Linking ck¢ and the Toulmin model

An original theoretical as well as methodological aspect of Bettina Pedemonte PhD work, was to use the Toulmin schema in relation with a knowledge model in the framework of the Theory of Didactical Situations. We have recently revisited this work and produced  a synthesis of this important outcome. This has led to a paper recently published in the Journal of Mathematical Behavior, in which we analyze students’ conceptions in geometrical problem-solving and their relations to proving. We show how students’ conceptions strongly impact the argumentation activity and the construction of a proof. This is illustrated by analyzing two pairs of students’ argumentations and proofs taken from a set of data collected from a teaching experiment. The use of the Toulmin's model enriched with the ck¢ model allows to elicit the complexity of a cognitive analysis of argumentation and proof that accounts for the students’ knowledge system. Toulmin's model is useful to select those elements in the argumentation that are part of students’ conceptions while ck¢ allows us to see the role they have inside the argumentation.
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