Reviews the basic precepts of the learning theories of Piaget and Ausubel. Although Piaget is credited for his contributions to educational psychology, the author supports Ausubel's theory of meaningful learning as more significant for future contributions in science and mathematics education. (CP)

Describes three activities that the teacher can employ to help students develop thinking skills through mathematics instruction: (1) memorization using the technique of chunking; (2) higher order thinking with magic squares; and (3) predicting games. Identifies eight facets of the teacher's role in promoting thinking skills. (MDH)

This study was designed to determine students' abilities and difficulties in articulating the relationship between function and derivative. High-school students were presented 15 problems during two 75-minute interviews in which they were asked to construct functions experimentally in three different contexts: motion, fluids, and number-change. In…

Discusses the potential that school mathematics has for being a source of exploration and discovery for students and teachers. Provides a process-oriented definition of understanding mathematics. Presents activities in which students construct computer and actual models of polyhedra and make conjectures regarding a medical research application of…

Describes the use and rationale of "Silent Teaching," a teaching technique in which the teacher remains silent as students generate and evaluate hypotheses while trying to understand an as-yet undiscovered concept. (MDH)