International Journal of Computers for Mathematical Learning

, Volume 13, Issue 1, pp 47–70

Computational Construction as a Means to Coordinate Representations of Infinity

Article

DOI: 10.1007/s10758-008-9127-5

Cite this article as:
Sacristán, A.I. & Noss, R. Int J Comput Math Learning (2008) 13: 47. doi:10.1007/s10758-008-9127-5

Abstract

In this paper, we describe a design experiment aimed at helping students to explore and develop concepts of infinite processes and objects. Our approach is based on the design and development of a computational microworld, which afforded students the means to construct a range of representational models (symbolic, visual and numeric) of infinity-related objects (infinite sequences, in particular). We present episodes based on four students’ activities, seeking to illustrate how the available tools mediated students’ understandings of the infinite in rich ways, allowing them to discriminate subtle process-oriented features of infinite processes. We claim that the microworld supported students in the coordination of hitherto unconnected or conflicting intuitions concerning infinity, based on a constructive articulation of different representational forms we name as ‘representational moderation’.

Keywords

Computational microworldInfinityInfinite sequencesLogoRepresentational moderationSituated abstractions

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of Mathematics EducationCentre for Research and Advanced Studies (Cinvestav)MexicoMexico
  2. 2.London Knowledge Lab, Institute of EducationUniversity of LondonLondonEngland, UK