Abstract
The case study of Topaze effect shows a networking practice of connecting two theoretical approaches, TSD and IDS. It investigates empirically two phenomena, Topaze effect and funnel pattern, of the two theories and networks the theories by comparing and contrasting these phenomena including also the semiotic game phenomenon. This process leads to deepening the understanding of the strengths and blind spots of the two theories on the one hand and provides enriched insight into the character of the phenomena and their common idea on the other.
With comments by Ferdinando Arzarello, Cristina Sabena, & Marianna Bosch
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Notes
- 1.
A summary of the chapter has been published in Haspekian et al. (2013).
- 2.
This connection is not obvious as explained above, all the more so as Giovanni did not say that the line or the curve were vertical, but it is not discussed at all in this episode.
- 3.
Emphasis added by us.
- 4.
We can speak about resistance, but if we take for granted that the teacher, through connotation, challenges the students, there is no resistance: Giovanni takes over the challenge and gives an answer.
- 5.
“didactic reticence” is the term used by Sensevy (2012) to characterize the teacher’s tension that Brousseau (1997) describes in the didactical relation. The teacher cannot directly mention to the students the things he wants them learn (because of the hypothesis that the learning happens through an interaction with a milieu, putting the teacher in a tension of not saying directly what he could be tempted to say). This constraint for the teacher to remain silent on things he knows is called the “réticence didactique.”
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Bikner-Ahsbahs, A., Artigue, M., Haspekian, M. (2014). Topaze Effect: A Case Study on Networking of IDS and TDS. In: Bikner-Ahsbahs, A., Prediger, S. (eds) Networking of Theories as a Research Practice in Mathematics Education. Advances in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-05389-9_12
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