But what is the University to do? Without the procedure outlined above, 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 matriculation 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. The student frustrations often seem most acute for majors in the College of Arts and Humanities, whose majors often have no specific mathematics requirements other than the general education requirement. But it is also a common problem all over the campus of UMCP, as students are placed in courses below their expectations.

In the Fall of 2000 the University formed a campus committee to investigate, among other things, the issue of remediation in mathematics. Chaired by the dean of the college in which the Mathematics Department resides, the members included faculty, advising staff, and students from around the campus, including several mathematicians. 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.

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; this article is designed to describe the various features of the program, and include data substantiating the claims of success.

DESCRIPTION OF THE NEW PROGRAM

MATH 003: Rather than having a two-level Developmental Mathematics curriculum for the lower 40% of those students who were judged deficient by the Placement Examination, a single self-paced course with a computer platform was created. The students began their program and progress according to their own needs and abilities, under guidance of a professional mathematician and a cadre of assistants. The course was labeled MATH 003 and met for 6 hours per week in a computer laboratory.

When the students entered MATH 003, they were placed into one of five modules, depending on the general education course they were headed for. There are four of these courses:

MATH 110 (Elementary Modeling): generally a terminal general education course

MATH 111 (Probability): prepares a student for a Statistics course in the student's major

MATH 113 (College Algebra and Applications): prepares a student for elementary calculus

MATH 115 (Precalculus): prepares a student for engineering calculus

Four of the five modules were designed to prepare the students for one of these four courses. The fifth module was designed for those students as yet unprepared to succeed in the other four modules. In any case, the course grade (pass/fail) was 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 success of this course is documented in data presented below.

MATH 01X: The remaining approximately 60% of those students not passing the Placement Examination were placed into a combination course we designated MATH 01X/11X, where the X represents 0, 1, 3, or 5. (Thus MATH 010/110 was a combination of a developmental mathematics course with MATH 110, etc.). The courses met 5 days a week, rather than the usual 3 days a week. The first 5 weeks of the course constituted MATH 01X, which reviewed the developmental mathematics topics (especially algebra) necessary for success in 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, about 89% of the students passed the Placement Exam at the required level after 5 weeks of MATH 01X, so were allowed to 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 110 or 111 or 113 or 115 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. At the end of the term the student was 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. And 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!

Observation: A side benefit of the new program was the flexibility of choices for students. For example, if a student in MATH 015 was preparing for the Engineering Calculus, but either decided he/she did not want to go into Engineering or did not place into MATH 115 at the 5 week point, but did place into the MATH 113 course, the student could shift to the 5-day-a-week MATH 113. Similarly a student might move "up" from MATH 010 to MATH 113 if the 5-week placement score merited it. Also, a few students in MATH 003 finished their self-paced course by the 5 week point, and were allowed to move into the appropriate MATH 11X course beginning in the sixth week.

RESULTS AFTER TWO YEARS

(Note that the MATH 011 is not in the table since it was not included in the program until Fall 2002). The percentage of students who moved from MATH 01X into MATH 11X in Fall 2001 was 89%, and in Spring 2002 was 95%. These numbers were substantially higher than we had expected.

Second, in Fall 2001 both groups of students (those starting in MATH 01X and those starting in MATH 11X) took the same final examination, and were given course grades prepared from comparable bases. As the table below indicates, both groups had similar course

grades:

More particularly, on the Fall 2001 final examination we obtained the following results: Those starting in MATH 013 got a median score of 76%, whereas those who started in MATH 113 got a median score of 77%. Similarly, those who started in MATH 015 got a median score of 66%, whereas those who started in MATH 115 got a median score of 68%. Also in MATH 110 the median scores on the final were at least as high in the sections starting with MATH 010, and often better, than the median scores of those who went directly into MATH 110.

Observations: We emphasize a significant point: The students starting in MATH 01X had lower MATH Placement scores than the other MATH 11X students and so started with weaker math skills, and still performed similarly to the other MATH 11X students. For the spring semester 2002 the corresponding table of course grades is as follows:

The fact that success in the Spring goes down is a familiar fact of university life. This spring group of students includes several mathematically weaker populations: the students who delay taking their Math requirements for one semester, the large group of students who had to begin in Math 003, and the freshmen and transfer students who begin at the university in the spring semester.

For Fall 2002 (the second year) the results were comparable to those in Fall 2001:

What happened to students when they completed the MATH 01X/11X course successfully? The students who began in MATH 010 and completed MATH 110 fulfilled their Mathematics requirement in one semester instead of two and went away very happy with the new program. For most of the students who succeeded with the MATH 013/113 course, the elementary calculus course MATH 220 awaited them; similarly, for most of the students who succeeded with the MATH 015/115 course, the engineering calculus course MATH 140 awaited them. We gathered follow-up data on these two groups, both in terms of the percent of students who enrolled in MATH 220 (MATH 140) after completing MATH 113 (MATH 115), and the percentage of those who received an A, B, or C in the successor course:

Now we consider the results of the MATH 003 students. In the table, MATH 001 was comparable to high school Algebra I, and MATH 002 was comparable to high school Algebra II. In 2001 these two courses were supplanted by MATH 003.

Comment: 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. Moreover, in general those in MATH 003 liked the "module" approach of the course, which was a feature they felt gave them more control over the pace of the course 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.

RESOURCES FOR THE NEW PROGRAM

CONCLUSIONS

ACKNOWLEDGMENTS