The Occurrence of Indirect Reasoning: An Analysis

• In Event: The Role of Errors and Faulty Reasoning in Mathematics Learning

Abstract

In this study, we analyzed the reasoning patterns used by elementary and middle-school students in order to gain insight into the use of indirect reasoning. We identified patterns among the arguments which were used to justify their solutions to fraction tasks. Our findings indicate that there is a connection between the use of counterarguments and indirect reasoning, and that faulty reasoning often led to the use of indirect reasoning. The findings suggest that by encouraging students to present arguments (valid or invalid) and inviting counterarguments to other students’ justifications, opportunities to use indirect reasoning can be created.

Authors

• Mary Frances Mueller, Seton Hall University

• Dina Yankelewitz, The RIchard Stockton College of NJ

• Carolyn Alexander Maher, Rutgers University