Developmental Mathematics: A New Approach
By William W. Adams
We begin with a familiar story. A student, we call him Tom, arrives at the University, happy to begin his college adventure. Almost immediately he is confronted with the Mathematics Placement Exam, designed to see if he is ready to enroll in a general education mathematics course (or in a credit-bearing course required by his major). The results of the Placement Exam unfortunately indicate that Tom is not prepared for the course he wants, and he must instead take a Developmental Mathematics Course. The results: he faces a delay in completing the needed mathematics course, he must take (for no credit) a course that he feels he has already taken, and to add insult to injury, he must pay an extra fee for the developmental course. Unhappiness, frustration and despair set in, the course is treated as a lowest priority (and often failed because of it), and an angry and frustrated student emerges.
But what is the University to do? Without such a test, Tom would register for a course he appears to be unprepared for. Data show that the result is frequently failure in the course, which would slow his progress and perhaps lead to his dropping out of the college.
Like numerous other institutions in the nation, the University of Maryland, College Park (UMCP), has been faced with this problem for many years. So, in the Fall of 2000 the University formed a campus committee to investigate, among other things, the issue of remediation in mathematics. The goal was to devise a plan that could be implemented for a large number of students, that would reduce the extra semester of developmental mathematics for many of these students, would be reasonably cost effective, and would not compromise teaching effectiveness in preparing the students for the course(s) they needed.
Debra Franklin works with students in Math010/110
What emerged from committee discussion was a radical solution that completely cast aside the old Developmental Math program. It gained immediate strong support from the campus administrators, both bureaucratically and monetarily. With great effort (including building a new computer laboratory, creating a new curriculum, training mathematics teachers and training advisors campus wide), the new program was put into place in Fall 2001. Now in Fall 2003 we see that the program has been very effective; the purpose of this article is to describe the various features of the program, and include data substantiating the claims of success.
In the new program, as before, all entering students are given the Placement Examination during orientation. About 20-25% of the entering freshman class (about 1000 students) are judged deficient in mathematics preparation for a general education math course. We now break up these students into two groups.
The lowest 40% are told, as before, to take a full semester of Developmental Mathematics. This course, called Math 003, is self-paced using a computer platform and meets for 6 hours per week in a specially designated computer laboratory. A professional mathematics educator assesses the students? needs and abilities. They progress through their program under the guidance of this person and another assistant. The students are placed into one of five modules, depending on the credit bearing course they are headed for, which is either the general education course or one that prepares them for a further course. In any case, the course grade (pass/fail) is based on written examinations, written (graded) homework, and attendance, in addition to success on the computer modules. It should be emphasized that the self-paced format of this course is critical for the implementation of the program for the other group of students to be discussed next.
The remaining approximately 60% are placed into a combination course. These courses correspond to credit bearing courses numbered 11x, so for the sake of this discussion we lump them together by calling them Math 01x/11x. The courses met 5 days a week, rather than the usual 3 days a week. The first 5 weeks of the course constitute Math 01x, which reviews the developmental mathematics topics (especially algebra) necessary for success in the credit-bearing course, Math 11x. Since the students enrolled in Math 01x were in the upper 60% of the students with deficient placement test scores, we felt that there was a good chance that an intense 5-week abbreviated form of the Developmental Mathematics course would suffice. However, to be sure, and to be legitimate about allowing the students to transfer to a credit-bearing course after 5 weeks, they were required to take the Placement Examination again at the end of 5 weeks. The same cut-off scores were required for a student to move into the Math 11x course as were required to enroll in Math 11x during orientation. If the student did not achieve such a score, then the student was placed back in the self-paced Math 003, with the good prospect of completing Math 003 by the end of the semester.
To our surprise and delight, we were able to let about 89% of the students proceed into the appropriate Math 11x course at the beginning of the 6th week. By continuing to meet 5 days a week until the end of the semester, the Math 11x course had approximately 45 sessions, which is about the number of sessions for the ordinary Math 11x course during the full semester. Moreover, the students in Math 11x continued in the same room with the same teacher as before. The re-registration from Math 01x to Math 11x was handled by the department, and the course Math 01x was erased from the student?s record and was substituted by Math 11x. As far as the student was concerned, he/she had one 5 day a week course that met for the entire semester. Those who completed Math 11x successfully had completed their math requirement in one semester rather than two, as would have happened under the earlier regime.
Students in these courses were given exactly the same uniform final examination taken by the regular Math 11x students. As a result, our department could directly compare the results of the students who had to start with remediation with those who did not. Since the new program has now been running for a while, we are able to assess the results. We will concentrate on the Fall 2001 semester, but the results for further semesters are similar. We compared the grades of the students in 01x/11x with those who went into 11x directly and found that each had about the same ABC rate. Moreover, the grades on the actual final exams taken by both groups were about the same and in fact were often higher for the students starting in Math 01x.
We also followed up on the students who completed the Math 01x/11x course successfully. Many of these students were only taking the course to fulfill their General University Mathematics requirement and thus had completed this requirement in one semester instead of two and went away very happy with the new program. Most of the rest of the students who succeeded with the Math 01x/11x course had to take the elementary calculus course or the engineering calculus course. The elementary calculus students who started in the combined course were successful ? in fact, about 7 percentage points more successful than the regular students. In the engineering calculus the combined course students did quite a bit worse in some semesters and about the same in others. Of course, the engineering sequence is much more demanding and the scores reflect the difficulty of catching up in a science/engineering track after inadequate high school preparation.
It is also important to be sure that the students who had to take the reformulated MATH 003, with its self-paced computer platform, were at least as successful as they were under the old program. For the Fall semester immediately preceding the institution of the new program we had two Developmental Math Programs, roughly high school Algebra I and II. Those who had to take Algebra I had about a 30% ABC rate in their next course, while those who had to take Algebra II had about a 47% ABC rate in their next course. The students who took Math 003 had a 35% ABC rate in the next course. Since these students are in fact the lower 40% among students who took these courses in the past. this self-paced course did its job at least as well as the old program.
We also conducted surveys of the students. The students were generally positive about the new program. Those in the Math 01x courses were especially pleased with the possibility of obtaining academic credit in one semester for the combined courses. Those in Math 003 liked the ?module? approach of the course, which they felt gave them more control over the pace and the outcomes for the course. We also heard from many of the advisors around the campus who reported a large decrease in frustration levels for students forced into Developmental Math.
The main expense in setting up the new program was in building two new dedicated computer labs for Math 003. The remaining costs were relatively small and mainly involved developing the curriculum for the new courses. As for the ongoing costs, they are comparable to the costs for running the old program. It should be noted that previously the students paid a fee for taking Developmental Mathematics, and that remained true for either Math 003 or Math 01x.
In conclusion we note that the new program prepared the students at least comparably well to the old one. But with the new program hundreds of students (373 students in Fall 2001 alone!) had completed their basic math requirement in one semester, rather than the two that all of these students would have needed under the old program. As a second measure of success of the new program, at the end of the Fall 2001 semester, 80% of the students placed in Developmental Math had either completed or were prepared to complete their math requirement at the beginning of Spring 2002. By contrast in Fall 1999 only 64% of these students were even prepared to move on to their Math requirement in Spring 2000 (and, of course, none had completed it). This is also a dramatic improvement.
William W. Adams has done work in Number Theory and, more recently, in Computational Algebra. He has been at the University of Maryland at College Park for 33 years. He spent many years as the Associate Chair for the Undergraduate Program and it was during the last of these terms he became heavily involved with the inception and the realization of this new
Developmental Math Program.