This paper discusses recent research on cognition and its implications for mathematics education. Learning as a generative process, structural organization, processing of information, processes and structures, individual differences, brain research, higher-order processes, motivation, and delay-retention effects are discussed. (MS)

An approach to teaching geometry is promoted that allows students to decide for themselves what they could prove from given information. Such an approach allows pupil involvement in the personal process of discovering mathematical ideas and formulating problems. It is noted these methods will not work for all. (MP)

The article emphasizes the importance of the teacher listening to the student's questions and problems in math classes in order to understand exactly what the student is misunderstanding. (CD)

The roles and uses of symbols in mathematical thinking are discussed. The thinking process is further subdivided into specialization, generalization, and reasoning. (MP)

The teaching of mathematics as a science to elementary school children is promoted. Use of the scientific method in learning is presented as a form of experiential or discovery teaching. (MP)

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)

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)

Focusing on how expert writers in various disciplines convey complex ideas, this paper shows how the techniques used by the mathematician, Clark Kimberling, in various writings can (1) be transferred to other disciplines, (2) show learning taking place, and (3) provide models for students to re-enact learning in all subject areas. The paper…

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)

The International Group for the Psychology of Mathematics Education (IGPME) was founded in 1976 at the Third International Congress for Mathematics Education, to promote international contacts and the exchange of scientific information in the psychology of mathematical education. The goal was to further a deeper and more correct understanding of…

Explores the role that symbolic-graphical calculators can play in the current calls for reform in the mathematics curriculum. Discusses symbolic calculators and graphing calculators in relation to problem solving, computational skills, and mathematics instruction. (MDH)

Chess experts remember meaningful knowledge in the form of networks or patterns. Applied to mathematics instruction, effective classroom approaches can use investigation to identify patterns or rules. Described are a class activity and a small-group activity to investigate addition of signed numbers and linear relationships. (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)