A campus-supported project is currently under way in the Department of Mathematics and Statistics at the University of Michigan - Dearborn to develop program content for a Mathematics Learning Center (MLC). Initial funding in support of the MLC concept was for equipment, including computers, peripherals and audio-visual equipment, and was obtained through a grant from the National Science Foundation under its Instrumentation and Laboratory Improvement Program (ILI).
The title of the successful equipment grant proposal, "Facilitating Student Access to Mathematics Programs - A Mathematics Learning Center," is indicative of the primary purpose and goal of the MLC. It is envisioned that, by way of the programs to be offered through this facility, improvements can be made in dealing with the common problem of identifying the most appropriate course election for students attempting to enter the mathematics program at UM-D, at levels ranging from freshman to senior. This problem had been observed informally and lamented frequently for years by many faculty in the Department, but its pervasiveness was brought home to the faculty as a whole by data generated during a 1994-95 implementation of an assessment plan designed by the Department. These data showed, among other things, major differences in performance, in numerous courses having a specified prerequisite course, between students who completed the prerequisite course at UM-D, and transfer students who took the equivalent prerequisite course elsewhere or in high school, with the first group significantly outperforming the second. This information confirmed a sense, widespread across the Department, of increasing difficulty experienced by students, ranging in class from entering freshman to senior, as they attempt to enter or reenter the mathematics program at a level appropriate to their needs and corresponding to their expectations.
At present, faculty advisors have nothing to offer students who marginally fail to qualify (based either on a placement exam at the freshman level or, at higher levels, on an analysis of topic coverage in prerequisite courses taken elsewhere) for a course they desire or need to enroll in, other than a choice between taking a prerequisite course in our Department (an inefficient, often redundant, and unpalatable option for many of our students) and signing up for the desired course (knowing of the statistically higher risk of failure for students who skip the prerequisite course at UM-D). The proposed remedy, designed after more than a year of discussion within the Department, was the establishment of a technology and student-tutor based learning facility, with equipment, staffing and programs targeted to the needs of the student populations just described. Three specific levels of frequent student entry, or reentry, into the mathematics program have been earmarked for attention under this program. They are:
Since the awarding of the equipment grant in 1997, the campus administration has allocated funding, in the form of salary payments and released time, for a program development project that began in Spring 1998. We shall report on our work at all three Levels. Results at Level I concern primarily our review of appropriate commercial instructional software, and the development of a roadmap, based on an item-by-item analysis of student placement exam results, to guide the student to appropriate sections of the software in the MLC. Work at Level II has involved, first, the developing of a list of calculus topics that have frequently been found to be absent from the backgrounds of students enrolling in our Calculus II and Calculus III, having taken the preceding calculus course or courses elsewhere. Second, a variety of computer-based modules are in preparation to remedy background deficiencies for particular topics. Work at Level III involves the creation of computer-based modules in such areas as set theory, logic and proof-writing, based on the approach of a published text by one of the project participants. Material at Levels II and III is designed to be used by students both in the Mathematics Learning Center on campus, and over the Worldwide Web, the latter allowing access by students from their homes, a particularly important aspect at a commuter campus such as the University of Michigan - Dearborn. In the material that follows, we address various aspects of the development of the MLC at Levels II and III, including the program content, and problems and solutions for presentation on the Worldwide Web. Other features we address include the capability for interactive testing and the use of movies to provide a dynamic view of the concept under study.