders. (MW)