Transition issues that reform calculus students experience in traditional second semester calculus

Primus: Problems, Resources, and Issues in Mathematics Undergraduate Studies, Jun 2003 by Chappell, Kelly K

* When placed back in a traditional environment, they were no longer content to work through procedural problems without a conceptual understanding of what they were doing.

* The amount of effort required to be successful in second semester calculus was much greater than the amount of effort required to be successful in first semester calculus.

* Conceptual instruction had helped when taking examinations because they had a thorough understanding of the material. In second semester calculus, they felt they had little conceptual understanding and relied primarily on memorization when taking examinations.

Most importantly, when reflecting on their experiences in first semester calculus, students felt that a concept-based course improved their test taking skills and studying skills. If a homework problem or test problem was not phrased like any problem that had been directly taught in class or completed for homework, they said that they resorted back to basic concepts that they knew related to the unfamiliar problem and worked from there. They were much less inclined to employ the "identify the problem type via the wording and conjure up a similar problem" strategy. If they happened to forget a procedure, they felt that their understanding of the meaning behind the procedural skills provided the necessary framework to reconstruct the procedure if memory failed them. These results, in and of themselves, make a powerful case for the importance of concept-based reform calculus instruction, especially since students often have a difficult time approaching and solving unfamiliar or non-routine problems.

When conceptually-taught students are outperformed by their traditionally-taught counterparts in traditionally-taught subsequent courses, critics of calculus reform often blame it on a lack of basic skills. The results of this study strongly suggest that it may not be basic skills that are at the root of the problem. When evaluating the success of reform calculus courses, mathematics departments must consider the whole host of issues that students face as they transition between learning environments. Research studies that explore transition issues are necessary if universities are to make informed decisions about the successfulness of mathematics reform. The present study is one step towards identifying such transition issues.

BIOGRAPHICAL SKETCH

Dr. Kelly Chappell is a sixth-year assistant professor in the Department of Mathematics at Colorado State University. Her research focus is mathematics education. Specifically, her research explores the effectiveness of mathematics programs that strive to balance conceptual understanding with procedural skill. She is the PI of a three-year project, funded by the Fund for the Improvement of Post-Secondary Education, that builds into the departmental structure time for teams of calculus instructors (faculty as well as graduate student instructors) to collaboratively design, implement, and improve lesson plans that develop the concepts central to calculus. The project was recently awarded the University's award for outstanding instructional innovation.