This article is concerned with cognitive aspects of students' struggles in situations in which familiar concepts are reconsidered in a new mathematical domain. Examples of such cross-curricular concepts are divisibility in the domain of integers and in the domain of polynomials, multiplication in the domain of numbers and in the domain of vectors,…

One of the most salient arguments in favor of a semiotic approach, put forward on various occasions among others by Luis Radford, claims that semiotics is most appropriate to treat the interaction between socio-cultural and objective aspects of knowledge problems. But if we want to take such claims seriously, we have to undertake revisions of our…

The author suggests that a close analysis of existing calculus courses indicates that some of the material can be explained much more clearly by using some of the language of set theory. He gives examples showing that many of the pedagogical problems arising in calculus can be overcome by using a graphical approach. (FL)

A response to recent criticisms of new mathematics programs in the elementary schools. Attempts to clarify some of the goals and methods of these programs. (BD)

Ten recent results in pure mathematics are described, covering the continuum hypothesis, Diophantine equations, simple groups, resolution of singularities, Weil conjectures, Lie groups, Poincare conjecture, exotic spheres, differential equations, and the index theorem. Proofs are omitted, but references are provided. (DT)

Demonstrated are binary operations on whole numbers which are commutative but not associative, or associative but not cummutative. Also presented are sets of numbers within which the Unique Factorization Theorem does not hold true. (JP)

The authors present an enrichment topic appropriate for use in grade 12. A mathematical system is defined using integer 3-tuples and it is shown that this system is a field isomorphic to the rational numbers. The unit is useful for illustrating the abstract nature of mathematics. (CT)

The author describes the concept of Randolph diagrams (R-diagrams) which is a scheme for simplifying set-theoretic and/or logical expressions. Several applications of R-diagrams are presented. [Not available in hardcopy due to marginal legibility of original document.] (FL)