The Interaction between Intuitive and Formal Mathematical Thinking: A Case Study

Autor/inn/en	Farmaki, V.; Paschos, T.
Titel	The Interaction between Intuitive and Formal Mathematical Thinking: A Case Study
Quelle	In: International Journal of Mathematical Education in Science and Technology, 38 (2007) 3, S.353-365 (13 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0020-739X
Schlagwörter	Mathematics; Thinking Skills; College Freshmen; Case Studies; Intuition; Logical Thinking; Calculus + Suchen Sie Ihr Suchwort? Mathematik; Denkfähigkeit; Studienanfänger; Case study; Fallstudie; Case Study; Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung
Abstract	This paper reports studies of the interaction between the intuitive, the formal and the procedural aspects in the processes of mathematical understanding of Peter, a first-year undergraduate of Mathematics. Using an activity and an interview, an attempt is made to analyse his mental operations. The way in which he handles visual-graphic representations in a problem of uniformly accelerating motion in order to reach mathematical conclusions and justify them with strict formal reasoning, making the transition from the intuitive assumptions to the mathematical argumentation, is studied. The "focal analysis" of the interview's content allows for an in depth investigation of qualitative elements of the student's mathematical thought. The study of the cognitive operations through the interconnection of various theoretical perspectives may lead to teaching interventions in order to develop students' intuitive forces in a controlled manner, so that the formal mathematical thinking process can be promoted. This case study is part of a wider action research aiming to introduce first-year undergraduates to basic Calculus concepts. (Contains 1 table and 1 figure.) (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10