Logical Reasoning beyond Classical Logic: An Illustration with Pythagoras Theorem

Autor/inn/en	Vargas, Francisco; Stenning, Keith
Titel	Logical Reasoning beyond Classical Logic: An Illustration with Pythagoras Theorem
Quelle	In: International Electronic Journal of Mathematics Education, 15 (2020) 1, (7 Seiten)Infoseite zur Zeitschrift PDF als Volltext kostenfreie Datei Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1306-3030
Schlagwörter	Geometry; Mathematics Instruction; Validity; Mathematical Logic; Error Patterns; Incidence; Barriers; Learning Processes; Undergraduate Students; Engineering Education; Foreign Countries; Schemata (Cognition); Colombia (Bogota) + Suchen Sie Ihr Suchwort? Geometrie; Mathematics lessons; Mathematikunterricht; Gültigkeit; Mathematical logics; Mathematische Logik; Fehlertyp; Vorkommen; Learning process; Lernprozess; Ingenieurausbildung; Ausland; Cognition; Schema; Kognition
Abstract	We report on a study conceived with the idea that the use of logic in regard to mathematical reasoning as it actually occurs in practice is not limited to its prominent role in formal deductions and proofs. Interpretation of different mathematical situations elicits in fact the use of mostly unconscious forms of reasoning, close to those of narrative processing, which do not coincide with the expectations of traditional logic. This is pervasive, in particular, in educational situations at different levels, as we illustrate with interpretations which can emerge alongside an apparently obvious mathematical statement, namely, Pythagoras Theorem. We defend the position that analyses of "errors", should start by understanding their prevalence and non arbitrariness. Accordingly, we use a nonclassical logics whose features may give new insights to the kind of learning obstacles often found in the literature, as well as in our results. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01