FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W1519462027> ?p ?o ?g. }

• W1519462027 endingPage "13" @default.
• W1519462027 startingPage "2" @default.
• W1519462027 abstract "In mathematical terms, there is a celebrated tension between forms of discourse and cognition that are delicately tuned to cultural practices and those that are focused explicitly on mathematics per se, recognisable by its symbolic forms and epistemological structures. This tension parallels (and is perhaps derived from) the epistemological duality of mathematical thought as both tool and object, simultaneously a component of pragmatic activity and theoretical endeavour. The preparation of this article has afforded an opportunity to reflect retrospectively on this duality and on a corpus of research in which I and my colleagues have been involved, spanning a variety of sub-fields and a couple of decades. I hope it is not too fanciful to impose upon this work a narrative that was not necessarily evident to any of us while we were engaged upon it. Here is a first outline of that narrative. I begin with a pervasive finding that arises from investigations with (mainly young) people expressing mathematical ideas with computers. These studies led to a series of thoughts concerning the generation of mathematical meanings that nagged away until the early nineteen-nineties, when Celia Hoyles and myself began to formulate a theoretical framework for describing the phenomena we encountered. Shortly after this, we had the opportunity to work in a variety of settings with the broad common aim of elaborating the mathematics used in working practices. I shall then illustrate how these studies began to throw light on some fundamental questions, particularly concerning the nature of mathematical practices, and encouraged us to investigate further the problem of mathematical meaning from both cognitive and socio-cultural perspectives. This effort has led to some general principles about the design of mathematical activity systems for learning and, in particular, the rather special role that digital technologies may play within them. Thus, perhaps fittingly but probably over-ambitiously, I will conclude where I began, with the assertion that digital technologies can play an unusually powerful role in helping to understand and reshape the nature of mathematical sense-making. I would like to make two general observations at the outset. The first concerns my wish to consider both cognitive and social dimensions. To steer a course between these two approaches is not easy, not least because proponents of each often ignore the work of the other, or denounce as mere eclecticism any attempt at synthesis (there are important exceptions to this: see, for example, Cobb and Bowers, 1999; Kieran, Forman and Sfard, 2001). One organising idea for thinking about this apparent dichotomy has been suggested to me by Andy diSessa who distinguishes between phenomena that are distally and proximally social. Much of what I have to say comes from a recognition that many phenomena concerned with mathematical meaning are proximally social, in that they manifestly involve social and cultural relations between people and within communities. But I also recognise that many facets of human thought are only distally social; while it is true that what I think, and the techniques I use for thinking and communicating are shaped both socially and culturally, I think in ways that are structured by my personal cognitive history at least as strongly as by the socio-cultural relationships in which I find myself embedded. No attempt to understand how mathematics is learned by human beings can afford to ignore this essentially cognitive element, any more than it can afford to ignore the social and cultural relations in which cognitive activity is embedded. Thus, in what follows, I hope to illustrate not only that such a perspective need not necessarily lapse into eclecticism, but rather that co-ordination of the two approaches provides a possible and even necessary methodological stance. The second observation concerns the title of this article. I recognise that it is bad form to tell a joke and then explain it. Forgive me then, if I explain the double entendre in the title. I want to talk about mathematical epistemology as it is found in work, to understand how mathematics is used and how it is conceived by participants in their cultural practices. But I also want to talk about mathematical epistemology as a crucial element at work in learning situations; how mathematics education researchers can develop not just new approaches to teaching, but new mathematical epistemologies that are more learnable and, at least for all but the few, more expressive." @default.
• W1519462027 created "2016-06-24" @default.
• W1519462027 creator A5044173563 @default.
• W1519462027 date "2002-07-01" @default.
• W1519462027 modified "2023-09-28" @default.
• W1519462027 title "Mathematical Epistemologies at Work." @default.
• W1519462027 cites W103465515 @default.
• W1519462027 cites W117531262 @default.
• W1519462027 cites W1989930562 @default.
• W1519462027 cites W1993149073 @default.
• W1519462027 cites W2010018059 @default.
• W1519462027 cites W2116199508 @default.
• W1519462027 cites W2143152055 @default.
• W1519462027 cites W2268321397 @default.
• W1519462027 cites W2953677877 @default.
• W1519462027 cites W2993839916 @default.
• W1519462027 cites W632278062 @default.
• W1519462027 cites W74402279 @default.
• W1519462027 cites W2127016660 @default.
• W1519462027 hasPublicationYear "2002" @default.
• W1519462027 type Work @default.
• W1519462027 sameAs 1519462027 @default.
• W1519462027 citedByCount "5" @default.
• W1519462027 countsByYear W15194620272013 @default.
• W1519462027 countsByYear W15194620272017 @default.
• W1519462027 crossrefType "journal-article" @default.
• W1519462027 hasAuthorship W1519462027A5044173563 @default.
• W1519462027 hasConcept C111472728 @default.
• W1519462027 hasConcept C127413603 @default.
• W1519462027 hasConcept C130327152 @default.
• W1519462027 hasConcept C136197465 @default.
• W1519462027 hasConcept C138885662 @default.
• W1519462027 hasConcept C144024400 @default.
• W1519462027 hasConcept C145420912 @default.
• W1519462027 hasConcept C154945302 @default.
• W1519462027 hasConcept C199033989 @default.
• W1519462027 hasConcept C2775922551 @default.
• W1519462027 hasConcept C2780506305 @default.
• W1519462027 hasConcept C2781238097 @default.
• W1519462027 hasConcept C33923547 @default.
• W1519462027 hasConcept C41008148 @default.
• W1519462027 hasConcept C41895202 @default.
• W1519462027 hasConcept C78519656 @default.
• W1519462027 hasConceptScore W1519462027C111472728 @default.
• W1519462027 hasConceptScore W1519462027C127413603 @default.
• W1519462027 hasConceptScore W1519462027C130327152 @default.
• W1519462027 hasConceptScore W1519462027C136197465 @default.
• W1519462027 hasConceptScore W1519462027C138885662 @default.
• W1519462027 hasConceptScore W1519462027C144024400 @default.
• W1519462027 hasConceptScore W1519462027C145420912 @default.
• W1519462027 hasConceptScore W1519462027C154945302 @default.
• W1519462027 hasConceptScore W1519462027C199033989 @default.
• W1519462027 hasConceptScore W1519462027C2775922551 @default.
• W1519462027 hasConceptScore W1519462027C2780506305 @default.
• W1519462027 hasConceptScore W1519462027C2781238097 @default.
• W1519462027 hasConceptScore W1519462027C33923547 @default.
• W1519462027 hasConceptScore W1519462027C41008148 @default.
• W1519462027 hasConceptScore W1519462027C41895202 @default.
• W1519462027 hasConceptScore W1519462027C78519656 @default.
• W1519462027 hasIssue "2" @default.
• W1519462027 hasLocation W15194620271 @default.
• W1519462027 hasOpenAccess W1519462027 @default.
• W1519462027 hasPrimaryLocation W15194620271 @default.
• W1519462027 hasRelatedWork W115494643 @default.
• W1519462027 hasRelatedWork W145774252 @default.
• W1519462027 hasRelatedWork W153499581 @default.
• W1519462027 hasRelatedWork W1970492857 @default.
• W1519462027 hasRelatedWork W1992574131 @default.
• W1519462027 hasRelatedWork W2024179187 @default.
• W1519462027 hasRelatedWork W2141925993 @default.
• W1519462027 hasRelatedWork W2156225114 @default.
• W1519462027 hasRelatedWork W242048365 @default.
• W1519462027 hasRelatedWork W2479298816 @default.
• W1519462027 hasRelatedWork W2555710370 @default.
• W1519462027 hasRelatedWork W2556638635 @default.
• W1519462027 hasRelatedWork W2746917338 @default.
• W1519462027 hasRelatedWork W2767754883 @default.
• W1519462027 hasRelatedWork W2792333338 @default.
• W1519462027 hasRelatedWork W2895181116 @default.
• W1519462027 hasRelatedWork W2921293342 @default.
• W1519462027 hasRelatedWork W2936278918 @default.
• W1519462027 hasRelatedWork W3155239720 @default.
• W1519462027 hasRelatedWork W2183803331 @default.
• W1519462027 hasVolume "22" @default.
• W1519462027 isParatext "false" @default.
• W1519462027 isRetracted "false" @default.
• W1519462027 magId "1519462027" @default.
• W1519462027 workType "article" @default.