Assessing Productive Meanings in Calculus

Abstract

We offer an analysis of calculus assessment items that highlights ways to evaluate students’ application of important meanings and support their engagement in generative ways of reasoning. Our central aim is to identify characteristics of items that require students to apply their understanding of key ideas. We coordinate this analysis of assessment items with a discussion of relevant findings from research on the teaching and learning of calculus, emphasizing the importance of promoting students’ engagement in quantitative and covariational reasoning. We conclude with a broader commentary on the importance of instructors attending to students’ meanings in their teaching, and offer suggestions for flexibly introducing these items as part of formative assessments throughout the life of a calculus course.