Abstract
This paper concerns a study analysing cognitive continuities and distances between argumentation supporting a conjecture and its algebraic proof, when solving open problems involving properties of numbers. The aim of this paper is to show that, unlike the geometrical case, the structural distance between argumentation and proof (from an abductive argumentation to a deductive proof) is not one of the possible difficulties met by students in solving such problems. On the contrary, since algebraic proof is characterized by a strong deductive structure, abductive steps in the argumentation activity can be useful in linking the meaning of the letters used in the algebraic proof with numbers used in the argumentation. The analysis of continuities and distances between argumentation and proof is based on the use of Toulmin’s model combined with ck¢ model.
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Notes
This answer was given in a test designed to evaluate algebraic competencies in a class of 13–14 year-olds.
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Pedemonte, B. Argumentation and algebraic proof. ZDM Mathematics Education 40, 385–400 (2008). https://doi.org/10.1007/s11858-008-0085-0
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DOI: https://doi.org/10.1007/s11858-008-0085-0