From Visual Reasoning to Logical Necessity through Argumentative Design

Autor/inn/en	Prusak, Naomi; Hershkowitz, Rina; Schwarz, Baruch B.
Titel	From Visual Reasoning to Logical Necessity through Argumentative Design
Quelle	In: Educational Studies in Mathematics, 79 (2012) 1, S.19-40 (22 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0013-1954
DOI	10.1007/s10649-011-9335-0
Schlagwörter	Persuasive Discourse; Conflict; Computer Software; Geometry; Computer Assisted Instruction; Cooperative Learning; Hypothesis Testing; Instructional Design; Intuition; Preservice Teacher Education; Thinking Skills; Discourse Analysis; Problem Solving; Logical Thinking; Mathematics Instruction; Case Studies; Learning Activities + Suchen Sie Ihr Suchwort? Persuasion; Persuasive Kommunikation; Konflikt; Geometrie; Computer based training; Computerunterstützter Unterricht; Kooperatives Lernen; Hypothesenprüfung; Hypothesentest; Lesson concept; Lessonplan; Unterrichtsentwurf; Lehramtsstudiengang; Lehrerausbildung; Denkfähigkeit; Diskursanalyse; Problemlösen; Mathematics lessons; Mathematikunterricht; Case study; Fallstudie; Case Study; Lernaktivität
Abstract	Our main goal in this study is to exemplify that a meticulous design can lead pre-service teachers to engage in productive unguided peer argumentation. By productivity, we mean here a shift from reasoning based on intuitions to reasoning moved by logical necessity. As a subsidiary goal, we aimed at identifying the kinds of reasoning processes (visual, inquiry-based, and deductive) pre-service teacher's students adopt, and how these reasoning processes are interwoven in peer-unguided argumentation. We report on a case study in which one dyad participating in a pre-service teachers program solved a mathematical task. We relied on three principles to design an activity: (a) creating a situation of conflict, (b) creating a collaborative situation, and (c) providing a device for checking hypotheses/conjectures. We show how the design afforded productive argumentation. We show that the design of the task entailed argumentation which first relied on intuition, then intertwined the activities of conjecturing and checking conjectures by means of various hypotheses-testing devices (measurement, manipulations, and dynamic change of figures with Dynamic Geometry software), leading to a conflict between conjectures and the outcome of the manipulation of DG software. Peer argumentation then shifted to abductive and deductive considerations towards the solution of the mathematical task. These beneficial outcomes resulted from collaborative rather than adversarial interactions as the students tried to accommodate their divergent views through the co-elaboration of new explanations. (Contains 1 footnote and 12 figures.) (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10