Motivated by the question, "What exactly about a mathematical concept should students discover, when they study it via discovery learning?", I present and demonstrate an interpretation of discovery pedagogy that attempts to address its criticism. My approach hinges on decoupling the solution process from its resultant product. Whereas theories of…

Discusses the role of play in the learning of mathematics. Describes a play for the third grade mathematics classroom that focuses on negative numbers and number concepts, and revisits Vygotsky from this point of view. Concludes that mathematically imaginative play can contribute greatly to mathematics learning in elementary school. (Contains 20…

Proposes an entirely different perspective and challenges both the current para-dogmatic character of constructivism in some quarters of mathematics education and the dismissive attitude towards 'humanist non-sense' in others. Discusses the linguistic aspects of mathematical knowledge through a language acquisition device and a language…

Discusses Brousseau's work on the theory of didactical situations in mathematics and its applications in mathematics classrooms which do not address the collection of obvious components, but instead discuss phenomena by analyzing knowledge in given situations. Meanings emerge in situations engineered by analyzing a situation and developing an…

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

Presents and criticizes current theories of multiplication in order to pave the way for an alternative foundation for the concept of multiplication. Formulates a uniform concept of multiplication that recognizes anew the importance of the roles of multiplier and multiplicand. (Contains 22 references.) (ASK)

Introduces a Vygotskian approach to learning with an emphasis on mediated activity within a particular socio-historical context. Addresses the relationship between mathematical learner and different sign systems (multiple representations) afforded by the graphic calculator. Contains 32 references. (ASK)

Discusses the similarities in learning outcomes from two very different environments: a research group and a problem-solving course. Provides examples that characterize the two environments and that point to similarities in outcomes. Speculates about why such similarities exist. (DDR)

Principles on which the teaching of mathematics is based are discussed. Sections concern the skill principle, the curriculum principle, and learning strategy, with many classroom illustrations. (MNS)

The ideas of Kuhn and Lakatos are used to study four issues in mathematics education related to values, units of analysis, theory of mind, and nature of mathematical entities. The goal is to determine whether differences between the assumptions are best understood in Kuhnian or Lakatosian terms. (MNS)

The constructivist perspective, which holds that children's learning of subject matter is an interaction between what they are taught and what they bring to a learning situation, could be used to improve mathematics teacher education. (PK)

The role of mental discipline theory in the history of mathematics education is considered. The author argues that we now remember mental discipline theory only as a caricature of what it was; moreover, it persists among both teachers and researchers. (MNS)

This paper is devoted to the relationship between mathematics and the social use of mathematics. Discussion includes definition of technology, examples of technology, technology in school mathematics and mathematics of social practice. (DC)

The question is raised: What comes first: rules of calculation or the meaning of concepts? The pressures on the teacher to teach and simplify knowledge to algorithms are discussed. The relation between conceptual and procedural knowledge in school mathematics and consequences for the teacher's professional knowledge are considered. (DC)

A description of De Morgan's life and work is followed with quotations of his thoughts and insights on the teaching and learning of mathematics. The purpose is to illustrate the sharpness of his ideas, his creative insights, and his wit for the enjoyment of the reader. (DC)