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

Peter Cho, Courtney Nagle

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This study extends past research on students‟ understanding of slope by analyzing college students‟ mistakes on routine tasks involving slope. We conduct both quantitative and qualitative analysis of students‟ mistakes on common slope tasks to extract information regarding procedural proficiencies and conceptual underpinnings required in order for students to reason successfully with various slope conceptualizations described in prior research. A case study analysis of the mistakes made by two students illustrates the importance of analyzing patterns of mistakes to reveal what conceptualizations of slope a student is fluent in working with. Results from this study delineate procedural proficiencies and conceptual underpinnings related to various slope conceptualizations that can help both teachers and researchers pinpoint students‟ understanding and make appropriate instructional decisions to help students advance their understanding.


Linear function; Slope; Procedural and conceptual knowledge; Covariational reasoning

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