Examined is the situation in which pupils invent mathematics on their own and teachers' reactions to this situation. The assimilation of students' original ideas into correct mathematical concepts is discussed. (CW)

In this study 34 spontaneous analogies produced by 16 college freshmen while solving qualitative physics problems are analyzed. A number of the analogies were invalid in the sense that they led to an incorrect answer from the physicist's point of view. However, many were valid, and a few were powerful in the sense that they seemed not only to help…

This study tested the effectiveness of having fifth-grade students generate their own examples of selected concepts on energy. Hypotheses were that subjects would perform better on sections of a test related to definitions and recognition of exemplars of the concepts for which they found their own examples than on sections related to comparible…

Reviews a monograph which addresses children's higher-order thinking skills. Suggests the following for teaching problem solving: identify and develop content-independent and content-dependent problem-solving skills, connect developed skills through workshop-style activities to subject discipline, and help students identify and reconstruct their…

Noting that successful comprehension, problem solving, and decision making are dependent upon activation and appropriate application of relevant schemata of existing knowledge, this report examines the practice of oversimplifying information in the content areas to make teaching and studying easier, and the dangers inherent in doing so. The report…