How do teachers relate to the "conflicts" that exist between scientific research findings and school institutional demands? Starting with a "provocative" statement by a primary school teacher, we interviewed eleven teachers asking them to express their opinions on this statement. Based on Brown's rereading of the four…

This paper takes a 'networking of theories' approach to understand the complexity of the phenomenon of agency. We examine an episode, where a kindergarten teacher and nine children work on an addition problem, from three different perspectives: Valsiner's zone theory; Radford's theory of objectification; and Pickering's dance of agency. Our…

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…

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…

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…

Findings from international assessments present an opportunity to reconsider mathematics education across the grades. If concepts taught in elementary grades lay the foundation for continued study, then children's introduction to school mathematics deserves particular attention. We consider Davydov's theory (1966), which sequences…

In this article, I build on the work of mathematics education researchers (Hackenberg, 2005; Sztajn, 2008) who have used Noddings's (1984) notion of caring to lend insights to the teaching of mathematics. In particular, I retrospectively analyze my actions when I was serving as a mathematics teacher educator seeking to provide professional…

As part of a larger project focused on transforming mathematics education for Aboriginal students in Atlantic Canada, this paper reports on the role of the Mi'kmaw language in mathematics teaching. Examining how mathematical concepts are described in Mi'kmaq gives insight into ways of thinking. Shifting classroom discussions to reflect Mi'kmaw…

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…

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…

This paper first reports on the methodology of a study of teacher knowledge for statistics, conducted in a classroom at the primary school level. The methodology included videotaping of a sequence of lessons that involved students in investigating multivariate data sets, followed up by audiotaped interviews with each teacher. These stimulated…

Research conducted during the Trends in International Mathematics and Science Study (TIMSS) and later (Stigler et al. 1999; Stigler and Hiebert 1999) undertook a thorough analysis of lessons in the United States, Japan, and Germany. This article focuses on certain aspects of mathematics lessons in Russia. Specifically, the attempt is made to…