Original Research

Examining mathematical discourse to understand in-service teachers’ mathematical activities

Margot Berger
Pythagoras | Vol 34, No 1 | a197 | DOI: https://doi.org/10.4102/pythagoras.v34i1.197 | © 2013 Margot Berger | This work is licensed under CC Attribution 4.0
Submitted: 17 September 2012 | Published: 19 April 2013

About the author(s)

Margot Berger, School of Education, University of the Witwatersrand, South Africa


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Abstract

In this article I use Sfard’s theory of commognition to examine the surprising activities of a pair of in-service mathematics teachers in South Africa as they engaged in a particular mathematical task which allowed for, but did not prescribe, the use of GeoGebra. The (pre-calculus) task required students to examine a function at an undefined point and to decide whether a vertical asymptote is associated with this point or not. Using the different characteristics of mathematical discourse, I argue that the words that students use really matter and show how a change in one participant’s use of the term ‘vertical asymptote’ constituted and reflected her learning. I also show how the other participant used imitation in a ritualised routine to get through the task. Furthermore I demonstrate how digital immigrants may resist the use of technology as the generator of legitimate mathematical objects.

Keywords

Commognition; technology; discourse analysis; teacher education; removable discontinuity

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