Rate of Change: AP Calculus Students' Understandings and Misconceptions After Completing Different Curricular Paths

Abstract

This study examined Advanced Placement Calculus students' mathematical understanding of rate of change, after studying four years of college preparatory (integrated or single‐subject) mathematics. Students completed the Precalculus Concept Assessment (PCA) and two open‐ended tasks with questions about rates of change. After adjusting for prior achievement with the Iowa Algebra Aptitude Test, students from these two paths performed comparably (F = 3.54, p = .063) on the PCA. Student errors on the three instruments revealed a lack of understanding of the interpretation or meaning of rate of change regardless of the curricular path. Students successfully calculated the rate of change of linear functions; however, when the function was not linear, students struggled to calculate it, model it on a graph, or interpret it in a real‐world context.