Radical constructivists advocate discovery-based pedagogical regimes that enable students to incrementally and continuously adapt their cognitive structures to the instrumented cultural environment. Some sociocultural theorists, however, maintain that learning implies discontinuity in conceptual development, because novices must appropriate expert…

A laboratory study was performed with four levels of discovery and two levels on an overlearning factor. An improved experimental paradigm was chosen so as to avoid a number of confusions which have obscured previous research. An operational definition was developed for discovery and guided discovery and discovery teaching, and inquiry learning.…

The authors briefly review some of the empirical studies which have compared discovery learning with expository learning. Essentially, their study replicates an earlier one in which these learning strategies were compared on two dimensions: (1) immediate acquisition; and (2) retention of concepts. Subjects were 228 seventh graders who had not…

Describes a unit on magnetism that utilizes hands-on activities in which students make hypotheses for discrepant behavior, discover whether a magnet attracts one object through another, measure the strength of magnets, explore levitating paper clips, and play a game dependent on magnetic attraction. (MDH)

Describes the Microworld Chance, a simulation-oriented computer environment that allows students to explore probability concepts in five subenvironments: coins, dice, spinners, thumbtacks, and marbles. Results of a teaching experiment to examine the effectiveness of the microworld in changing students' misconceptions about probability are…

Explores the use of dialogue and dramatization to reconstruct the formation of mathematical concepts. An appendix provides the synopsis of a 6-scene play that portrays the rise of negative numbers over a period of 300 years. (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…

Presents a series of activities that help students discover the Pythagorean Theorem and extension activities to explore various dissection proofs of the Pythagorean Theorem. Includes reproducible worksheets. (MDH)

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)

The 1989 document, "Curriculum and Evaluation Standards for School Mathematics," provides a vision and a framework for revising and strengthening the K-12 mathematics curriculum in North American schools and for evaluating both the mathematics curriculum and students' progress. This book, one in a series designed to interpret and…