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ZDM

, Volume 40, Issue 1, pp 83–96 | Cite as

Iconicity and contraction: a semiotic investigation of forms of algebraic generalizations of patterns in different contexts

  • Luis Radford
Original article

Abstract

The aim of this paper is to investigate the progressive manner in which students gain fluency with cultural algebraic modes of reflection and action in pattern generalizing tasks. The first section contains a short discussion of some epistemological aspects of generalization. Drawing on this section, a definition of algebraic generalization of patterns is suggested. This definition is used in the subsequent sections to distinguish between algebraic and arithmetic generalizations and some elementary naïve forms of induction to which students often resort to solve pattern problems. The rest of the paper discusses the implementation of a teaching sequence in a Grade 7 class and focuses on the social, sign-mediated processes of objectification through which the students reached stable forms of algebraic reflection. The semiotic analysis puts into evidence two central processes of objectification—iconicity and contraction.

Keywords

Algebraic thinking Contraction Generalization Iconicity Objectification Meaning Semiotics Signs 

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Copyright information

© FIZ Karlsruhe 2007

Authors and Affiliations

  1. 1.École des Sciences de l’éducationLaurentian UniversitySudburyCanada

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