High School Precalculus Students' Understanding of Slope as Measure

Twenty-two high school precalculus students were interviewed to examine their understanding of slope as measure. The students examined and discussed real-world situations involving slope: physical situations involving slope as a measure of steepness and functional situations involving slope as a measure of rate of change. For the various physical situations, students measured steepness with angles instead of ratios. Overall, they demonstrated a better understanding of slope in functional situations, but many students had trouble interpreting slope as a measure of rate of change. Instruction should focus on helping students form connections and providing opportunities for students to communicate their understanding.