NotesFAQContact Us
Search Tips
Peer reviewed Peer reviewed
Direct linkDirect link
ERIC Number: EJ948398
Record Type: Journal
Publication Date: 2012-Jan
Pages: 22
Abstractor: As Provided
ISSN: ISSN-0013-1954
From Visual Reasoning to Logical Necessity through Argumentative Design
Prusak, Naomi; Hershkowitz, Rina; Schwarz, Baruch B.
Educational Studies in Mathematics, v79 n1 p19-40 Jan 2012
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.)
Springer. 233 Spring Street, New York, NY 10013. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-348-4505; e-mail:; Web site:
Publication Type: Journal Articles; Reports - Research
Education Level: Higher Education; Postsecondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A