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.
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Notes
This contrasts sharply with the typical maximum integer size of 231 (ten decimal digits), which are those that fit in 32 bits (with one bit used for specifying the sign).
After analysing the data we noticed the ambiguity of the word “countable” caused confusion. A revised version of the activity materials should be revised to avoid this.
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Acknowledgments
The WebLabs project was funded by Grant IST 2001-3220 of the Information Society Technologies Programme of the European Commission. We wish to thank the European Union for funding this project. We are indebted to the Bulgarian institutions which provided excellent conditions for organizing the sessions on infinity: Twenty First Century Academy in Plovdiv, The Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences, The Faculty of Mathematics and Informatics at Sofa University. Our deep gratitude to the Bulgarian coordinator, Dr Iliana Nikolova, and the teachers involved in the WebLabs project (George Gachev—in Sofia, and Liliana Moneva—in Plovdiv). And last, but not least—to the youngest participants in the project, the students, for their infinite creativity. We are very grateful to the UK schools Theydon Bois Primary School and the Cherwell School in Oxford and their students who spent many hours using our software and learning materials to explore infinity.
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Kahn, K., Sendova, E., Sacristán, A.I. et al. Young Students Exploring Cardinality by Constructing Infinite Processes. Tech Know Learn 16, 3–34 (2011). https://doi.org/10.1007/s10758-011-9175-0
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DOI: https://doi.org/10.1007/s10758-011-9175-0