n Pythagoras - Examining mathematical discourse to understand in-service teachers' mathematical activities : original research

Volume 34, Issue 1
  • ISSN : 1012-2346
  • E-ISSN: 2223-7895



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.

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