| IN THIS ISSUE |
| Seventh Annual Conference on the Teaching of Mathematics |
| Assessing Reform Calculus Judith Baxter |
| The Rest of the Story: Putting the US Twelfth Grade TIMSS Mathematics Achievement Results in Perspective William H. Schmidt and Leland S. Cogan |
| On-Line Assessment with Wiley Web Tests John Lindsay Orr and William J. Lewis |
| Upcoming Chautaugua Courses |
| From the Publisher |
| About this Newsletter |
Modular Precalculus, Clustering, and Reform Mathematics
Nancy C. Marcus, University of Texas at El Paso
The University of Texas at El Paso has an innovative and successful program for entering students that is reforming pedagogy across campus. The Department of Mathematics plays a major role in the program. While very few math majors enroll in precalculus, precalculus is the gateway course to degrees in science and engineering at UTEP. In 1992 we decided to make this service course our priority. We interviewed faculty in the colleges of science and engineering to see how we could integrate our curriculum with their labs, a sort of "just in time" mathematics. Since it took a number of students two or three tries to pass the course, we restructured the course so the repeats were productive. To help entering students who feel isolated and without a sense of belonging to the university community, we now teach networking skills along with mathematics.
A modular program evolved with an overall objective to increase the pass rates in precalculus and calculus. Our target course was calculus, and we measured the efficiency of the modular design by tracking precalculus students through calculus. The premise of the modular program is that students fail precalculus because they fail to grasp one or more of the course concepts. We intercept failing students in midstream by requiring them to repeat failed material during the semester before they continue to new concepts--a sort of mastery model.
The modular design divides the curriculum into four parts and the semester into four times. All courses in a modular group are offered during the same time, and each part of the curriculum is offered during every time interval in the semester. Students are allowed to start the course at one of four levels depending on their placement exams, and they are allowed three tries to pass each part. (See page 3 for a diagram of the modular course design.) Students can take one semester or three semesters to complete the course without a grade penalty. The trade off for the extra tries is a more rigorous course.
The three-year modular pilot was approved and started in 1993. During the pilot phase, half the precalculus courses were modular and half were traditional. Students registered for precalculus without knowing there was a difference in the courses. Although we informally tracked all the precalculus students through calculus, we wanted real data that stood up to scrutiny. Drawing on a pilot assessment project from the Puerto Rican AMP, Sally Andrade, Director of the UTEP Center for Institutional Research and Planning, and Simon Bernau, the chair of the Department of Mathematics at the time, designed a longitudinal evaluation model that measured the efficiency and effectiveness of the course. The ICE index serves as a measure of the course's efficiency by taking into consideration the pattern of behavior in the precalculus course. The ICE2 index measures the course effectiveness by tracking student behavior in the target course, calculus.
Low ICE2 scores represent a course which is working well; a perfect course has an ICE2 index of 1.0. In 1993, the course index was 14.6, and by 1995 the index had dropped to 3.6. The percentage of precalculus students entering and passing calculus increased from 28.7% in 1993 to 81.0% in 1995.
About the time the modular pilot began, reform calculus was on the drawing board with a pilot due to start in 1994. We dovetailed the modular precalculus program into reform calculus by means of out-of-class reform projects that required teamwork.
Modular Math Course Design
The figure below illustrates how students may progress through the modular course segments.
Figure 1
We presented our findings to a university committee charged with designing an entering students program. The committee recommended that students be clustered into several classes (precalculus, English, and either a science or engineering course) at registration, that the curriculum in the classes be integrated, and that students and faculty work in teams. We just completed our fourth year of clustering and the results are positive. The cluster students stay in school longer and have higher grader point averages than the non-cluster students.
We adopted Functions Modeling Change, by Connally, Hughes-Hallett, Gleason, et al., for the fall 1998 semester to complement the reform text in calculus. We piloted between-semester, on-line mini-courses for Parts 3 and 4 of modular precalculus during the Christmas break this year. Those students who did not complete the course during the fall semester had the option to complete it during the holidays. Over 100 students actively participated in the on-line course. The on-line course chat rooms were so successful that we are implementing them during the regular semester. Our very popular Cyber Exam site has hundreds of precalculus exams and we have added Wiley Web Tests to the design. (See page 7 for more about Web Tests.) We are in the process of creating on-line supplementary material for the Functions Modeling Change text.
Change begets change. In the past five years, the Department of Mathematical Sciences at UTEP has reformed precalculus, calculus, differential equations, linear algebra, and the remedial courses. We created the successful on-line math site, SOSMath, available in English and Spanish, that is linked to boards of education in almost every state and in several countries. We have implemented a successful undergraduate research program where undergraduate students work on research projects that were previously the sole domain of graduate students. Faculty and staff across campus are collaborating with individuals from various disciplines to create integrated curriculums.
The modular precalculus program and the cluster program work. The icing on the cake is that both are relatively inexpensive to implement and administer. See www.math.utep.edu/classes/precalculus/a1.html for the on-line precalculus manual, and www.math.utep.edu/sosmath/ for the on-line math tutorial Web site.