Children bring a wealth of mathematical knowledge from home to school. This paper describes one six/seven year old girl's home interactions over 20 weeks about measurable quantities. Almost all measurement discussions occurred when actions were not straightforward. Consequently the measurement attributes usually used to introduce measurement at…

This article explores the inter-relationship between the embodied processes of pattern generalisation and the visualisation of pictorial cues. A research framework is established for analysing pupils' multiple visualisations of figural cues in the context of pattern generalisation. The research framework centres on a novel combination of three…

In this article, I focus on what can be termed "the domestication of the eye"--that is to say, the lengthy process during which we come to see and recognize things according to "efficient" cultural means. This is the process that converts the eye into a sophisticated intellectual organ--a "theoretician" as Marx put it. In particular, I focus on…

As the end result of metaphysics, the Kantian and constructivist mind is not present in the world but withdrawn into the netherworld of its representations and constructions. First phenomenology then the embodied cognition research showed how there could be no cognition without the human body. There is something unsatisfying and lacking, however,…

An episode of two students working collaboratively on a mathematical problem is analysed combining two approaches, namely the process model for mathematical level raising and role theory. The process model stresses the importance of key and regulating activities, while role theory deals with the inter- and intrapersonal concerns of the…

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…

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…

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…

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…

Mutual Interrogation is a research methodology for ethnomathematics proposed by Alangui in 2006 in an attempt to avoid the potential inequality set up when a restricted cultural practice is viewed through the lens of the near-universal and highly developed research domain of mathematics. Using three significant examples of mutual interrogation in…

Metaphors are a fundamental mechanism we use to make sense of our world. They structure our interpretations of and interactions with ideas, including mathematical ideas. Thus, the sense students make out of mathematical ideas depends upon the metaphor they use to structure their thinking. This paper examines the metaphors used in one fourth-grade…

Mathematics as a field of study is often encountered in its written form, captured in texts of various genres at primary and (post)secondary school levels. The way mathematics is WRITTEN (being referred to here as wrotographic evidence) determines to a greater extent how it is read and spoken (verbalized). This exploratory article has poetic…

A well-documented experience of students of elementary Euclidean geometry is "seeing" a geometric result and being sure about its truth; this sort of experience gives rise to the notion of geometrical visualisation that is developed here. In this essay a philosophical argument for the epistemic potential of geometrical visualisation is reviewed,…

We report on an experiment conducted with pre-service teachers in France and in Quebec. They were submitted to a classroom situation involving regular polyhedra. We expected that through the activities of defining, of exploring and experimenting via concrete constructions and manipulation, students would reflect on the link face angle--dihedral…

The algebraic expertise that mathematics education is aiming for includes both procedural skills and conceptual understanding. To capture the latter, notions such as symbol sense, gestalt view and visual salience have been developed. We wonder if digital activities can be designed that not only require procedural algebraic skills, but also invite…