Our study concerns the conceptual mathematical knowledge that emerges during the resolution of tasks on the equivalence of polynomial and rational algebraic expressions, by using CAS and paper-and-pencil techniques. The theoretical framework we adopt is the Anthropological Theory of Didactics ("Chevallard" 19:221-266, 1999), in…

In this paper we describe learners being asked to generate examples of new mathematical concepts, thus developing and exploring example spaces. First we elaborate the theoretical background for learner generated examples (LGEs) in learning new concepts. The data we then present provides evidence of the possibility of learning new concepts through…

Presents a two-phase investigation of how Israeli students understand the concept of periodicity. Discusses related research with teachers and students (N=895) employing both qualitative and quantitative research methodologies. Concludes that students understand periodicity as a process. Students' errors and preferences are discussed with…

Establishes six levels from an inductive proof to an algebraic demonstration on the bases of three axes in lower secondary school mathematics. Examines the meanings of demonstration and proof in lower secondary school mathematics and shows the relationships between them. Illustrates the discussion with a seventh grade student's activities.…

The author lists and discusses each of six stages of mathematical learning. The stages are: (1) interaction, (2) rule construction and manipulation, (3) isomorphisms, (4) representations, (5) symbolization, and (6) formalization. Examples from geometry are used to demonstrate the learning processes. (JG)

Considers radical constructivism in light of poststructuralism and hermeneutic phenomenology and shows how this forces a reassertion of the teacher's role in the student's constructing of mathematical knowledge. (48 references) (Author/MKR)

A semiotic perspective on mathematical activity provides a way of conceptualizing the teaching and learning of mathematics that transcends and encompasses both psychological perspectives focussing exclusively on mental structures and functions, and performance-focussed perspectives concerned only with student's behaviours. Instead it considers the…

This study considers two problems related to cognitive development: "Is development hierarchical?" and "If so, what are the mechanisms involved in the process of development?" Analysis of the results of an experiment lead to differentiation of stages of development, and problem-solving strategies at each level are discussed.…

The theoretical and reference frameworks developed in a 1982 study proved effective for developing a constructivist approach leading children to build a meaningful and efficient symbolism of number. Results of a three-year longitudinal study are described. (MNS)

A multidisciplinary team research project to document the relationship between environmental and cultural features of Papua New Guinea, cognitive development, and mathematics learning is described. (MP)

Analyzed are the different stages in the conceptual evolution of infinity as developed historically through the work of Bolzano and Cantor. Results of a study of 18 to 20 year old's concept of infinity prior to instruction produced aspects of the passage between conceptual levels of infinity. (MDH)

Described is the Educational Leaders in Mathematics (ELM) Project, a four-stage inservice teacher program designed to stimulate teachers' development of a constructivist view of learning. The impact of the intervention was studied, and results indicated that teachers' beliefs were affected, producing changes in teaching strategies. (MDH)

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.…