Learning mathematics is often justified as supporting students to make rational decisions, an important goal given the misinformation spread through social media every day. However, when asking preservice teachers to engage in a critical mathematics education activity in which they had to produce an argumentation that would persuade people to…

Much of the education research on implicit differentiation and related rates treats the topic of differentiating equations as an unproblematic application of the chain rule. This paper instead problematizes the legitimacy of this procedure. It develops a conceptual analysis aimed at exploring how a student might come to understand when and why one…

The article discusses the role of body movement, perception and kinaesthesia in mathematical thinking and accounts for the virtuality of mathematical concepts. A first person experience with a graphing motion software (WiiGraph), which involves ample body movements and is used to draw a circle, is presented. To study the unfolding of the…

In this article we address the 'educationalization' of authentic marine navigation tasks for upper secondary mathematics classrooms and their potential for students' learning. Our approach is based on boundary crossing and as well as on the distinction between realistic tasks (targeting students' familiarization with the marine navigation…

An important issue in mathematics education in many countries has long been how to make use of students' daily life mathematics (informal mathematics) in teaching mathematics at school (formal mathematics). This communication proposes an alternative framework of mathematics education that bridges informal and formal mathematics using…

In this article, I examine how a focus on preciseness in the mathematics classroom could affect group activity. The preciseness relates to the ways mathematical concepts, in this case angles are described in discourse between students. In this context, I consider how 'micro-invalidations', can limit students' opportunities to learn in a social and…

A poetic structure occurs when a speaker's comment repeats some of the syntax and words of a previous comment. During a collaborative algebra task, a student explained a property five times over a few minutes, in slightly different ways. He consistently used poetic structures that were marked elaborately through discursive modes such as pause,…

In this article we compare two frameworks for analysing young children's responses to the task of copying and extending a 6-dot triangle pattern. We used Mulligan & Mitchelmore's Awareness of Mathematical Pattern and Structure (AMPS) and then Biggs & Collis' SOLO taxonomy, both of which provide criteria for assigning levels. In comparison…

When deciding what constitutes students' "on task" or "off task" mathematical communication, teachers and researchers are also making judgements about what is, and what is not, mathematics. In this paper, we question our ability to separate the mathematical from the nonmathematical. We explore intersecting storylines in Grade…

Originating from interviews with mathematics colleagues, written accounts of mathematicians engaging with mathematics, and Wes's reflections on his own mathematical work, we describe a process that we call mathematical foresight: the imagining of a resolution to a mathematical situation and a path to that resolution. In a sense, mathematical…

Mathematical conventions -- which account for the choices of mathematics community regarding definitions of concepts, their names and symbols -- are the focus of this paper. We introduce the task of unpacking, that is, offering plausible explanations and arguments for the choice of conventions. Using responses of four prospective teachers to the…

In this article I present examples of young children's interaction in collaborative group work in mathematics and consider how the children shared intentions, that is, how they influenced the thinking of another. By analysing the children's use of deixis as an aspect of indexicality, I examined how the students pointed out mathematical…

The paper presents and analyses a sequence of events that preceded an insight solution to a challenging problem in the context of numerical sequences. A three­week long solution process by a pair of ninth­-grade students is analysed by means of the theory of shifts of attention. The goal for this article is to reveal the potential of this theory…