Conjecture and proof, as opposed to numerical calculation, are presented as being the primary focus for teaching mathematics. (MP)

Numerous mathematical examples are presented which illustrate and raise questions about students' tendencies to overgeneralize. (BB)

This book represents a compilation of the views and ideas of the late Hans Freudenthal, representing his last major contribution to the field of mathematics education. Rather than a presentation of new views, Freudenthal selected and streamlined old ideas, many gathered from his lectures in China, and formed a review of questions and issues in…

Proposes the use of conceptualization, exploration, and higher-level problem solving in differential equations courses as a replacement for some of the traditional material that can now be delegated to the computer. (MKR)

This paper describes student performance and beliefs regarding fractions resulting from a five-phase approach toward developing mathematical intuition via physical materials. Interviews with students using this approach and with students using a conventional textbook approach indicated significant differences in problem-solving abilities and…

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…

Challenged is the traditional model for the transmission of mathematics in the elementary school classroom. An inquiry approach to learning mathematics is proposed and supported with results of a year long research project that exposed second graders to mathematical learning experiences using this approach. (MDH)

Presents a series of 5 reproducible worksheets for grade levels 5-10 that provide hands-on activities to help develop the concept of slope. (MDH)

Described is the attempt to identify relationships between pedagogy and student behavior in a mathematical microworld. The patterns of teaching associated with LOGO-based computer activities involving ratio and proportion and the teachers role in helping students bridge the gap between LOGO- and school-mathematics practices are explored. (MDH)

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)

Proposes a novel method of introducing and promoting the topic of geometric sequences through the problem of calculating the number of games necessary to determine the winner of a single elimination tournament in which two, three, or more teams compete at a time. (MDH)

Argues that mathematics education at the preschool and primary level should emphasize child-centered, hands-on, discovery learning, rather than paper-and-pencil tasks that may be too abstract for young children. Suggests that this holistic approach to mathematics fosters concept development and higher order thinking skills on a broad level. (MDM)

Describes one teacher's reflection concerning the quest to develop an understanding of school mathematics that promotes and sustains students' opportunities for exploration and conjecture. Recounts that a particular student's exploration of the features of parabolas eventually led to an understanding of the quadratic formula precisely because of…

Reviews research on (1) schemata acquisition while learning mathematics and techniques for detecting schema in mathematics learners; and (2) assessment of the distribution of cognitive resources while learning mathematics that lead to the design of instructional techniques to facilitate schema acquisition. (26 references) (MDH)