Michael Tallman, Zackery Reed, Michael Oehrtman, & Marilyn P. Carlson
What Meanings Are Assessed in Collegiate Calculus in the United States?
Keywords: Calculus; Assessment; Mathematical reasoning; University level mathematics
Abstract: This article presents the results of our analysis of a sample of 254 Calculus I final exams (collectively containing 4,167 individual items) administered at U.S. colleges and universities. We characterize the specific meanings of foundational concepts the exams assessed, identify features of exam items that assess productive meanings, distinguish categories of items for which students' responses are not likely to reflect their understanding, and suggest associated modifications to these items that would assess students' possession of more productive understandings. The article concludes with a discussion of what our findings indicate about the standards and expectations for students' learning of calculus at institutions of higher education in the United States. We also discuss implications for calculus assessment design and suggest areas for further research. (Click here for article)