Certain aspects of theoretical frameworks in mathematics education can remain unexplained in the literature, hence unnoticed by the readers. It is thus interesting to participate in a dialogue where they can be discussed and compared in terms of the aims, objects studied, results and their relation to teaching. This study is focused on how APOS…

Part 1 of a three-part article analyzing radical constructivism (as one interpretation of Piaget) and the socio-cultural perspective (as one interpretation of Vygotsky), including major principles, primary contributions to mathematics education, and potential limitations. Introduces an integration of the two theories through a feminist…

Shows similarities between realism and radical constructivism by presenting examples of using children's ideas in order to create education in the context of teaching spherical geometry. (18 references) (MKR)

Discusses the gap between educational theories and practice and focuses on constructivism in mathematics classrooms. Contains 12 references. (ASK)

Discusses partitioning and hierarchical types of classification, a theoretical analysis of the role and function of hierarchical classification in mathematics, and the teaching of a hierarchical classification of quadrilaterals. (Contains 21 references.) (MKR)

Discusses formalizing in mathematics and provides anecdotal illustrations of formalizing in a constructivist environment, using students aged 12 and 8 involved in fraction work. (Contains 19 references.) (MKR)

Discusses, through quotes about mathematical understanding from mathematicians, the experience of understanding, a nonobjectivist theory of meaning, the origins of mathematical objects, and reification as the birth of metaphor.(Contains 35 references.) (MKR)

Suggests an approach to the analysis of mathematical texts that makes use of linguistic theory to provide insights into how the language of a text may influence the ways in which readers make sense of it. Focuses on the ways in which teacher-readers may make sense of texts produced by students. Contains 33 references. (DDR)

Provides details of a study on mathematics learning that applies Bruner's concept of format of interaction which is employed in language acquisition theory and in understanding mathematical augmentation. Describes the interactions among tutors, students, and their linear algebra text. (DDR)

Provides examples and a discussion of the Inquiry Cooperation Model (ICM). The ICM is a way of describing a pattern of communicative cooperation between teacher and students. It tries to develop students' preconceptions into mathematical competence. Contains 15 references. (DDR)

Focuses on the understanding of the concept of function and presents discussions of the topological properties of functions and of students' mathematical thinking when they are asked to determine whether a property of a function is a topological property or not. Contains 15 references. (DDR)