New forms of mathematical knowledge are growing in importance for mathematics and education, including tacit knowledge, knowledge of particulars, language, and rhetoric in mathematics. Highlights the importance of attending to rhetoric and the range of rhetorical styles in school mathematics, and the need for explicit instruction in this area.…

This paper contains the comments of a discussant reviewing the paper, "The Role of Visual Representations in the Learning of Mathematics" (Abraham Arcavi). A research-based evaluation is made that focuses on the ideas of stochastics and the epistemological triangle. (Contains 28 references.) (DDR)

This essay is based on observation and interpretation of the mathematical language of children while they engage in situations involving fractional numbers. This interpretation includes the consideration of various levels of language use, informal metamorphic and metonymic uses of fractional number language, and the interplay between language use…

This paper gives a brief introduction to a discipline called the cognitive science of mathematics. The theoretical background of the arguments is based on embodied cognition and findings in cognitive linguistics. It discusses Mathematical Idea Analysis, a set of techniques for studying implicit structures in mathematics. Particular attention is…

This paper suggests that the systems of representations that we use in mathematics have a cultural origin and concludes that the knowledge produced with the help of these systems of representation likewise has a cultural origin. This assertion forces a reformulation of the issue of objectivity in terms that differ from those inherited from…

Distinguishes educational constructivism, which has its origins in the theories of children's learning, from constructivism in the philosophy of science and from constructivism in the sociology of science. Notes the evolution of educational constructivism and identifies some theoretical problems concerning constructivist teaching of science…

Explores the promises that von Glasersfeld's constructivism holds for the reform of science and mathematics education. Argues that a powerful social epistemology is needed to serve as a referent for regenerating the culture of science education. Contains 48 references. (DDR)

This paper focuses on the cultural aspects of research in mathematics learning. The shift to a more socio-cultural emphasis in mathematics education research is valid. The paper explores this point by examining challenges to the former research paradigm. These challenges include culturally-based mathematical knowledge and hidden values in…