It has become gradually accepted that proof and proving are essential at all grades of mathematical learning. Among the various aspects of proof and proving, this study addresses proofs and refutations described by Lakatos, in particular a part of increasing content by deductive guessing, to introduce an authentic process into mathematics…

This article examines the shifts in attention and focus as one teacher introduces and explains an image that represents the processes involved in a numeric problem that his students have been working on. This paper takes a micro-analytic approach to examine how the focus of attention shifts through what the teacher and students do and say in the…

The notion of temporal range is introduced and discussed in this paper. Two dimensions of temporal range are identified: mathematical temporality relating to mathematical ideas, their precursors and horizons; and a mathematical learning temporality where what students say/do provides the ground on which future learning can be built. These…

Identifying mathematical and didactical conditions under which mathematics learners can encounter an intellectual need for defining and proving is recognized as a challenging research enterprise. This paper presents a particular configuration of conditions under which a group of pre-service mathematics teachers successfully constructed a…

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.…

I argue for the inclusion of topics in high school mathematics curricula that are traditionally reserved for high achieving students preparing for mathematical contests. These include the arithmetic mean--geometric mean inequality which has many practical applications in mathematical modelling. The problem of extremalising functions of more than…

Focuses on elementary school teachers' perceptions of creativity and logic and their places within mathematics education. Explores themes arising from the ways in which creativity and logic were talked about, addressing the extent to which the teachers believed that mathematics was creative or logical and whether these two characteristics were…

Discusses whether verbal interaction is recognized as the source from which co-operative groups draw their power to facilitate mathematical learning. Reflects on a group in a mathematics course for prospective secondary teachers focused on problem solving where silence was commonplace. (ASK)

Considers how the domains of mathematics education and history of mathematics may interact in the process of mathematics teaching. Focuses on the teachers' role and explores the relationship between research in mathematics education and the history of mathematics. Contains 24 references. (DDR)

Speculates on whether our knowledge of a mathematical topic is really the same as the knowledge of the topic held by our mathematical ancestors centuries ago. Provides specific examples of using the cultural context of mathematics as an instructional strategy. (DDR)

Presents the text of a message sent to Susan Gerofsky by Robert Thomas after reading her article on a linguistic and narrative view of word problems in mathematics education. Gerofsky's response is also included. (DDR)

Discusses the similarities in learning outcomes from two very different environments: a research group and a problem-solving course. Provides examples that characterize the two environments and that point to similarities in outcomes. Speculates about why such similarities exist. (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)

This study concerned conceptual difficulties of college students learning programming and ways the teacher can simplify the process. An analysis of general strategies used in solving problems involving loops is given, with four types of hierarchical strategy categorized. Students had difficulty transforming their algebraic descriptions into…

How students are convinced that they have the correct solution to a problem, free of contradiction, is discussed. The role of counterexamples and the need for a situational analysis of problem-solving behaviors are each included. (MNS)