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Intensional and extensional reasoning: Implications for Mathematics Education

  • This thesis presents the results of a series of studies (on syllogisms, on the interpretation of mathematical statements and on probabilistic thinking) conducted with the idea that different, legitimate kinds of reasoning are used by humans in a contextual way, and that therefore no single logic (e.g., classical logic) can be expected to account for this diversity. The crucial role of interpretation is highlighted, showing how intensional and extensional reasoning may be mobilized according to it. In particular, in communication settings, this depends on our adoption of a cooperative, credulous disposition, or on the contrary, of an adversarial, sceptical one. In reasoning about mathematics in an educational setting, students (and teachers) may be enrolled in a back and forth between believing, doubting, making sense, giving arguments and proving. These changes in dispositions imply changes in the logics used. All the studies presented show, in different ways, evidence for cooperative, intensional reasoning and, in some cases, the possibility of a shift towards the acquisition of an extensional view. This suggest that if we expect as educators the adoption of specific norms and the development of reasoning skills from students, we need first to know well what the point of departure is where they are, and that it is often not at all “irrational”.

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Author:Francisco Vargas
Referee:Timo Leuders, Joachim Engel, Laura Martignon, Keith Stenning
Advisor:Laura Martignon, Keith Stenning
Document Type:Doctoral Thesis
Publishing Institution:Pädagogische Hochschule Ludwigsburg
Granting Institution:Pädagogische Hochschule Ludwigsburg, Fakultät für Kultur- und Naturwissenschaften
Date of final exam:2020/11/16
Release Date:2021/06/02
Year of Completion:2020
Tag:Bounded Rationality; Logical Pluralism; Mathematics Education; Proof; Reasoning
GND Keyword:Mathematikunterricht; Rationalität; empirische Studie; logisches Denken; mathematische Logik
Faculties:Fakultät für Kultur- und Naturwissenschaften / Institut für Mathematik und Informatik
DDC class:300 Sozialwissenschaften / 370 Erziehung, Schul- und Bildungswesen
500 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):License LogoCreative Commons - CC BY-NC - Namensnennung - Nicht kommerziell 4.0 International