Slope, Rate of Change, and Steepness: Do Students Understand These Concepts?

How do mathematics teachers introduce the concepts of slope, rate of change, and steepness in their classrooms? Do students understand these concepts as interchangeable or regard them as three different ideas? In this article, the authors report the results of a study of high school Advanced Placement (AP) Calculus students who displayed misunderstandings about the meaning of these three concepts. They then share an example of a typical rate-of-change problem commonly found in mathematics textbooks that may contribute to the development of these misconceptions. Finally, they provide a classroom task that supports the discussion of the differences among these three concepts, and they ask readers to reflect on ways to help students differentiate among them. (Contains 3 figures and 1 table.)