Explores first-year students' understanding of fundamental calculus concepts using written tests and interviews. Analysis of the written and verbal responses to the test items revealed significant misconceptions on which students' mathematical activities were based. Describes some of those misconceptions and errors relating to students'…

Pre- and posttests and interviews concerning misconceptions and alternate conceptions of rates of change were administered to (n=42) students in first-semester calculus using a conceptually-motivated curriculum. Suggests that an emphasis on visual representations through construction and interpretation in conjunction with teacher-student analysis…

Describes a test using 155 third-year undergraduates in 15 different institutions to examine the extent to which certain core first-year material is retained and understood. Includes an analysis of the answers given by students to each question as well as some of their comments. Students' misconceptions indicate that foundations laid in the first…