The Bundling Hypothesis

How Perception and Culture Give Rise to Abstract Mathematical Concepts in Individuals

Authored by: Kristen P. Blair , Jessica M. Tsang , Daniel L. Schwartz

International Handbook of Research on Conceptual Change

Print publication date:  June  2013
Online publication date:  July  2013

Print ISBN: 9780415898829
eBook ISBN: 9780203154472
Adobe ISBN: 9781136578212


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The “bundling hypothesis” describes the development of abstract mathematical concepts through learning. We present its elements through the investigation of a single conceptual change using multiple methodologies ranging from functional magnetic resonance imaging (fMRI) to novel classroom instruction. The conceptual change of interest is the transition from natural numbers to integers, which further include zero and the negative numbers. The transition is a non-destructive conceptual change. It does not require “a radical reorganization of what is already known” about natural numbers (Stafylidou & Vosniadou, 2004, p. 504). Yet it is still a strong instance of a conceptual change, because the integers cannot be derived from the natural numbers. They depend on the additional mathematical structure of the additive inverse: X + −X = 0. For the integers, people need to realize a fundamentally new structure within their concept of number.

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