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Unformatted text preview: Common sense and good sense: using complexity theory to visualise mathematics learning Diana Coben and Ian Stevenson Department of Education and Professional Studies King’s College, London Common sense and good sense: using complexity theory to visualise mathematics learning • We shall present dynamic formulations of Gramsci’s conceptualisation of ‘common sense’ and ‘good sense’ (Gramsci, 1971) and exemplify these formulations using data from secondary students learning mathematics. • We shall explore the following questions: – how might various formulations of the relationship between common sense and good sense be expressed visually and dynamically? – could these representations help us to visualise what happens when someone learns (or does not learn) mathematics? • These questions are explored through metaphor in the belief that metaphor may illuminate considerations relevant to educators. Gramsci constantly employs spatial metaphors (Jessop,2005) and consequently various spatial metaphors  visual representations of ‘common sense’ and ‘good sense’ and the relationship between them  are considered. • In earlier work, Coben (2002) concluded that metaphors from the mathematical world of fractals, selfsymmetry and dynamical systems may have considerable explanatory power for adult educators. This presentation takes this work forward in collaboration with Stevenson (2008; Stevenson & Noss, 1991), applying it to mathematics learning. Common sense and mathematical learning 1. Gramsci on common sense and good sense 2. Common sense and mathematical learning • Dynamic models of the relationship between common sense and good sense • Explorations using data from students learning mathematics Antonio Gramsci 18911937 Italian political theorist and activist Common sense • “a conception which, even in the brain of one individual, is fragmentary, incoherent and inconsequential, in conformity with the social and cultural position of those masses whose philosophy it is.” (Gramsci, 1971:419) • “‘Common sense’ is the folklore of ‘philosophy’ and stands midway between real ‘folklore’ (that is, as it is understood) and the philosophy, the science, the economics of the scholars. ‘Common sense’ creates the folklore of the future, that is a more or less rigidified phase of a certain time and place.” (PN1:173) Nonetheless, it contains • “a healthy nucleus of good sense [...] which deserves to be made more unitary and coherent.” (Gramsci, 1971:328). Good sense “…an intellectual unity and an ethic in conformity with a conception of reality that has gone beyond common sense and become, if only within narrow limits, a critical conception. ” (Gramsci, 1971:333) Gramsci’s distinction between good sense and common sense… …is not fully worked out in his prison notebooks. It is: “both epistemological and sociological: both a distinction between...
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This note was uploaded on 11/11/2011 for the course MATH 110 taught by Professor Staff during the Winter '08 term at BYU.
 Winter '08
 Staff
 Math, The Land

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