Reasoning about Steepness

📙 Facility with algebra is essential to productive members of our technology-laden society. Algebra is necessary for success in almost all professions, especially careers in science, technology, engineering, and mathematics (STEM). Since STEM careers are growing faster than other careers, it is even more important that the youth who will enter the workforce in a few years are proficient in algebra. Slope, or rate-of-change, is a concept in elementary algebra which stands out as both central to the understanding of higher algebra and most problematic for students. Since steepness of an incline and slope are closely related concepts, many ideas connected to slope relate directly to measuring steepness of inclines. This study investigated fifth through eighth grade students’ reasoning about steepness. The study explored whether success rate was affected by grade, numerical complexity, and structure of the steepness problem. The sample included 205 students in grades 5 through 8.