This communication supports an argument that preservice elementary teachers ought to study number language as part of their mathematics content courses, just as they study relationships between numeration and quantity. In particular, the paper spells out some ways in which number language can be seen as problematic by carefully detailing various…

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)

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…

Investigates the question, Can the mathematics students are taught be cast in such a form that it can be apprehended with the abilities they have and if so, how? Focuses on the language of student abilities, the nature of abilities, and individual differences. (MM)

Discusses some aspects of learning to read the process of the variation in congruence and relate it to the original geometry of the sphere since it touches on more general questions about how models are appropriated and used. Presents a learning episode that implemented projective models for both spherical and hyperbolic geometry in Object Logo.…

Reflects on four years of teaching a course called Principle of Major Teachers for pre-service elementary school teachers. Identifies and describes the discord between their formal mathematical knowledge and their informal language used in the context of elementary number theory. Presents encouraging results from a code-switching experiment.…

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)