Affect and mathematical competence are each multifaceted constructs. Accordingly, the studies in this Special Issue address multiple pathways between the two in young children. This commentary highlights the variability of these pathways and asks how affective variables are specifically related to core mathematical activities such as problem…

In some circles of mathematics education, repetition and rote are somehow conflated in terms of their pedagogical uses and ramifications. In this paper, I argue for the separation of the two, relying upon a framework suggested by Martin Buber's "I-Thou" ontology. In the presentation of Buber's ideas, I highlight the notion of…

In this paper, we propose an approach to analysing teacher arguments that takes into account field dependence--namely, in Toulmin's sense, the dependence of warrants deployed in an argument on the field of activity to which the argument relates. Freeman, to circumvent issues that emerge when we attempt to determine the field(s) that an argument…

While reading the articles assembled in this volume, one cannot help asking "Why gestures?" What's all the fuss about them? In the last few years, the fuss is, indeed, considerable, and not just here, in this special issue, but also in research on learning and teaching at large. What changed? After all, gestures have been around ever since the…

This paper comments on the expanded repertoire of techniques, conceptual frameworks, and perspectives developed to study the phenomena of gesture, bodily action and other modalities as related to thinking, learning, acting, and speaking. Certain broad issues are considered, including (1) the distinction between "contextual" generalization of…

Discusses characteristics in feminist pedagogy literature and situates them with respect to four dialectical aspects (passivity/active participation, omission/inclusion, silence/speech, and powerlessness/empowerment). These characteristics are combined with nondiscriminatory classroom practices to develop a frame of reference for inclusive…

My purpose in this paper is to present a didactic tool--a set of specially designed problems and questions for discussion--that can help making students better aware of the various aspects of the formal notion of limit of a sequence. The didactic tool will be justified using results from my own and other authors' research on students' naive or…

How to integrate mathematics, psychology, pedagogy, and practical teaching within the didactics of mathematics in order to get unified theories and conceptions of mathematics teaching is considered. An approach based on teaching units is suggested. (MNS)

Examines discourse, not strictly mathematical, that teachers might adopt in a mathematics class and presents three major functions of such discourse: communication; structuring and labeling; and reflection. Develops lines for further inquiry, notably on the third function, the most likely focus for specific preparation by the teacher. (13…

This article discusses an approach to teacher belief systems which casts an eye away from cognitive constructs toward sociological constructs to complement existing ideas about the nature and genesis of beliefs. I offer some theoretical ideas for extending the notion of beliefs and describe two contrasting senior mathematics teachers,…

Changes in mathematics education from the 1950s to the 1980s are briefly described by the author, who was a leading mathematics educator in Hungary. Illustrations focus on personal experience and small group interaction. (MNS)

It is argued that the view of mathematics as an activity emphasizing intuitive thinking is compatible with an axiomatic-deductive approach. (MP)

Burn (2005) proposes a "genetic approach" to teaching limits of numerical sequences. The article includes an explanation of the Method of Exhaustion, a generalization of this method, and a description of how this method was used for obtaining areas and lengths in the seventeenth century. The author uses these historical and mathematical analyses…

The author shows some causes of failure in the creation of mathematical concepts. One is the stiffening of concept cores, which prevents identification of atypical exemplars and solution of atypical problems and causes a bifurcation between the natural system of everyday concepts and the formal system of school concepts. (Author/MDH)

This is a commentary paper in the volume on "Teachings situations as object of research: empirical studies within theoretical perspectives". An essential object of mathematics education research is the analysis of interactive teaching and learning processes in which mathematical knowledge is mediated and communicated. Such a research perspective…