Negotiating different disciplinary discourses: biology students’ ritualized and exploratory participation in mathematical modeling activities

Non-mathematics specialists’ competence and confidence in mathematics in their disciplines have been highlighted as in need of improvement. We report from a collaborative, developmental research project which explores the conjecture that greater integration of mathematics and biology in biology study programs, for example through engaging students with Mathematical Modeling (MM) activities, is one way to achieve this improvement. We examine the evolution of 12 first-semester biology students’ mathematical discourse as they engage with such activities in four sessions which ran concurrently with their mandatory mathematics course and were taught by a mathematician with extensive experience with MM. The sessions involved brief introductions to different aspects of MM, followed by small-group work on tasks set in biological contexts. Our analyses use the theory of commognition to investigate the tensions between ritualized and exploratory participation in the students’ MM activity. We focus particularly on a quintessential routine in MM, assumption building: we trace attempts which start from ritualized engagement in the shape of “guesswork” and evolve into more productively exploratory formulations. We also identify signs of persistent commognitive conflict in the students’ activity, both intra-mathematical (concerning what is meant by a “math task”) and extra-mathematical (concerning what constitutes a plausible solution to the tasks in a biological sense). Our analyses show evidence of the fluid interplay between ritualized and exploratory engagement in the students’ discursive activity and contribute towards what we see as a much needed distancing from operationalization of the commognitive constructs of ritual and exploration as an unhelpfully dichotomous binary

Subjectivity and cultural adjustment in mathematics education: a response to Wolff-Michael Roth

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 how discourses in mathematics education shape subjective action within a Lacanian model that circumnavigates both “psychology” and “sociology”. From that platform, this paper responds to Roth through problematising the idea of the individual as a subjective entity in relation to the two perspectives, with some consideration of corporeality and of how the Symbolic encounters the Real. The paper argues for a Lacanian conception of subjectivity for mathematics education comprising a response to a social demand borne of an ever-changing symbolic order that defines our constitution and our space for action. The paper concludes by considering an attitude to the production of research objects in mathematics education research that resists the normalisation of assumptions as to how humans encounter mathematics

Mathematical talent in Braille code pattern finding and invention

The recognition of patterns and creativity are two characteristics associated with mathematical talent. In this study, we analyzed these characteristics in a group of 37 mathematically talented students. The students were asked to find the pattern the Braille code had been built upon and reinvent it with the aim of making its mathematical language become more functional. Initially, the students were unable to identify the formation pattern of Braille, but after experiencing the difficulties that blind people face when reading it, they recognized the generating element and the regularity. The results were in contrast with those of a control group, and it is noted that the students with mathematical talent were more effective in using visualization to identify the regularity of the pattern and their invention proposals were more sophisticated and used less conventional mathematical content.This research is part of the R+D+I project EDU2015- 69,731-R (Spanish Government/MinEco and ERDF)

Theory in and for mathematics education: in pursuit of a critical agenda

© 2016 The Author(s)This special issue of Educational Studies in Mathematics, developed from the Mathematics Education and Contemporary Theory (MECT) conferences in Manchester, U.K., follows up an earlier double special issue in Volume 80 (2012) of this journal, which comprised 18 papers authored from a dozen countries. These efforts—both in conference and in print—to develop theory in and for mathematics education should be seen as part of our community’s collective effort to offer mathematics education broader yet more rigorous “thinking tools”. We argue in this introduction that in these times where ideology so often defines “improvement” in preference to rigorous analysis, this effort is more important than ever before. The selected papers span two broad areas: theory is used to develop critical conceptual frameworks for studies in mathematics education by Llewellyn, Nolan, Barwell, Nardi, Pais; and philosophical dimensions of mathematical learning are discussed by Ernest, Skovsmose, and Boylan

At the intersection between the subject and the political: a contribution to an ongoing discussion

The issue of subjectivity has recently occasioned a lively discussion in this journal opposing socioculturalism and Lacanian psychoanalysis. By confronting Luis Radford’s cultural theory with Jacques Lacan’s psychoanalysis, Tony Brown sought to show the limitations of socioculturalism. This article takes advantage of that discussion to develop a critique of Radford’s theory of objectification, taken as an exemplary sociocultural theorization of the teaching and learning of mathematics. It does so by extending the criticism made by Brown at the level of the subject, namely by showing what is lost in socioculturalism when it reduces the Hegelian notion of dialectics to a relation between constituted entities; but mostly by exploring the possibility opened by contemporary theory to posit the discussion around subjectivity in the political. While socioculturalism assumes the possibility of a synthesis between person and culture thus making education possible, it will be argued that a theory which assumes the impossibility of education is in a better position to, on the one hand, conceptualize the resistance of many towards the learning of mathematics, and on the other hand, to address the ongoing political failure in achieving the desired goal of “mathematics for all”

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 Freud’s psychoanalytic theory with processes of signification as developed in the work of de Saussure and Peirce. The paper positions Lacan’s 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 Lacan’s conception of subjectivity provides a development of Peircian semiotics that has been influential for some recent work in the area. Through this route Lacan’s work enables a conception of subjectivity that combines yet transcends Piaget’s psychology and Peirce’s 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

Symbolising the real of mathematics education

This text, occasioned by a critical reading of Tony Brown’s new book Mathematics Education and Subjectivity, aims at contributing to the building of a sociopolitical approach to mathematics education based on Lacanian psychoanalysis and Slavoj Žižek’s philosophy. Brown has been bringing into the field of mathematics education the work of these two scholars, and his work has been important in understanding the cultural dynamics of school mathematics. This article highlights the limitations of Brown’s use of Lacanian theory and outlines a framework to understand students’ learning not in terms of the inherent properties of mathematics but in terms of the role this school subject plays within political economy

Signifying “students”, “teachers” and “mathematics”: 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