Procedural and Conceptual Difficulties with Slope: An Analysis of Students' Mistakes on Routine Tasks.

Abstract

This study extendspast research on students’ understanding of slope by analyzing collegestudents’ mistakes on routine tasks involving slope. We conduct bothquantitative and qualitative analysis of students’ mistakes on common slopetasks to extract information regarding procedural proficiencies and conceptualunderpinnings required in order for students to reason successfully withvarious slope conceptualizations described in prior research. A case studyanalysis of the mistakes made by two students illustrates the importance ofanalyzing patterns of mistakes to reveal what conceptualizations of slope astudent is fluent in working with. Results from this study delineate proceduralproficiencies and conceptual underpinnings related to various slope conceptualizationsthat can help both teachers and researchers pinpoint students’ understandingand make appropriate instructional decisions to help students advance theirunderstanding.