Young Students Exploring Cardinality by Constructing Infinite Processes Ken Kahn Email author Evgenia Sendova Ana Isabel Sacristán Richard Noss Article

First Online: 19 April 2011 DOI :
10.1007/s10758-011-9175-0

Cite this article as: Kahn, K., Sendova, E., Sacristán, A.I. et al. Tech Know Learn (2011) 16: 3. doi:10.1007/s10758-011-9175-0
Abstract 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.

Keywords Infinity Cardinality ToonTalk Constructionism Programming

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Authors and Affiliations Ken Kahn Email author Evgenia Sendova Ana Isabel Sacristán Richard Noss 1. London Knowledge Lab, Institute of Education London UK 2. Institute of Mathematics and Informatics Bulgarian Academy of Sciences Sofia Bulgaria 3. Department of Mathematics Education Centre for Research and Advanced Studies (Cinvestav) Mexico Mexico