Abstract
Slope is one of the most important mathematical concepts that students encounter in middle school and high school. The concept of slope “weaves its way through algebra, geometry, trigonometry, and calculus” (Anderson and Nelson 1994, p. 27), yet research with high school students shows that they can often calculate slope but are unable to interpret its meaning (Newburgh 2001; Stump 2001). This is a familiar problem in mathematics education; students learn a formula for solving a particular type of problem without conceptually understanding the relevant mathematical ideas. One way to enhance students' understanding of slope is to introduce it conceptually in middle school (Beckmann and Rozanski 1999), with the understanding that this conceptual foundation will provide a basis for the formal definition of slope to be introduced later on. In this article, we describe two related lessons for sixth-grade students that were designed to accomplish this goal.
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