Connecting Research to Teaching: Slope, Rate of Change, and Steepness: Do Students Understand these Concepts?

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How do we mathematics teachers introduce the concepts of slope, rate of change, and steepness in our classrooms? Do students understand these concepts as interchangeable or regard them as three different ideas? Here we report the results of a study of high school Advanced Placement (AP) Calculus students who displayed misunderstandings about the meaning of these three concepts. We 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, we provide a classroom task that supports the discussion of the differences among these three concepts, and we ask readers to reflect on ways to help students differentiate among them.


Edited by Thomas A. Evitts,, Shippensburg University, Shippensburg, PA 17257

Karen Heinz,, Rowan University, Glassboro, NJ 08028

Contributor Notes

Dawn Teuscher,, is assistant professor of mathematics education at Arizona State University, and Robert E. Reys,, is Curators' Professor of Mathematics Education at the University of Missouri in Columbia. Both are interested in high school mathematics curriculum and student learning.

(Corresponding author is Teuscher author is Reys
The Mathematics Teacher


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