What does it mean for a student to understand the first-year calculus? Perspectives of 24 experts

This article presents the views of 24 nationally recognized authorities in the field of mathematics, and in particular the calculus, on student understanding of the first-year calculus. A framework emerged that includes four overarching end goals for understanding of the first-year calculus: (a) mastery of the fundamental concepts and-or skills of the first-year calculus, (b) construction of connections and relationships between and among concepts and skills, (c) the ability to use the ideas of the first-year calculus, and (d) a deep sense of the context and purpose of the calculus. Each end goal for student understanding is explored in detail and the potential for using the framework as an organizational tool is discussed.

Research highlights
► Twenty-four calculus experts define what it means to understand first year calculus.
► Four end goals and 19 sub-goals for understanding first-year calculus emerged.
► A framework organizes prior research on student misconceptions relating to end goals.
► The framework identifies end goals in need of further research.