Abstract
Over the last few decades, there have been numerous studies exploring students’ understanding of fractions in mathematics. These have focused on the types of conceptions that students develop regarding the concept of fraction, and the difficulties that they encounter because of these conceptions. Many studies have presented reasons behind the development of these conceptions as well as the difficulties students and teachers encounter and have offered methods of addressing these difficulties and helping students to build a deeper understanding of fractions. However, even with the multitude of research conducted on fractions, students and teachers alike today still are experiencing some of the same problems as in the past. As such, perhaps the ways in which student and teacher understandings of fractions are being investigated are limiting and or do not provide enough detail or insight into how to address the problem. The present study is an attempt to offer a different perspective, coming from a sociocultural perspective. This study will investigate the types of interactions that occur among elementary school students as they are engaged in fraction multiplication and division tasks. Specifically, the study will examine what these interactions look like, the role that representations play in the interactions, how these interactions unfold in the classroom, and consider the implications these social interactions have on students’ understanding of fraction multiplication and division.