Backward Reasoning and Epistemic Actions in Discovering Processes of Strategic Games Problems
1
Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain
2
Dipartimento di Matematica “G. Peano”, Università degli Studi di Torino, 20123 Turin, Italy
3
Instituto de Matemática Interdisciplinar, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain
*
Authors to whom correspondence should be addressed.
Mathematics 2020, 8(6), 989; https://doi.org/10.3390/math8060989
Received: 6 May 2020
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Revised: 1 June 2020
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Accepted: 15 June 2020
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Published: 17 June 2020
(This article belongs to the Special Issue Mathematical Modeling and Simulation in Science and Engineering Education)
The paper focuses on the cognitive and epistemic characterization of backward reasoning in strategy games resolution. It explores the use of abstraction in context (AiC) theory as a tool for the analysis of the epistemic actions involved in these processes. We follow a qualitative methodology based on design experiments, focusing on a study carried out with mathematics and engineering students. The analysis allowed us to combine the two models derived from the epistemology of mathematical backward reasoning and AiC theory in a unified framework that allowed us to focus both short-term and long-term processes in mathematical activities. Recurring patterns of epistemic actions were identified.
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Keywords:
reasoning and proof; strategy games; backward reasoning; engineering education; mathematical education; abstraction processes; epistemic actions
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MDPI and ACS Style
Barbero, M.; Gómez-Chacón, I.M.; Arzarello, F. Backward Reasoning and Epistemic Actions in Discovering Processes of Strategic Games Problems. Mathematics 2020, 8, 989. https://doi.org/10.3390/math8060989
AMA Style
Barbero M, Gómez-Chacón IM, Arzarello F. Backward Reasoning and Epistemic Actions in Discovering Processes of Strategic Games Problems. Mathematics. 2020; 8(6):989. https://doi.org/10.3390/math8060989
Chicago/Turabian StyleBarbero, Marta, Inés M. Gómez-Chacón, and Ferdinando Arzarello. 2020. "Backward Reasoning and Epistemic Actions in Discovering Processes of Strategic Games Problems" Mathematics 8, no. 6: 989. https://doi.org/10.3390/math8060989
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