Document Type

Conference Proceeding

Publication Title

Electronic Proceedings for the Tenth Special Interest Group of the Mathematical Association of America on Research in Undergraduate Mathematics Education: Conference on Research in Undergraduate Mathematics Education


Mathematical Association of America

Publication Date


Publisher location

San Diego, CA

Abstract/ Summary

The study of calculus requires an ability to understand algebraic variables as generalized numbers and as functionally-related quantities. These more advanced uses of variables are indicative of algebraic thinking as opposed to arithmetic thinking. This study reports on entering Calculus I students’ responses to a selection of test questions that required the use of variables in these advanced ways. On average, students’ success rates on these questions were less than 50%. An analysis of errors revealed students’ tendencies toward arithmetic thinking when they attempted to answer questions that required an ability to think of variables as changing quantities, a characteristic of algebraic thinking. The results also show that students who more successfully demonstrated the use of variables as varying quantities were more likely to earn higher grades in Calculus I.