Designing to See and Share Structure in Number Sequences
IJFTME Volume 13, Number 2, ISSN 1744-2710
This paper reports on a design experiment in the domain of number sequences conducted in the course of the "WebLabs" project. We iteratively designed and tested a set of activities and tools in which 10-14 year old students used the "ToonTalk" programming environment to construct models of sequences and series, and then shared their models and their observations about them utilising a web-based collaboration system. We report on the evolution of a design pattern (or programming method) called "streams" which enables students to engage in the process of summing and "holding the series in their hand", and consequently make sophisticated arguments regarding the mathematical structures of the sequences without requiring the use of algebra. While the focus of this paper is mainly on the design of activities, and in particular their epistemological foundations, some illustrative examples from the work of one group of students indicate the potential of the activities and tools for expressing and reflecting on deep mathematical ideas. (Contains 2 tables and 8 figures.)
Mor, Y., Noss, R., Hoyles, C., Kahn, K. & Simpson, G. (2006). Designing to See and Share Structure in Number Sequences. International Journal for Technology in Mathematics Education, 13(2), 65-78.
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