Extending the coordination of cognitive and social perspectives. 'Extensión de la coordinación de las perspectivas cognitiva y social (original) (raw)
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Extending the cordination of cognitive and social perspectives
Cognitive analyses are typically used to study individuals, whereas social analyses are typically used to study groups. In this article, I make a distinction between what one is looking with!one's theoretical lens!and what one is looking at!e.g., an individual or a group!. By emphasizing the former, I discuss social analyses of individuals and cognitive analyses of groups, additional analyses that can enhance mathematics education research. I give examples of each and raise questions about the appropriateness of such analyses.
Extensión de la coordinación de las perspectivas cognitiva y social
2012
Cognitive analyses are typically used to study individuals, whereas social analyses are typically used to study groups. In this article, I make a distinction between what one is looking with -one’s theoretical lens-and what one is looking at -e.g., an individual or a group-. By emphasizing the former, I discuss social analyses of individuals and cognitive analyses of groups, additional analyses that can enhance mathematics education research. I give examples of each and raise questions about the appropriateness of such analyses.Los análisis cognitivos se usan típicamente para estudiar individuos mientras que los análisis sociales se usan normalmente para estudiar grupos. En este artículo, distingo entre lo que se usa para mirar -el lente teórico propio- y lo que se mira -por ejemplo, un individuo o un grupo-. Enfatizando lo primero, discuto los análisis sociales de individuos y los análisis cognitivos de grupos sociales, análisis adicionales que pueden enriquecer la investigación en...
Social theory in mathematics education: Guest editorial
mathematics education research during the last two decades involving what has been called the "social turn" (Lerman, 2000). Researchers concerned with a wide variety of issues within mathematics education have come increasingly to see the inseparability of culture, context and cognition. Even within research that focuses primarily on cognitive aspects of learning and knowledge, notions of situated learning and distributed knowledge (Lave & Wenger, 1991) are widely used, as well as other theoretical perspectives that emphasise social aspects of learning, drawing in particular on Vygotskian psychology (Vygotsky, 1978). Moving beyond seeing mathematics learning solely as the endeavour of individual students and teachers has been reflected in a broader conceptualization of the subject matter of the field of mathematics education research. Valero (2010) has drawn our attention to the complexity of the networks of communities, interest groups and practices relevant to mathematics education and to the need for research to address this multiplicity of social practices and the connections between them. We are thus aware of the importance of studying the various communities and practices in which students and teachers participate, both within the classroom and beyond. We recognise the influence of policy and institutional structures and constraints at local, national and international levels. We appreciate the impact of the various discourses available inside and outside the school-discourses in the sense written with a capital D by Gee (1996) and defined as incorporating "theories" about what is normal and right and structuring the kinds of identities available to participants. This increasing attention to social aspects of learning has been accompanied by a growth in research foregrounding issues of social justice. Differing levels of achievement in mathematics in particular as well as in education as a whole have been associated with membership of various social groups and the effects of such factors as gender, ethnicity, class and linguistic background on the achievement of students in school mathematics have long been a focus of study. However, our ways of understanding the phenomenon of school failure have developed. In particular, there has been a move from locating the reasons for failure in the characteristics of the individuals concerned or of their communities towards seeking to understand how the
Learning Discourse
Commentary on the Special Issue of Educational Studies in Mathematics 'Bridging the Individual and the Social: Discursive Approaches to Research in Mathematics Education'. I am delighted and honoured to have been given the opportunity to provide a commentary on the papers presented in this special issue of Educational Studies in Mathematics, edited by Carolyn Kieran, Ellice Forman and Anna Sfard. It has given me the impetus to read with care accounts of research studies that define themselves as within the socio-cultural paradigm. 1 The editors should be congratulated on bringing together a rich mix of papers that take different, but complementary, perspectives on the theme of the issue and together make a serious elaboration of the principles underlying this paradigm. My starting point was as a learner. The papers collectively provided me with excellent summaries of a range of general theories underpinning the emerging social paradigm. I asked myself the following questions. What would the theoretical framing and methodologies of a socio-cultural approach add to the collective understandings developed in our field over the past thirty years? How can socio-cultural theory help us to understand and support students developing mathematical learning? Could I propose a novel slant on some of the ideas or analyses in the papers that might offer alternative but, to me at least, fruitful interpretative frameworks? Could I identify any omissions in analytic focus that, if addressed, might usefully form part of a future research agenda? 1 In the interests of clarity I have chosen to use the term socio-cultural throughout this commentary while recognising that others, including Cole, Wertsch, van Oers and Vygotsky, may use different terms.
Social Theories of Learning: A Need for a New Paradigm in Mathematics Education
This paper explores the limitations of the current field of mathematics education which has been dominated by social theories of learning. It is proposed that the field is approaching its limits for these theories and there is a need for shift that moves from the idiosyncratic possibilities of subjective meaning making and identity formation to a more profound position of “knowledge making”. There has been little, if any, advances in equity target group performance so questions are posed as to the viability of social theories for changing the status quo. If equity target groups are to be successful, then success needs to be more aligned with knowledge making processes. This paper is theoretical in its orientation and aims to explore possibilities and limitations of an approach that prioritises learning mathematics aligned with dominant knowledge forms.
Debate about the interplay between social and individual aspects of mathematics teaching and learning remains at the cutting edge of theoretical understanding of mathematics education research. In trying to make sense of the insights of these divergent perspectives I ask: How is it that social reality exists? What are the merits and limitations of considering the students in our classrooms as only collections of individual minds, in contrast with perspectives that posit the primacy of the social in determining the identity of mathematics learners? Can each be accorded its relative legitimacy in a rigorous and rational manner? Recent developments in analytical social theory may have the potential to address this issue productively. This paper covers the conflict between social-constructivist and socio-cultural perspectives in the literature and the critical role of inter-subjectivity in communicating mathematics through interaction. The paper concludes by drawing on Searle’s notion of collective intentionality to address the networking and complementary use of theories based in cognitive science and critical theory and the interplay of the individual and social in school mathematics.
The Social Construction of Mathematical Knowledge: Presented Problems in Mathematics Classrooms
1996
Author(s): Stone, Lynda | Abstract: This study examined how mathematical problems are articulated, i.e., identified and defined, in the context of a fiflh-grade lesson on equivalent fractions. Opportunities to participate in mathematical discourse and reasoning activities were closely related to the structure, organization, and content of classroom presented problems. In this lesson, the presented problem took the form of a concatenation of tasks. Each task in the series became the mathematical context that animated students' talk about solution methods. Classroom discourse limited to serial tasks constrained students' opportunities to develop relational knowledge about the properties and principles of equivalent fractions. "Does a child learn only to talk, or also to think? Does it learn the sense of multiplication before or after it learns multiplication?" -- Wittgenstein, Zettel, p. 324
Learning and Individual Differences, 2010
This study tested a set of hypotheses derived from the model of academic achievement in mathematics of the Social Cognitive Career Theory in a sample of Argentinean middle school students. To this aim, 277 students (male and female; age: 13-15 years) were assessed using the following instruments: logical-mathematical self-efficacy scale, mathematics outcome expectations, mathematics performance goals, and mathematics ability test. All of these instruments had been adapted for use in Argentinean students. Academic achievement in mathematics (i.e., grades obtained on regular school exams) was the variable to be modeled through the path analysis technique. The analysis allowed identification of interrelations among the variables and identification of direct and indirect effects. Academic achievement in mathematics was partially explained by the model. Overall, the results support the theoretical postulates of Social Cognitive Career Theory.