Educational Studies in Mathematics
, Volume 79, Issue 2, pp 157173
‘Warrant’ revisited: Integrating mathematics teachers’ pedagogical and epistemological considerations into Toulmin’s model for argumentation
 Elena NardiAffiliated withSchool of Education, University of East Anglia Email author
 , Irene BizaAffiliated withMathematics Education Centre, Loughborough University
 , Theodossios ZachariadesAffiliated withDepartment of Mathematics, University of Athens
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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.
Keywords
Teacher knowledge and beliefs Freeman’s classification of warrants Toulmin’s model for argumentation Practical rationality of teaching Visualisation Example use Tangent line Title
 ‘Warrant’ revisited: Integrating mathematics teachers’ pedagogical and epistemological considerations into Toulmin’s model for argumentation
 Journal

Educational Studies in Mathematics
Volume 79, Issue 2 , pp 157173
 Cover Date
 201202
 DOI
 10.1007/s106490119345y
 Print ISSN
 00131954
 Online ISSN
 15730816
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 Teacher knowledge and beliefs
 Freeman’s classification of warrants
 Toulmin’s model for argumentation
 Practical rationality of teaching
 Visualisation
 Example use
 Tangent line
 Authors

 Elena Nardi ^{(1)}
 Irene Biza ^{(2)}
 Theodossios Zachariades ^{(3)}
 Author Affiliations

 1. School of Education, University of East Anglia, Norwich, NR4 7TJ, UK
 2. Mathematics Education Centre, Loughborough University, Loughborough, LE11 3TU, UK
 3. Department of Mathematics, University of Athens, Panepistimiopolis, 15784, Athens, Greece