Inferentialism as an alternative to socioconstructivism in mathematics education

The purpose of this article is to draw the attention of mathematics education researchers to a relatively new semantic theory called inferentialism, as developed by the philosopher Robert Brandom. Inferentialism is a semantic theory which explains concept formation in terms of the inferences individuals make in the context of an intersubjective practice of acknowledging, attributing, and challenging one another’s commitments. The article argues that inferentialism can help to overcome certain problems that have plagued the various forms of constructivism, and socioconstructivism in particular. Despite the range of socioconstructivist positions on offer, there is reason to think that versions of these problems will continue to haunt socioconstructivism. The problems are that socioconstructivists (i) have not come to a satisfactory resolution of the social-individual dichotomy, (ii) are still threatened by relativism, and (iii) have been vague in their characterization of what construction is. We first present these problems; then we introduce inferentialism, and finally we show how inferentialism can help to overcome the problems. We argue that inferentialism (i) contains a powerful conception of norms that can overcome the social-individual dichotomy, (ii) draws attention to the reality that constrains our inferences, and (iii) develops a clearer conception of learning in terms of the mastering of webs of reasons. Inferentialism therefore represents a powerful alternative theoretical framework to socioconstructivism

Is my memory an extended notebook?

Clark and Chalmers' conception of spatially extended memory is under- pinned by an objectified conception of biological memory. To the extent that this can be identified with a ‘storage’ approach to memory, criticisms of it are well known and an alternative approach, perhaps more suited to an enactive account of cognition, might be one which focuses on remembering as a type of action. In the Otto story the objectification of memory is apparent not only in C&C’s characterization of the notebook but also in the notion that Inga’s memory is notebook-like. Insofar as Inga’s practices, or conceptions, of remembering might be notebook-like this should not be taken as evidence of the existence of an internal store, but could instead be the result of prior interaction with notebook-like artifacts

Philosophy, activity, life

This paper, written to honor Prof. Vladislav Lektorsky on the occasion of his 90th birthday, addresses a subject to which Lektorsky has returned many times in the course of his long and distinguished career: the concept of activity. I begin with the distinction between activity and action, arguing against the view, associated with Leontiev, that actions are components of activities. In my view, the distinction between activity and action is an aspectual rather than ontological or mereological one. I then draw on the analysis of intentional action offered by G.E.M. Anscombe to argue that her understanding of action, intention and practical knowledge, when supplemented by insights from MacIntyre, McDowell and others, provides grounds to endorse three theses central to the activity approach (theses I find in Prof. Lektorsky’s recent summation of the tradition): that (i) consciousness, the inner plane of our mental lives, can be understood only in relation to the forms of our activity as embodied beings; (ii) human agency and behavior cannot be described or explained without essential reference to the social, cultural and historical context; and (iii) selves or persons are constituted in and through their activity. I then consider the objection that my analysis is too focused on the intentional activities of the individual, at the expense of the collective. I reply that the unit of analysis is neither the individual nor the collective, but the human life form. There is plenty of room, as there must be, for countenancing joint, shared and collective intentionality, and for recognizing that individuals and collectives do many things unintentionally. But no sense can be made of any of that without a robust account of intentional action. I believe my findings are congenial to three themes that characterize the legacy of Vladislav Lektorsky: (i) respect for the phenomenology of everyday thought and experience; (ii) humanism; and (iii) the belief that much is to be gained by bringing Russian philosophy into constructive dialogue with fruitful trends in Anglo-American philosophy.</jats:p

Towards an understanding of teacher judgement in the context of social moderation

Social moderation involves teachers gathering together to discuss their judgements of the quality of student work and to reach agreement regarding the standard awarded. This qualitative study conducted over a three-year period investigated the social practice of moderation and the influence on teachers’ judgements of students work. An initial survey of teachers’ understandings of moderation and standards, pre-interviews of teachers who participated in the moderation meetings, observations of these meetings with a particular focus on one teacher (focus teachers) comprised the data collection methods. Data analysis involved organising, matching, coding, identifying patterns and themes using a constant comparative method. Socio-cultural theories of learning and assessment underpinned the approach to data analysis and proved helpful in explaining the diverse influences on teachers’ judgements beyond the task criteria, and the progressive development of shared understandings through engaging in professional discussions of students’ work. The study revealed that the process is not clear and linear and is influenced by factors such as the representation of the standards and the knowledge base of the teachers