Background Information

An integrated Calculus with Precalculus course addresses the problem of making calculus accessible to students with weak algebra and problem-solving skills. By providing conceptual background and discussing specific algebra techniques just prior to introducing a calculus topic, students can better understand the usefulness of the techniques and also immediately apply them to calculus problems. This course has been taught since 1988 at Moravian College and is currently taught at many other colleges and universities.

The key to success in integrating precalculus topics in a calculus course is to have good supplemental material to provide the review necesssary for understanding and doing calculus. In 1991-1993, drafts of a text were developed by four faculty members at Moravian College and Northampton Community College:  Doris Schattschneider, Kay Somers, Alicia Sevilla, and Dennis Ebersole.  The authors identified the most common problems that underprepared students face in a calclulus course and specifically addressed these problems in chapters intended to be introduced on a just-in-time basis within a calculus course.   The materials were class-tested at several institutions.*  Published by Brooks/Cole, A Companion to Calculus is intended to be used along with a calculus text; it sets the stage for calculus topics and uses calculus terminology and notation. Chapters are keyed to primary topics in a first calculus course. The text emphasizes teaching all concepts in four ways: descriptive (verbal and written), symbolic, numeric, and graphic.

In 1994, this project received the national distinction of being chosen by PROJECT KALEIDOSCOPE  as one of their featured “Programs that Work.”

During 1995-1997, with a dissemination grant*, the authors of the Companion formally assisted six widely differing institutions in the process of developing and instituting their own courses that adapt the integrated model of precalculus review within the first course in calculus.  An outside evaluator wrote a brief report on the dissemination project.  Several other institutions have also been informally assisted in instituting an integrated course.

*Supported by the Fund for the Improvement of Post-Secondary Education (FIPSE), U.S. Department of Education.

 
 Read articles about the course and the projects

        Integrating Precalculus Review with the First Course in Calculus.
        Alicia Sevilla and Kay Somers, PRIMUS, vol. III, no. 1, 1993, pp. 35-41.   

        A report on a FIPSE-funded project to integrate precalculus with the first course in calculus.
        D. Schattschneider, K.Somers, and A. Sevilla, Preparing for a New Calculus, Anita Solow, ed., Mathematical Association of America, 1994, pp. 121-124, 180.

        Instituting Calculus-with-Precalculus on Different Campuses.
        Doris Schattschneider, Alicia Sevilla, and Kay Somers, MER Newsletter, Vol. 10 No. 2, spring 1998.

        College Precalculus Can Be a Barrier to Calculus;  Integration of Precalculus with 
Calculus Can Achieve Success.
        Doris Schattschneider, in A Fresh Start for Collegiate Mathematics: Rethinking the Courses below Calculus, ed. Nancy Baxter Hastings, MAA Notes vol. 69, 2006, pp. 285-294.