Backward Reasoning in problem-solving situations: a multidimensional model

Barbero, Marta (2020) Backward Reasoning in problem-solving situations: a multidimensional model. PhD thesis, Università degli Studi di Torino and Universidad Complutense de Madrid.

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The increasing technological progress has highlighted the importance of problem-solving processes and skills connected to programming methods. Among them, backward reasoning is recognized as a critical issue in advanced mathematics education. This, together with the growing interest in recent years of game-based university education is at the base of this research project. Two objectives are established: on the one hand, to extend the epistemic model of backward reasoning, existing in the mathematical literature, to a cognitive and didactic one; on the other hand, to establish principles for the design of university teaching situations focused on backward reasoning. To reach these objectives, four design experiments using strategy games and mathematical problems are developed. These involved a total of 322 university students, from first year of bachelor to PhD, attending the Universidad Complutense de Madrid (Spain) and the Università di Torino (Italy). They are involved in scientific careers (Mathematics, Mathematics Engineering and Computer Science) and teacher training careers (future mathematics professors in secondary school). The research project is framed on qualitative studies based on a networking of two theories, the Game Theory Logic (Hintikka, 1999) and the Abstraction in Context theory (Dreyfus, et al., 2015), with subsequent hybridization through a fragment of the Commognition approach (Sfard, 2008). From the emerging theoretical framework, a multidimensional analysis tool is developed to analyse students’ resolution protocols, video-recordings, and interview and identify backward reasoning moments. As research result, eleven Backward Reasoning Indicators (BRI), that represent the cognitive dimensions of backward reasoning, are pointed out. They allow to respond to both research objectives and to make some further didactic conclusions.

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