The development of understanding of the concept of variable in grade seven beginning algebra students: the role of student interaction

Abstract

This thesis reports on a qualitative study of student interactions in one grade seven mathematics classroom as the students worked through a series of tasks exploring multiple uses of variables. Student tasks were planned out by me, as the teacher and the researcher, and they were executed in my classroom, where I had worked to create a constructivist classroom environment. This study posed two research questions: (1) In what ways do student interactions during group activities promote the development of individual and collective understanding of the concept of variable? and (2) In what ways do student interactions during whole-class discussions promote the development of individual and collective understanding of the concept of variable? I used research methods in which I was a participant. Data was collected in the form of audio taped discussions for the participants (working in three groups of four). Audio files of class discussions were accumulated and stored for later review. Written student work and reflections were collected for all class members at the time of the study. From these data sources, the relevant data set emerged. Analysis came in the form of thick description of eight episodes of importance in which the multiple data sources came together to highlight how student interactions in the form of negotiations may have promoted a shift in understanding of variable. The data showed the complex nature of student interactions along with the potential benefits to student learning. The data showing these benefits were outlined as three patterns of negotiations. These were: negotiations with other students, negotiations with self, and negotiations with the teacher.