Proof Image

Autor/inn/en	Kidron, Ivy; Dreyfus, Tommy
Titel	Proof Image
Quelle	In: Educational Studies in Mathematics, 87 (2014) 3, S.297-321 (25 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0013-1954
DOI	10.1007/s10649-014-9566-y
Schlagwörter	Mathematics Instruction; Mathematical Logic; Validity; Persuasive Discourse; Logical Thinking; Intuition; Mathematical Concepts; Knowledge Level + Suchen Sie Ihr Suchwort? Mathematics lessons; Mathematikunterricht; Mathematical logics; Mathematische Logik; Gültigkeit; Persuasion; Persuasive Kommunikation; Wissensbasis
Abstract	The emergence of a proof image is often an important stage in a learner's construction of a proof. In this paper, we introduce, characterize, and exemplify the notion of proof image. We also investigate how proof images emerge. Our approach starts from the learner's efforts to construct a justification without (or before) attempting any formal argument, and it focuses on the process by which a complete but not necessarily communicable image of that justification becomes available to the learner and provides explanation with certainty. We consider the interplay between the learner's intuitive and logical thinking and, using the theoretical framework of Abstraction in Context, we trace the construction of knowledge that results from and enables progress of this interplay. The existence and identification of proof images and the nature of the processes by which they emerge constitute the theoretical contribution of this paper. Its practical value lies in the empirical analyses of these processes and in the potential to apply them to the design of tasks that support students in constructing their own proofs images and proofs. We believe that such processes are likely to considerably enrich students' mathematical experience. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10