This paper charts the design and application of a system to support 11-14 year old students' learning of algebraic generalisation, presenting students with the means to develop their understanding of the meaning of generality, see its power for mathematics and develop algebraic ways of thinking. We focus squarely on design, while taking account of…

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)

The learning of mathematics is presented as a cognitive process rather than as a behavioristic one. A generative model of mathematics learning is described. Learning with understanding can occur with discovery or reception treatments. Relevant empirical research is discussed and implications for teaching mathematics as a generative process are…

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

Investigated strategies that 7- to 12-year-old children (n=96) spontaneously applied in solving novel combinatorial problems. With experience in solving two-dimensional problems, children were able to refine their strategies and adapt them to three dimensions. Results on some problems indicated significant effects of age. (Contains 32 references.)…

This monograph focuses on educational research on the processes and natures of problem-solving activities in mathematics. The first chapter presents an overview to both the field and the document itself. All of the studies reported reflect interrelated investigations carried out at the University of Madison-Wisconsin, as partial fulfillments of…

A review is made of that literature which focuses on the relationship of instructional method, internal cognitive activity and performance measures. This includes literature concerned with the issue of "discovery versus reception learning" and the effects of different instructional methods on retention, delayed retention and transfer tasks. The…

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)

Summarizes experiments indicating that a basic key to learning is the development of concepts of pattern recognition and the appropriateness of using a particular theorem. (Author/SK)

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…

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)

Offers LOGO as an environment that facilitates the development of cognitive strategies useful in problem solving. Presents LOGO activities requiring students to combine preprogramed procedures to produce worksheet patterns. Using this approach promotes using LOGO as a vehicle for problem solving and results in a more positive attitude toward LOGO.…