45 research outputs found
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 anotherās 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
Lacan, subjectivity and the task of mathematics education research
This paper addresses the issue of subjectivity in the context of mathematics education research. It introduces the psychoanalyst and theorist Jacques Lacan whose work on subjectivity combined Freudās psychoanalytic theory with processes of signification as developed in the work of de Saussure and Peirce. The paper positions Lacanās subjectivity initially in relation to the work of Piaget and Vygotsky who have been widely cited within mathematics education research, but more extensively it is shown how Lacanās conception of subjectivity provides a development of Peircian semiotics that has been influential for some recent work in the area. Through this route Lacanās work enables a conception of subjectivity that combines yet transcends Piagetās psychology and Peirceās semiotics and in so doing provides a bridge from mathematics education research to contemporary theories of subjectivity more prevalent in the cultural sciences. It is argued that these broader conceptions of subjectivity enable mathematics education research to support more effective engagement by teachers, teacher educators, researchers and students in the wider social domain
Signifying āstudentsā, āteachersā and āmathematicsā: a reading of a special issue
This paper examines a Special Issue of Educational Studies in Mathematics comprising research reports centred on Peircian semiotics in mathematics education, written by some of the major authors in the area. The paper is targeted at inspecting how subjectivity is understood, or implied, in those reports. It seeks to delineate how the conceptions of subjectivity suggested are defined as a result of their being a function of the domain within which the authors reflexively situate themselves. The paper first considers how such understandings shape concepts of mathematics, students and teachers. It then explores how the research domain is understood by the authors as suggested through their implied positioning in relation to teachers, teacher educators, researchers and other potential readers
Gender and choice in education and occupation
Gender and choice in education and Occupation will be of inerest to students and practioners in education, management, psycology, the social scienceand social services, and to all those interested in social equality.xii, 187 p.: ill.; 23 c
The mediating role of a teacherās use of semiotic resources in pupilsā early algebraic reasoning
The final publication is available at Springer via http://dx.doi.org/10.1007/s11858-012-0421-2.This paper focuses on the semiotic resources
used by an experienced sixth-grade teacher when her pupils
are working on a mathematical task involving written text
and the two inscriptions of figure and diagram. Socio-cultural
analytical constructs such as semiotic bundle, space of
joint action and togethering are applied in order to enable
and frame the collective activity of the teacher and pupils.
Four extracts from different situations in the classroom
illustrate the important role of both teacher gestures and
pupil gestures, interacting with other modalities such as
speech and inscription, in the process of making sense of
pupilsā appropriation of coordinating two dimensions in a
diagram. It is argued that the nature of the mathematical
task is an important entry point into early algebraic reasoning.
The study emphasises the mediating role of the
dynamics of semiotic bundles produced in teacherāpupil
dialogues as a promising way to address the fundamental
relationships between mathematics, pupil and teacher in a
classroom context in order to provoke pupil involvement
and engagement when experiencing mathematics