Technology, Knowledge and Learning

, Volume 16, Issue 1, pp 3–34

Young Students Exploring Cardinality by Constructing Infinite Processes

  • Ken Kahn
  • Evgenia Sendova
  • Ana Isabel Sacristán
  • Richard Noss


In this paper, we describe the design and implementation of computer programming activities aimed at introducing young students (9–13 years old) to the idea of infinity, and in particular, to the cardinality of infinite sets. This research was part of the WebLabs project where students from several European countries explored topics in mathematics and science by building computational models and programs, which they shared and discussed. We focus on a subset of the work in which students explored concepts of cardinality of infinite sets by interpreting and constructing computer programs in ToonTalk, a programming language and environment that is especially well-suited for young students. Our hypothesis is that via carefully designed computational explorations within an appropriately constructed medium, infinity can be approached in a learnable way that does not sacrifice the rigour necessary for mathematical understanding of the concept, and at the same time contributes to introducing the real spirit of mathematics to the school classroom.


Infinity Cardinality ToonTalk Constructionism Programming 


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Ken Kahn
    • 1
  • Evgenia Sendova
    • 2
  • Ana Isabel Sacristán
    • 3
  • Richard Noss
    • 1
  1. 1.London Knowledge Lab, Institute of EducationLondonUK
  2. 2.Institute of Mathematics and InformaticsBulgarian Academy of SciencesSofiaBulgaria
  3. 3.Department of Mathematics EducationCentre for Research and Advanced Studies (Cinvestav)MexicoMexico

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