When a Year 7 student physically reacted to a prompt of another student by anxiously drumming the desk with his ruler, exclaiming "uuuuhh", the initial thought of the observing researcher, Laura, was: "this is an interesting account". This started a reflective journey of first applying robust research methodologies to the…

This paper introduces a model built upon the Method of Varying Inquiry, offering a didactical approach to problem posing and solving activities that stimulates inquiry-based learning in mathematics classrooms. The model combines the inquiry-based framework with the variation theory and with specific didactical and theoretical elements (the…

In this article, we analyse a script of an imagined classroom interaction from the perspectives of politeness and positioning. The script was written by a prospective teacher, Cara, as part of her Lesson Play. The Lesson Play was prompted by her reflection on how the needs of students who are disaffected with mathematics might be met, an issue…

What does it mean to have mathematical authority? How does it differ from pedagogical authority? We drew upon Goffman's (1981) ideas of author and animator to exemplify modes of mathematical authority that extend beyond the authorship of ideas. Through a series of excerpts from lessons in middle-grades mathematics classrooms, this paper emphasizes…

Building from the concept of verbing mathematics as a culturally consistent and enabling mathematics education practice for Mi'kmaw learners, the authors present an elementary multiplication lesson affectionately named "Sets of, Rows of, Jumps of". Through examination of this specific set of tasks emerging notions of structuring, play,…

In this article, we explore Whitehead's claim that experience is fundamentally affective. We do so in the context of an Italian primary school classroom featuring the use of the multitouch application "TouchCounts." We study the way in which the children and the iPad take each other up and the meanings of number and arithmetic that…

In Norway, children are encouraged to pose a problem that they can solve using an arithmetical calculation. This is known as 'regnefortelling'. During a larger project, we became interested in a small group of "regnefortelling" which used unusual contexts, contexts that made us uneasy and invoked a feeling of uncertainty about how we…

This paper initiates a discussion around the potential of Dynamic Measurement, an alternative approach to geometric measurement that focuses on how space is generated, and thus measured by the lower-dimensional objects that define it. I use data from a series of design experiments with fourth-grade students to illustrate some forms of reasoning…

Dialogue has been characterised as a communicative pattern that supports critical learning in education. Seeking to analyse this relationship, we investigated the interaction between teachers and students in two classes, a Third Grade and a Fifth Grade of São Paulo State public school. During the interaction, we identified a variety of dialogic…

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…

L.V. Zankov (1901-1977), a student and colleague of Vygotsky, developed a system of developmental education for elementary education through 20 years of extensive research. Since 2009, a number of Norwegian schools have been using textbooks in mathematics based on Zankov's system. In this article, we present and discuss the experiences of some…

Tensions are an integral part of mathematics teachers' practice and have been recognised as playing a pivotal role in guiding teachers' choices, and in driving teacher change. Professional development particularly elicits dilemmas. Tensions appear to be a crucial aspect of mathematics teacher education and therefore a deeper understanding of…

Mathematics is often positioned as being difficult for Ghanaian teachers to teach and pupils to learn. Although literature point to the educational and scientific relevance of many of the socio-cultural practices in the Ghanaian society, many mathematical concepts are taught out of context in schools. In this paper I will draw on Bishop's (1988)…

This article presents a case study of a small group of Grade 8 students performing bricolage during a classroom mathematics task. The data analysis involves the use of 'tapestries', a style of transcript that enables the consideration of both the group and individuals within the group as learning agents. I characterize bricolage as an emergent,…

We provide a conceptual analysis of how combinatorics problems have the potential to support students to establish non-linear meanings of multiplication (NLMM). The problems we analyze we have used in a series of studies with 6th, 8th, and 10th grade students. We situate the analysis in prior work on students' quantitative and multiplicative…