Educational Studies in Mathematics

, Volume 60, Issue 3, pp 333–358 | Cite as

Diagrammatic Reasoning as the Basis for Developing Concepts: A Semiotic Analysis of Students' Learning about Statistical Distribution

Article

Abstract

In recent years, semiotics has become an innovative theoretical framework in mathematics education. The purpose of this article is to show that semiotics can be used to explain learning as a process of experimenting with and communicating about one's own representations (in particular ‘diagrams') of mathematical problems. As a paradigmatic example, we apply a Peircean semiotic framework to answer the question of how students develop a notion of ‘distribution' in a statistics course by ‘diagrammatic reasoning' and by forming ‘hypostatic abstractions', that is by forming new mathematical objects which can be used as means for communication and further reasoning. Peirce's semiotic terminology is used as an alternative to concepts such as modeling, symbolizing, and reification. We will show that it is a precise instrument of analysis with regard to the complexity of learning and communicating in mathematics classrooms.

Key Words

concept development diagrammatic reasoning distribution hypostatic abstraction semiotics statistics education 

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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Freudenthal InstituteUtrecht UniversityUtrechtThe Netherlands
  2. 2.School of Mathematics, Science and Technology Institute of EducationUniversity of LondonLondonUnited Kingdom
  3. 3.University of VictoriaCanada
  4. 4.School of Public Policy Georgia Institute of TechnologyAtlantaU.S.A.

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