‘Warrant’ revisited: Integrating mathematics teachers’ pedagogical and epistemological considerations into Toulmin’s model for argumentation

Abstract

In this paper we propose an approach to analysing teacher arguments that takes into account fielddependence-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.

Analysis of a teacher’s pedagogical arguments using Toulmin’s model and argumentation schemes

“…Argumentative norms that encourage critical debate usually favor the co-construction of arguments and a consequential change in a teacher's argumentation skills. The findings in the present research results are in the same line with other research on integration of different argumentation perspectives into a richer and more fine-grained analysis tool (e.g., Aberdein, 2007;Knipping, 2008) or other results concerning the origins of the teachers' argumentations (Nardi et al, 2012). Open questions regarding the exact relation between the basic elements of the two approaches could be of importance in education research also.…”

“…Other researchers have used Toulmin's model to analyze teachers' mathematical argumentation including the modeling of mathematical argumentation (Inglis, Mejia-Ramos, & Simpson, 2007), teachers' engagement in semantic warrant production (Walter & Johnson, 2007), teachers' engagement in refuting students' invalid claims (Giannakoulias, Mastoridis, Potari, & Zachariades, 2010), and comparison of pedagogical and mathematical reasoning structures (Steele, 2005). Nardi, Biza, & Zachariades (2012) proposed an approach that involves an adaptation of Toulmin's model with Freeman's (2005) refinement of Toulmin to analyze teacher arguments. This study through the analysis of warrants and backings addresses Bthe range of influences (epistemological, pedagogical, curricula, professional, and personal) on the arguments teachers put forward in their scripts^ (Nardi et al, 2012, p. 160).…”

When does an argument use a generic example?

“…This last part can be difficult if the argument is terse, which is an issue with coding arguments in general. There has been recent work on reconstructing arguments that have vague or implicit warrants (e.g., Nardi, Biza, & Zachariades, 2012); further work in this area should augment the applicability of our framework.…”

Prospective and in-service teachers’ perspectives about launching a problem

“…The scheme includes six main components: (1) data or evidence used, (2) a claim or conclusion, (3) a warrant that justifies the claim, (4) a backing or a reason that supports the warrant, (5) a rebuttal or a case where the claim does not hold, and (6) a qualifier stating the strength of the claim. Toulmin's scheme has been used to identify teachers' perspectives on teaching actions Nardi et al 2012). Following , we identified as data any moment in the vignette when the participants noted the basis for a claim.…”