Abstract
Drawing on the hypothesis that an epistemology of school mathematics is interactively constituted in the classroom, we assume that different epistemological stances may lead students to get differently involved in the production and evaluation of arguments as part of their mathematical activity. Based on a case study, in this chapter we focus on how students exploit teacher’s interventions to produce arguments to validate different solutions to a mathematical problem within a problem-solving situation. We show that it may happen that teacher’s interventions do not have the intended effect, in spite of their potential to foster students’ reflection upon the adequacy of these solutions to the proposed empirical situation. Instead, a particular interpretation of the situation emerges through reflection on the solution ultimately validated by the teacher. We depart from this observation to discuss some aspects of the mathematical culture of the classroom .
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Acknowledgements
The second author’s participation in this study has been partly funded by the Spanish Grant EDU2012-31464 and the Catalan Grant SGR2014-972.
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Mariotti, M.A., Goizueta, M. (2018). Constructing and Validating the Solution to a Mathematical Problem: The Teacher’s Prompt. In: Stylianides, A., Harel, G. (eds) Advances in Mathematics Education Research on Proof and Proving. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-70996-3_6
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