Fallacious argumentation in student reasoning: Are there benefits?

This article reports on an analysis of episodes of invalid or controversial arguments that occurred while two different groups of students worked on similar fraction tasks and examine the role that these types of arguments played in the development of students' reasoning. One group consisted of suburban, middle-class, fourth graders who worked on these tasks during the regular school day. The other group was comprised of sixth-graders from an urban community working on similar tasks as part of an informal learning after-school project. The findings of this study indicate that allowing students to share and discuss incorrect arguments promoted rich mathematical discourse and argumentation. The invalid arguments triggered the use of varied reasoning by other students and cleared up previous [mis]understandings.