In this paper, I comment on the set of papers in this special issue on mathematical problem posing. I offer some observations about the papers in relation to several key issues, and I suggest some productive directions for continued research inquiry on mathematical problem posing.

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…

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…

The purpose of this article is to consider what methods from ethnopoetics--a field at the intersection of linguistics and anthropology--may add to narrative inquiry in mathematics education. I build a theoretical framework to argue for the use of narrative inquiry and ethnopoetics in studies of teacher knowledge. I report ethnopoetic analyses of…

In this volume, Wolff-Michael Roth provides a critical but partial reading of Tony Brown's book "Mathematics Education and Subjectivity". The reading contrasts Brown's approach with Roth's own conception of subjectivity as derived from the work of Vygotsky, in which Roth aims to "reunite" psychology and sociology. Brown's book, however, focuses on…

In this article, I make a case for the inputs that Martin Heidegger's theoretical perspective offers to current concerns about the nature of mathematics, its teaching and learning, and the problem of subjectivity. In particular, I consider Heidegger's notion of positive science and discuss both its applicability to mathematics and its importance…

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…

I begin by appreciating the contributions in the volume that indirectly and directly address the questions: Why do gestures and embodiment matter to mathematics education, what has understanding of these achieved and what might they achieve? I argue, however, that understanding gestures can in general only play an important role in "grasping" the…

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…

In this response we address some of the significant issues that Tony Brown raised in his analysis and critique of the Special Issue of "Educational Studies in Mathematics" on "Semiotic perspectives in mathematics education" (Saenz-Ludlow & Presmeg, Educational Studies in Mathematics 61(1-2), 2006). Among these issues are conceptualizations of…

Everyday Mathematics has contributed in important ways to long-standing debates about mathematical concepts, symbolic representation, and the role of contexts in thinking--the latter topic reaching back at least as far as Kant's notion of scheme. The descriptive work plays a role, of course. But it is only by making sense of the observations that…

In the last three decades there have been a variety of studies of what is often referred to as "everyday" or "street" mathematics. These studies have documented a rich variety of arithmetic practices involved in activities such as tailoring, carpet laying, dieting, or grocery shopping. More importantly, these studies have helped to rectify…

Macroeconomic forces, globalization, transnational capital flight, and massive migration have global and local reverberations that affect our classrooms, teachers, communities, and students. In particular, teaching and learning mathematics in multiple language contexts is affected by these broader dynamics. Thus, politicizing the discussion around…

Meaning is one of the recent terms which have gained great currency in mathematics education. It is generally used as a correlate of individuals' intentions and considered a central element in contemporary accounts of knowledge formation. One important question that arises in this context is the following: if, in one way or another, knowledge…

This comment attempts to identify different "semiotic perspectives" proposed by the authors of this special issue according to the problems they discuss. These problems can be distinguished as problems concerning the representation of mathematical knowledge, the definition and objectivity of meaning, epistemological questions of learning and…