We examine teachers' classroom activities with the spreadsheet, focusing especially on episodes marked by improvisation and uncertainty. The framework is based on Saxe's cultural approach to cognitive development. The study considers two teachers, one positively disposed towards classroom use of technology, and the other not, both of them…

The CAME project was inaugurated in 1993 as an intervention delivered in the context of mathematics with the intention of accelerating the cognitive development of students in the first two years of secondary education. This paper reports substantial post-test and long-term National examination effects of the intervention, yet, by discussing the…

Discussed are difficulties which occur while the student is using mathematical induction as a tool to prove theorems. An appropriate approach is suggested. (MP)

Niels Bohr's term "complementarity" has been used by several authors to capture the essential aspects of the cognitive and epistemological development of scientific and mathematical concepts. In this paper we will conceive of complementarity in terms of the dual notions of extension and intension of mathematical terms. A complementarist approach…

The author shows some causes of failure in the creation of mathematical concepts. One is the stiffening of concept cores, which prevents identification of atypical exemplars and solution of atypical problems and causes a bifurcation between the natural system of everyday concepts and the formal system of school concepts. (Author/MDH)

Experiments by Russian educators on teaching algebra in elementary grades are summarized by the author. The algebra taught consisted of generalized solutions to concrete problems that are usually presented with fixed numerical values. (JP)

When we consider the gap between mathematics at elementary and secondary levels, and given the logical nature of mathematics at the latter level, it can be seen as important that the aspects of children's logical development in the upper grades in elementary school be clarified. In this study we focus on the teaching and learning of "division with…

Diagnostic interviews were conducted with third graders to determine why they made mistakes on sixteen arithmetical tasks. A modified version of the Newman method of analyzing errors is discussed and applied to these interviews. (MP)

Analyzes how practice in mathematics education might be reformed toward a professional practice. Argues that conventional school mathematics be replaced by a constructivist school mathematics based on children's use of their schemes of actions and operations in learning situations as illustrated through examples of the numerical schemes of…

Three teaching experiments are reported which study aspects of a diagnostic teaching methodology. An experiment in the field of directional quantities showed a positive relationship between the intensity of discussion and amount of learning; one on fractions and another on geometric reflections showed good two-month retention under the…

Sketches a theory for designing teaching based on mathematical activity, situations, tasks, and interventions, exposing and resolving cognitive conflicts, changes of structure and context, feedback, reflection and review. Reviews the main psychological principles underlying this theory, then considers some examples of teaching designs in light of…

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)

This paper is concerned with pupils' learning of the concept of variable in the LOGO programing environment and how this relates to teaching. Results from three research projects are described and compared in a discussion of how improvements in learning have been influenced by a refinement in teaching method. (Contains 21 references.) (Author/MDH)

Described is a year-long study of the way a group of six 12-year-old children went about solving a special class of geometric problems using a computer and a limited set of LOGO programing tools. Examines solution strategies deciding whether those strategies led to insights about mathematical relations. (Author/MVL)

An analysis of a 10-minute episode in which 7-year-old students (n=3) engage in collaborative small group activity is presented to explore the relationship between individual learning and group development. Students learned as they interactively constituted situations for justification or validation, yielding an institutionalized solution method.…