PROCEEDINGS OF THE 15TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 2)
2012
Portland, Oregon
Expanding Toulmin’s Model: The Development of Four Expanded Argumentation Schemes from Analysis in Linear Algebra
Page: 2-242
In this presentation, I define four types of argumentation schemes that are expanded versions of Toulmin’s (1969) model of argumentation. These expanded schemes—Embedded, Proof by Cases, Linked, and Sequential—developed out of necessity when the original 6-part Toulmin scheme proved inadequate while analyzing argumentation of an inquiry-oriented linear algebra classroom community. Aspects of these four expanded schemes were adapted from and are compatible with those presented by Aberdein (2006, 2009). Within this presentation, I investigate how Toulmin’s is used within mathematics education research, as well as other fields of research, propose how the expanded schemes provide needed detail when analyzing complex argumentation, and provide examples of each from the whole-class discussion of the introductory linear algebra course.