Students' Use of Slope Conceptualizations When Reasoning about the Line of Best Fit

Learning experiences regarding the line of best fit are typically students' first encounters with the fundamental topic of statistical association. Students bring with them into these learning experiences prior knowledge and experiences about mathematical lines and their properties, namely slope. This study investigated the role students' conceptions of slope play in their conceptualization of the line of best fit and approaches to placing it informally (i.e., by eye). Task-based interviews concerning the meaning and placement of the line of best fit conducted with seven grade 8 students were analyzed for this study. The results showed that students' conceptualizations of slope can play a significant role in their reasoning about the line of best fit, in both productive and unproductive ways. Analysis of associations between slope conceptualizations and students' criteria for placing the line, accuracy of the placed line, and meaning of the line of best fit are presented. The discussion highlights implications of the study for the teaching of lines in both mathematical and statistical settings. (As Provided)