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…

This research was conducted during an after-school partnership between a University and school district in an economically depressed, urban area. The school population consists of 99% African American and Latino students. During the informal after-school math program, a group of 24 6th-grade students from a low socioeconomic community worked…