Types of Mathematical Reasoning Evidenced by a Middle School Teacher in Pattern Generalization

The objective of this article is to describe types of mathematical reasoning evidenced by a middle school mathematics teacher, when answering two generalization questions in a figural pattern generalization task, related to quadratic sequences. Reasoning is delimited from teacher's arguments, reconstructed from a theoretical-methodological proposal that combines Peirce's definitions with some elements of Toulmin's argumentative model. The results show that the teacher evidenced abductive, inductive, and deductive reasoning, based on cognitive actions such as the decomposition of the figure, strategic counts, recognition of the behavior of the figural pattern, formulation, verification, and validation of conjectures. [For the complete proceedings, see ED630210.]