No abstract

No 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.

In this article, we elaborate methodologies to study the argumentation speech of a teacher involved in argumentative activities. The standard tool of analysis of teachers' argumentation concerning pedagogical matters is Toulmin's model. The theory of argumentation schemes offers an alternative perspective on the analysis of arguments. We propose an integrated way of analysis employing Toulmin's model and argumentation scheme, based on Walton's taxonomy. We examine the change of pedagogical argumentation of a teacher that participated in a graduate course that was based on the analysis of hypothetical classroom scenarios on the teaching of calculus in high school. By exhibiting our methodological analysis in a particular case, we show that by adopting two different analytical perspectives, we gain a deeper understanding of the structure and quality of teachers' argumentation on pedagogical matters. The integration of the two qualitative methodologies could help identify several aspects of possible construction of knowledge in argumentative activities.

No abstract