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Lessons Learned from FIPSE Projects IV - May 2000 - Moravian College Cluster
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Integration of Precalculus Topics into the First Course in Calculus


Doris Schattschneider, Mathematics Department


DePauw University, The George Washington University, Hudson Valley Community College, University of Puerto Rico-Mayagúez, University of Puerto Rico-Río Piedras, United States Military Academy

The Innovation

Students who come to college unprepared to enroll in a required calculus course characteristically take precalculus first. There they study a number of topics they will need in calculus, but often they study them with no sense of the relationship of those topics to their later study in mathematics. By the time the students need to apply their prior learning in the calculus sequence, they have often forgotten what they learned earlier.

To address this problem, Moravian College developed a two-course sequence, "Calculus I with Review," integrating precalculus and the first semester of calculus. Precalculus topics are introduced at the time they are needed to understand the calculus concepts. This "just in time" approach is supported by a published text, A Companion to Calculus, developed by members of the Moravian College faculty. Adapters used this text along with their regular calculus in their newly established integrated sequence.


At four of the six adapting institutions the new integrated course is fully institutionalized. Its status is somewhat uncertain at the two University of Puerto Rico campuses, where the mathematics department has somewhat less control over course placement and course approval processes are more cumbersome.

This innovation apparently responds to widespread frustrations of mathematics faculty about the precalculus-calculus sequence. Though each campus experienced resistance to the new course from some faculty members, the superior effects on student persistence in the integrated sequence were hard to argue with. And where students had a choice of pursuing an integrated sequence rather than the traditional sequence they overwhelmingly chose the former. In view of the evidence, dubious faculty had little choice but to accede to departmental decisions to adopt the integrated sequence exclusively.

Of all the innovations disseminated through the "Disseminating Proven Reforms" competition, this one seems the most readily and broadly transferable. It deals with courses that virtually all institutions offer on a large scale and addresses a widely felt need. It is accompanied by strong, straightforward assessment questions and methods that seem always to show better student retention for the integrated course than for traditional courses. Finally, although it requires faculty to change the logic and organization of their courses, it does not require them to change their teaching styles.


The adapters used the same assessment strategy that the mentors had when they instituted the original program. They looked at: student persistence rates from the first semester of the sequence to the second, and rates of completion for the second course; the performance of integrated-course students compared to students in the traditional sequence on a set of problems included in the final examinations of both courses; instructor attitudes, including comparative assessment of the integrated and traditional sequences; and student attitudes.

Uniformly, student persistence through the sequence was higher for the integrated course than for calculus preceded by precalculus. Integrated-sequence students performed at least as well on a set of common problems as the traditional-course students, and sometimes better. In general, both faculty and students liked the integrated sequence better.

Further Dissemination

Moravian faculty continue to get inquiries about their course and to be invited to make presentations. During the time of the project they and the adapters made eight conference presentations. As a result of the work at Hudson Valley Community College, the Moravian group has been invited to work with faculty at the State University of New York, Albany, which is the main transfer institution for Hudson Valley students. The project Web site is located at the community college.

Available information:

Further information may be obtained from:

Doris Schattschneider
Mathematics Department
Moravian College
1200 Main St.
Bethlehem, PA 18018 6650
Telephone: 610-861-1373
Fax: 610-861-4162

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Last Modified: 09/10/2007