Technology, Knowledge and Learning

, Volume 16, Issue 1, pp 3-34

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

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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