About five years ago we introduced EXCEL (Math 153-154), our version of Uri Treissman's PDP project. EXCEL showed us that students could learn from "workshops" (working in small groups on non-routine problems, with problem solutions required to be written up in standard English format). EXCEL's workshops met for three 80-minute periods each week, in addition to two 80-minute lectures each week. The workshops were small and well-staffed, with about 15 to 20 students in each and with an instructional staff of one graduate student and one undergraduate. We were able to document increased GPA's and retention in technical majors of students who had taken EXCEL. The effort and expense of using this model more widely were forbidding. We decided to try some changes in one of our large calculus sequences.
We changed texts from Thomas and Finney to the third edition of Stewart's Text. We decided not to jump to a "reformed" calculus curriculum (e.g., the Harvard text) because it would have been too radical a change for us and because there were some doubts about the usefulness of certain aspects of "reformed" instruction.
We decided to introduce "technology": for us in the first two semesters, this meant the use of graphing calculators. (We plan to use maple in the third semester of this sequence of courses.) The TI-82 was chosen to be the "supported" calculator, although any other instrument which did not have a QWERTY keyboard was allowed on exams.
Students were allowed to bring one "cheat" sheet of notes and formulas to exams. Because we were unsure that students would really learn the algorithmic aspect of the course as well as they should, we also instituted several computational tests (one on limits and one on derivatives). The tests were graded for answers alone, no notes or calculators were allowed, and versions of the test could be taken repeatedly until a student passed both. Only a few students in each lecture were not able to do this, and they were penalized by having their course grade lowered one grade.
The courses were coordinated more closely than had been the custom at Rutgers. We had a number of meetings, and a constant series of exchanges using e-mail.
We opted for the "early transcendentals" version of Stewart for several reasons. First, it was a way to alert the faculty strongly and directly that change was taking place. Second, it seemed appropriate because the graphing calculators had a number of buttons whose use would remain undiscussed until the elementary transcendental functions were introduced.
Our greatest change lay in what had been the recitations. We changed to workshops. We decreased recitation size to at most 30 students. Each recitation section was staffed by one experienced graduate student and one undergraduate peer mentor. The recitation time was lengthened from 55 minutes to 80 minutes. The substance of the recitation was changed from passive question and answer to the workshop model. Students had to hand in weekly writeups of one problem (almost always chosen by the lecturer) of each workshop. They were not told which problem would be required to hand in until near the end of the workshop. Each workshop writeup was graded by either the teaching assistant or the lecturer for both mathematical content and expository style. Additionally we wanted every exam to have some questions which required written exposition for answers earning full credit. Peer mentors corrected some textbook homework problems for each section each week, which was also a departure from past practice when frequently little or no homework grading was done.
The changes met with some success. We are evaluating further adjustments to make. Some of the changes certainly increased the workload of the instructional staff of the course. The peer mentors, who were paid, generally enjoyed the experience. Students seemed to have fewer complaints.
What is described above took a great deal of administrative support, which came principally from Dr. Charles Sims, Undergraduate Vice-chair of the Department of Mathematics. These changes were substantially supported by funding from the Rutgers-New Brunswick Learning Resource Center, the Rutgers-New Brunswick Teaching Excellence Center, the office of the Vice President for Undergraduate Education, Dr. Susan Forman, and the Rutgers-New Brunswick Faculty of Arts and Sciences.
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