In this article, I present the notion of a set-oriented perspective for solving counting problems that emerged during task-based interviews with postsecondary students. Framing the findings within Harel's "ways of thinking", I argue that students may benefit from this perspective, in which they view attending to sets of outcomes as…

In this paper I argue my opposition to the consensus which has dominated the literature that young children view shapes as a whole and pay no attention to shape structure and that geometrical thinking can be described through a hierarchical model formed by levels. This consensus is linked to van Hiele's weok by van Hiele-based research. In the…

I argue that until ethnomathematical frameworks are explicitly used to investigate the specific mathematical practices in networks of powerful elites the term will continue to index that which is Other to "traditional" mathematics and run a risk of desubstantialization. I suggest that the field ally itself with disciplines and perspectives in…

Indulging in recounting a few salient memories of what seems now like a dim and distant past, I raise questions about the ebb and flow, the waxing and waning of salient themes in mathematics education. I mention some of the most inspirational influences on my thinking and on my behaviour with learners of all ages. I take the opportunity to ask…

Discusses public indifference and student ignorance toward mathematics in the U.S. Presents a basic core of mathematics knowledge that everyone should know. (KHR)

Discusses the meaning of the phrase "mathematics is everywhere." Introduces the book "Reconstructing School Mathematics: Problems with Problems and the Real World", written by Stephen Brown, which emphasizes mathematical modeling and the connection between mathematics and students' lives. (KHR)

Discusses the life of David Hawkins, one of the most influential educators involved in school reform in the 1960s. Focuses on the aesthetic as the center of Hawkins' vision of schooling. Compares Hawkins' perspective to Dewey's in terms of the aesthetic. (KHR)

Discusses the question "why teach mathematics to all students"? Clarifies, elaborates, and abdicates a previous article on the same subject. (Contains 18 references.) (ASK)

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 issues related to orality, aurality, and literacy in the teaching and understanding of mathematics. Also discusses ritual and tradition in mathematics instruction. (MM)

Disscusses the history of Theo van Doesburg's painting Arithmetic Composition 1. Relates the work to that of Mondrian and Malevich. (MM)

The third of three articles considers the necessary, which lies in the realm of awareness. Discusses the nature of awareness and its relationship to mathematics learning. (MM)

Addresses the question of what mathematicians can do for mathematics education. Discusses mathematization as the mental processes which produce mathematics. (MM)

Presents a conversation between Lesley Lee and David Pimm about David Wheeler. Discusses the concept of complementarist epistemology. (MM)

Describes the process of the generation of an International Commission on Mathematics Instruction (ICMI) report. Analyzes a particular volume, 'History in Mathematics Education', in detail. (MM)