The purpose of this paper is to reclaim the place of specific examples. It is argued that a plausible step in experiencing the general is to start with a certain general process that can be applied to an already known and specific-for-the-learner object; the specific object is supposed to be there to be treated as a non-specific, particular…

Current conceptualizations of knowing and learning tend to separate the knower from others, the world they know, and themselves. In this article, we offer "relationality" as an alternative to such conceptualizations of mathematical knowing. We begin with the perspective of Maturana and Varela to articulate some of its problems and our alternative.…

This communication aims at revealing the potential of statement-posing tasks to facilitate students' thinking and strategies of understanding proof. Besides outlining the background of statement-posing tasks, four points were advanced as potential benefits of the tasks: (1) focusing on the logic of arguments in addition to the meaning of…

What is the relationship between research mathematics and the mathematics that arises in non-academic mathematical practices? I answer this question in terms of situated mathematical research, which comprises situated mathematical interpretations and situated mathematical applications. A situated mathematical interpretation of a practice takes…

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)

Draws on a range of Japanese work and unifies it under an integrating theme of 'surprise' to help gain insight into a characteristic of mathematics lessons which make students interested in mathematical ideas. (MM)

Word problems have several purposes in mathematics education. Concentrates on two of these purposes--word problems as applications and word problems as mental manipulatives--and compares them with each other. (ASK)

Argues that any mathematical construct can acquire multiple referential meanings beyond its specific mathematical meaning as it is assigned several different mappings when applied to different real-world situations. Claims that the teaching of mathematics in schools is a vehicle for an ideology concerning mathematical activity and its outcomes.…

Reviews M.B. DeBevoise's "Conversations on Mind, Matter, and Mathematics," (a book of translated conversations between Jean-Pierre Changeux and Alain Connes), which explores the question of whether a machine could reproduce the activity of the human brain. Explains how mathematics might be able to mediate between mind and matter. (DDR)

Reflecting the author's experiences in Mozambique, some conditions and strategies for mathematics education in underdeveloped countries are suggested. How mathematics education can be used for emancipation is discussed, with extensive comments on problemising reality in classroom situations and creating confidence. (MNS)

The impact and role of social needs, including computer technology, on the secondary school mathematics curriculum are considered. Their role in the American curriculum, mathematical applications, institutionalized needs, and alternatives are discussed. (MNS)

Historical issues concerning the role of mathematics in the school curriculum are considered, with numerous examples illustrating varying emphases. (MNS)

This paper is devoted to the relationship between mathematics and the social use of mathematics. Discussion includes definition of technology, examples of technology, technology in school mathematics and mathematics of social practice. (DC)

Offers examples of non-standard mathematical application problems. The applications come from a variety of areas including industry and other cultures. (PK)

The kaleidoscope is presented as a suitable topic for a preservice mathematics teacher's first contact with a nontrivial mathematical phenomenon. Included are historical notes on the kaleidoscope, explanation of the inner mechanisms of various kaleidoscope designs, and suggestions for further student investigations. (JJK)