Identifying Kinds of Reasoning in Collective Argumentation

Abstract

We combine Peirce’s rule, case, and result with Toulmin’s data, claim, and warrant to differentiate between deductive, inductive, abductive, and analogical reasoning within collective argumentation. In this theoretical article, we illustrate these kinds of reasoning in episodes of collective argumentation using examples from one teacher’s practice. Examining different kinds of reasoning in collective argumentation can inform how students engage in generating and examining hypotheses using inductive and abductive reasoning and move toward the deductive reasoning required for proof. Mathematics educators can build on their understanding of these kinds of reasoning to support students in reasoning in productive ways.

Notes

2. ¹We are not saying that every episode of collective argumentation requires multiple people to contribute orally to the argument. Rather, there are multiple people potentially involved in the argumentation.

3. ²As a simple example, consider a student who used a dynamic geometry program to examine the sum of the measures of the interior angles of a triangle. He or she might claim that the sum of the interior angles of a triangle is 180 degrees, showing only one example on the screen. The reasoning is inductive, with multiple results linked to the rule by multiple cases. The student, however, may say that the rule is established and cite only one case and one result.