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Title: ‘Warrant’ revisited: integrating mathematics teachers’ pedagogical and epistemological considerations into Toulmin’s model for argumentation
Authors: Nardi, Elena
Biza, Irene
Zachariades, Theodossios
Keywords: Teacher knowledge and beliefs
Freeman’s classification of warrants
Toulmin’s model for argumentation
Practical rationality of teaching
Visualisation
Example use
Tangent line
Issue Date: 2012
Publisher: © Springer Science+Business Media B.V.
Citation: NARDI, E., BIZA, I. and ZACHARIADES, T., 2012. ‘Warrant’ revisited: integrating mathematics teachers’ pedagogical and epistemological considerations into Toulmin’s model for argumentation. Educational Studies in Mathematics, 79 (2), pp.157-173.
Abstract: In this paper, we propose an approach to analysing teacher arguments that takes into account field dependence—namely, in Toulmin’s sense, the dependence of warrants deployed in an argument on the field of activity to which the argument relates. Freeman, to circumvent issues that emerge when we attempt to determine the field(s) that an argument relates to, proposed a classification of warrants (a priori, empirical, institutional and evaluative). Our approach to analysing teacher arguments proposes an adaptation of Freeman’s classification that distinguishes between: epistemological and pedagogical a priori warrants, professional and personal empirical warrants, epistemological and curricular institutional warrants, and evaluative warrants. Our proposition emerged from analyses conducted in the course of a written response and interview study that engages secondary mathematics teachers with classroom scenarios from the mathematical areas of analysis and algebra. The scenarios are hypothetical, grounded on seminal learning and teaching issues, and likely to occur in actual practice. To illustrate our proposed approach to analysing teacher arguments here, we draw on the data we collected through the use of one such scenario, the Tangent Task. We demonstrate how teacher arguments, not analysed for their mathematical accuracy only, can be reconsidered, arguably more productively, in the light of other teacher considerations and priorities: pedagogical, curricular, professional and personal.
Description: This article was published in the journal, Educational Studies in Mathematics [© Springer Business + Media] and the original publication is available at www.springerlink.com
Version: Accepted for publication
DOI: 10.1007/s10649-011-9345-y
URI: https://dspace.lboro.ac.uk/2134/8868
Publisher Link: http://dx.doi.org/10.1007/s10649-011-9345-y
ISSN: 0013-1954
Appears in Collections:Published Articles (Mathematics Education Centre)

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