In this article, I argue that the common practice across many school mathematics curricula of using a variety of different representations of number may diminish the coherence of mathematics for students. Instead, I advocate prioritising a single representation of number (the number line) and applying this repeatedly across diverse content areas.…

In the last two decades some researchers have been using elements of Critical Theory to rethink the aims and the possibilities of school mathematics. The field known as critical mathematics education has become an important research area, and has been informing teachers who felt the need to change their practices. In this article, we explore the…

This article explores the factors that may cause teachers to defer to the textbook as the ultimate authority on curriculum and pedagogy, drawing on Bakhtin's notion of authoritative and personally persuasive discourse. We found that although teachers deferred to the textbook as the "authority" of what should be taught, they did not fully implement…

Views the mathematics curriculum in terms of things that can be worked out by someone (necessary) and things about which everyone needs to be informed (arbitrary). This view clarifies the roles that teachers and students have within the complexities of teaching and learning. (Contains 11 references.) (ASK)

Develops in detail implications for teaching of the arbitrary and necessary curriculum divide. Discusses practical ways forward for teachers who plan lessons and work in the classroom with sensitivity to this divide. Concentrates on teaching and learning arbitrary aspects of the curriculum. Arbitrary is in realm of memory and students have the job…

Discusses suggestions for the learning and teaching of mathematics based on a study examining the mathematics practices of carpet layers. Suggestions are made from the areas of (1) the school mathematics curriculum; (2) the methods used to teach school mathematics; and (3) research in mathematics education. (MDH)

The roles of skills and meaning in mathematics are discussed, with concern expressed over the little time spent on developing understanding. Approaches to proportion are described, levels of meaning are proposed, and proportion as a unifying idea for geometry are among the topics discussed. (MNS)

Presents examples of the use of mathematical modeling in mathematics courses in order to not lose sight of the essence of the mathematical attitude; encourage students' concern with problems that surround them; appreciate human resources; and associate mathematics with other sciences. (MKR)

Some concrete examples of the use of historical materials in developing certain topics from precalculus and calculus are presented. Ideas which can be introduced with a reformulated curriculum are discussed in five areas: algorithms, combinatorics, logarithms, trigonometry, and mathematical models. (MNS)

The need for improving the dialog between teacher and student is promoted as an important step towards improving the mathematics curriculum. (MP)

Presents reasons advanced for using history in mathematics education, ways of using history in the mathematics classroom and the use of history in teaching mathematics. Provides distinctions between the latter two points. (MDH)

Mathematics is perceived as a boring subject by some secondary students. Lists and describes 10 types of mathematical surprises across the secondary mathematics curriculum that help to make mathematics more interesting. (YP)

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)

This article arises from a broader study that investigates the benefits and forms of mathematical writing and written texts produced by twelve- to thirteen-year-old students in grade seven classes in six junior high schools in KwaZulu-Natal, particularly in the context of major curriculum changes within South Africa, These recent changes in…

Given the recent reconceptualizations about the nature and the role of writing within the mathematics curriculum, the proposal to instigate similar reconceptualizations, regarding the nature and the role of reading mathematics within curricular designs, is discussed with respect to appropriate strategies and relevant contexts. (JJK)