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The Micro-Evolution of Mathematical Knowledge: The Case of Randomness

Noss, Richard and Pratt, Dave (2002) The Micro-Evolution of Mathematical Knowledge: The Case of Randomness. Journal of the Learning Sciences, 11 (4). pp. 453-488. ISSN 1050-8406

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Abstract

In this paper we explore the growth of mathematical knowledge and in particular, seek to clarify the relationship between abstraction and context. Our method is to gain a deeper appreciation of the process by which mathematical abstraction is achieved and the nature of abstraction itself, by connecting our analysis at the level of observation with a corresponding theoretical analysis at an appropriate grain size. In this paper we build on previous work to take a further step towards constructing a viable model of the micro-evolution of mathematical knowledge in context. The theoretical model elaborated here is grounded in data drawn from a study of 10-11 year olds’ construction of meanings for randomness in the context of a carefully designed computational microworld, whose central feature was the visibility of its mechanisms-how the random behavior of objects actually worked. In this paper, we illustrate the theory by reference to a single case study chosen to illuminate the relationship between the situation (including, crucially, its tools and tasks) and the emergence of new knowledge. Our explanation will employ the notion of situated abstraction as an explanatory device that attempts to synthesize existing micro- and macro-level descriptions of knowledge construction. One implication will be that the apparent dichotomy between mathematical knowledge as de-contextualized or highly situated can be usefully resolved as affording different perspectives on a broadening of contextual neighborhood over which a network of knowledge elements applies.

Item Type: Article
Additional Information: Explores the growth of mathematical knowledge and seeks to clarify the relationship between abstraction and context. Builds on previous work to take a further step towards constructing a viable model of the micro-evolution of mathematical knowledge in context. This paper breaks new ground in terms of developing a theoretical framework for understanding abstraction in context. It explores the growth of mathematical knowledge and seeks to clarify the relationship between abstraction and context. Methodologically, it aims to gain a deeper appreciation of the process by which mathematical abstraction is achieved and the nature of abstraction itself, by connecting the analysis at the level of observation with a corresponding theoretical analysis at an appropriate grain size. This is an electronic version of an article published in Noss, Richard and Pratt, Dave (2002) The Micro-Evolution of Mathematical Knowledge: The Case of Randomness. Journal of the Learning Sciences, 11 (4). pp. 453-488. Journal of the Learning Sciences is available online at: http://www.informaworld.com/10.1207/S15327809JLS1104_2
Controlled Keywords: Maths , ICT
Divisions: IOE Departments > Departments > Geography, Enterprise, Mathematics and Science
IOE Departments > Departments > Curriculum, Pedagogy and Assessment
IOE Departments > Departments > London Knowledge Lab
Depositing User: IOE Repository Editor (2)
Date Deposited: 06 Apr 2009 11:53
Last Modified: 14 Oct 2013 11:25
URI: http://eprints.ioe.ac.uk/id/eprint/202

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