Biosemiotics 8 (2):325-340 (2015)

Mikkel Johansen
University of Copenhagen
Morten Misfeldt
Aalborg University
This paper investigates the notion of semiotic scaffolding in relation to mathematics by considering its influence on mathematical activities, and on the evolution of mathematics as a research field. We will do this by analyzing the role different representational forms play in mathematical cognition, and more broadly on mathematical activities. In the main part of the paper, we will present and analyze three different cases. For the first case, we investigate the semiotic scaffolding involved in pencil and paper multiplication. For the second case, we investigate how the development of new representational forms influenced the development of the theory of exponentiation. For the third case, we analyze the connection between the development of commutative diagrams and the development of both algebraic topology and category theory. Our main conclusions are that semiotic scaffolding indeed plays a role in both mathematical cognition and in the development of mathematics itself, but mathematical cognition cannot itself be reduced to the use of semiotic scaffolding
Keywords Semiotic scaffoldings  Cognitive artifacts  Mathematics  Cognition  Development of mathematics
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DOI 10.1007/s12304-014-9228-6
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References found in this work BETA

Intelligence Without Representation.Rodney A. Brooks - 1991 - Artificial Intelligence 47 (1--3):139-159.
Mathematical Thought From Ancient to Modern Times.M. Kline - 1978 - British Journal for the Philosophy of Science 29 (1):68-87.
Magic Words: How Language Augments Human Computation.Andy Clark - 1998 - In Peter Carruthers & Jill Boucher (eds.), Language and Thought: Interdisciplinary Themes. Cambridge: Cambridge University Press. pp. 162-183.

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Computers as a Source of A Posteriori Knowledge in Mathematics.Mikkel Willum Johansen & Morten Misfeldt - 2016 - International Studies in the Philosophy of Science 30 (2):111-127.

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