Technology, Knowledge and Learning
, Volume 16, Issue 1, pp 334
First online:
Young Students Exploring Cardinality by Constructing Infinite Processes
 Ken KahnAffiliated withLondon Knowledge Lab, Institute of Education Email author
 , Evgenia SendovaAffiliated withInstitute of Mathematics and Informatics, Bulgarian Academy of Sciences
 , Ana Isabel SacristánAffiliated withDepartment of Mathematics Education, Centre for Research and Advanced Studies (Cinvestav)
 , Richard NossAffiliated withLondon Knowledge Lab, Institute of Education
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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 wellsuited 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.
Keywords
Infinity Cardinality ToonTalk Constructionism Programming Title
 Young Students Exploring Cardinality by Constructing Infinite Processes
 Journal

Technology, Knowledge and Learning
Volume 16, Issue 1 , pp 334
 Cover Date
 201104
 DOI
 10.1007/s1075801191750
 Print ISSN
 22111662
 Online ISSN
 15731766
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 Infinity
 Cardinality
 ToonTalk
 Constructionism
 Programming
 Authors

 Ken Kahn ^{(1)}
 Evgenia Sendova ^{(2)}
 Ana Isabel Sacristán ^{(3)}
 Richard Noss ^{(1)}
 Author Affiliations

 1. London Knowledge Lab, Institute of Education, 2329 Emerald Street, London, WC1N 3QS, UK
 2. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev bl. 8, 1113, Sofia, Bulgaria
 3. Department of Mathematics Education, Centre for Research and Advanced Studies (Cinvestav), Av. IPN 2508, 07360, Mexico, DF, Mexico