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In this paper, we use the work of philosopher Gilles Châtelet to rethink the gesture/diagram relationship and to explore the ways mathematical agency is constituted through it. We argue for a fundamental philosophical shift to better conceptualize the relationship between gesture and diagram, and suggest that such an approach might open up new ways of conceptualizing the very idea of mathematical embodiment. We draw on contemporary attempts to rethink embodiment, such as Rotman's work on a “material semiotics,” Radford's work on “sensuous cognition”, and Roth's work on “material phenomenology”. After discussing this work and its intersections with that of Châtelet, we discuss data collected from a research experiment as a way to demonstrate the viability of this new theoretical framework.

If mathematics is a male domain, where does this leave women who do mathematics? In a world where there is little or no discursive space in which to be female, women who enter in must do identity work in order to achieve what is often an uneasy presence.This paper builds on recent research which suggests that some undergraduate women are however finding new spaces for belonging in the world of mathematics through critical reflection and collective challenge to dominant discourses. Focussing on an analysis of two women's narratives of their success in mathematics, it explores their multi-voiced accounts of self through the lens of Bakhtin's dialogism. It discusses the scope of reflexivity in creating new identity spaces in refigured worlds.

In this article, I deal with the question of emancipation in education. In the first part of the article, I argue that contemporary concepts of emancipation are explicitly or implicitly related to the idea of the sovereign subject articulated by Kant and other philosophers of the Enlightenment. I contend that our modern enlightened concepts of emancipation rest on a dichotomy between an autonomous and self-sufficient subject and its sociocultural world. Referring to current research in mathematics education, I show how this dichotomy leads to intrinsic contradictions that haunt ongoing educational practices.These contradictions, I contend, are manifested in the hopeless efforts to bridge the gap between the deeds and thoughts of an autonomous individual and the regimes of reason and truth in which the individual finds itself subsumed. In particular, I argue that emancipation as understood in the enlightened modern sense remains a chimeric and unfulfillable dream. In the second part of the article, I suggest that emancipation can still be an orienting vector of educational practice and research, but it needs to be conceptualized differently: emancipation needs not be predicated in terms of individuals' freedom and individualist autonomy, but in critical-ethical terms.

In underscoring the affective elements of mathematics experience, we work with contemporary readings of the work of Spinoza on the politics of affect, to understand what is included in the cognitive repertoire of the Subject. We draw on those resources to tell a pedagogical tale about the relation between cognition and affect in settings of mathematical learning. Our interest is first captured in the way in which one teacher's priority of establishing an inclusive learning community occasionally harboured what appeared to be pedagogically restrictive conceptions of mathematics. Yet, the classroom practices that produced these conceptions promoted the students' motivation and provided meaningful access to mathematical learning within the classroom collectivity. In a second example, the postponement of scientific encapsulation in bodily imitations of planetary movement kept alive a shared dynamic sense of an elliptical orbit. In both of these cases, we draw on Spinoza's work to show how the affectivity of classroom practice constituted conceptions of cognition and of mathematical activity crucially linked to the imperatives of participation.

This analysis of the writing in a grade 7 mathematics textbook distinguishes between closed texts and open texts, which acknowledge multiple possibilities. I use tools that have recently been applied in mathematics contexts, focussing on grammatical features that include personal pronouns, modality, and types of imperatives, as well as on accompanying structural elements such as photographs and the number of possibilities presented. I extend this discussion to show how even texts that appear open can seduce readers into feeling dialogue while actually leading them down a narrow path. This phenomenon points to the normalizing power of curriculum. For this analysis and reflection, I draw on mathematics textbook material that I wrote. As a way of modelling an alternative to normalization, I identify myself as a self-critical author and thus invite readers to be critical of their reading and writing of mathematics texts.

Symbolic power is discussed with reference to mathematics and formal languages.Two distinctions are crucial for establishing mechanical and formal perspectives: one between appearance and reality, and one between sense and reference. These distinctions include a nomination of what to consider primary and secondary. They establish the grammatical format of a mechanical and a formal world view. Such views become imposed on the domains addressed by means of mathematics and formal languages. Through such impositions symbolic power of mathematics becomes exercised. The idea that mathematics describes as it prioritises is discussed with reference to robotting and surveillance. In general, the symbolic power of mathematics and formal languages is summarised through the observations: that mathematics treats parts and properties as autonomous, that it dismembers what it addresses and destroys the organic unity around things, and that it simplifies things and reduces them to a single feature. But, whatever forms the symbolic power may take, it cannot be evaluated along a single good-bad axis.