Placement was the issue at this large, comprehensive school. This article explains, among other initiatives the department took to improve its accessibility to students, a Mathematics Readiness Testing Program. Statistics measuring the reliability of the testing are included.
Background and Purpose
The University of Arizona is a large research institution with approximately 35,000 students. The mathematics department consists of 59 regular faculty, 8-12 visiting faculty, 20-25 adjunct lecturers, and 60-70 teaching and research assistants. Each semester the department offers between 250 and 300 courses serving about 10,000 undergraduates and graduate students. There are approximately 350 majors in mathematics including mathematics engineering and education students.
During the 1970s the University of Arizona experienced a large growth in enrollment in entry level mathematics courses. An advisory placement program was initiated in 1978. It did not work very well since anywhere from 25% to 50% of the students did not take the test and the majority of those who took it ignored the results. The placement test was given in a single session prior to the first day of classes. This, together with an inadequate allocation of resources, resulted in average attrition rates (failures and withdrawals) of almost 50%. In the mid 1980s the mathematics department, with support from the administration, took a number of steps to reverse the trend. They included the implementation of a mandatory Mathematics Readiness Testing Program (MRT), a restructuring of beginning courses, providing students a supportive learning environment, and an outreach program to schools and community colleges. The mathematics department appointed a full time faculty member as an MRT program coordinator with a charge to work with the student research office to analyze MRT scores. By 1988, the MRT program was fully implemented for all new students enrolling in courses from intermediate algebra to Calculus I.
Over 5,000 students participate in the MRT program each year. Although placement tests are given throughout the year, most are taken during summer orientation sessions, which are mandatory for all new students. These two-day sessions accommodate 350-400 students at a time, and provide testing, advising, and registration for the following semester. During lunch on the first day, the MRT coordinator gives an explanation of the placement process and testing procedures. Students may ask questions during this hour before breaking into groups of 50 to be escorted to various testing sites. Administration of the tests, electronic scoring/coding, printing of results, and data analysis are handled by the University Testing Office.
Students choose between two timed multiple-choice tests adopted from the 1993 California Mathematics Diagnostic Testing project. The version currently being used allows a variety of calculators (including graphing calculators). For test securing reasons, those with QWERTY keyboards are not allowed at this time. Test A is a 50-minute, 45-question test covering intermediate algebra skills. This test is used to place students into one of three levels of algebra or a liberal arts mathematics course. Test B is a 90-minute, 60-question test covering college algebra and trigonometry skills. It is used to determine placement in finite mathematics, pre-calculus, or calculus. The students' choice of test depends primarily on their mathematical background and to some extent, on their major.
The tests are scored electronically, and results are printed that evening. Students pick up their results (in mathematics, English, and languages) early the next morning prior to their academic advising sessions. Each student receives a profile sheet indicating their mathematics placement and a breakdown of their total score by topic. (Questions are grouped into 7-8 topic areas, such as linear functions, simplifying expressions, and solving equations.) Students may place into one of three levels of courses through Test A, the lowest level being a non-credit beginning algebra course offered by the local junior college (the community college course is offered on our campus), while the highest level is college algebra and trigonometry. Although Test B can also place a student into college algebra, it is primarily designed to place students into one of 5 levels above college algebra. The lowest of these includes finite mathematics and brief calculus, while the highest level is an honors version of Calculus I. Students may register for courses at their level or lower. The computerized registration process blocks students from registering for courses at a higher level.
Due to the complexity of the levels of courses and the wide variety of mathematics requirements by major, experienced mathematics advisors are available to answer student questions during the 90-minute period after profiles are distributed. Although placement is initially based on a test score, other factors are considered. One of these is the high school GPA which is automatically considered for freshmen whose scores fall near a cut-off. Appropriate GPA cut-off values have been determined by measuring success rates for courses at each level. A pilot placement program began this year in which freshmen can place into calculus based on high RSAT1 or ACT mathematics scores without taking Test B. Transfer students are allowed to use prerequisite coursework in addition to their test results. The coordinator makes final decisions when overriding any initial placement based on test results.
Occasionally, students take the wrong test. In such cases, they may take the correct test on the second day of the session. These tests are hand-scored. As a general rule, the same test cannot be taken more than once within any three-month period. This has lowered the number of appeals from students claiming, "I just forgot the material, but I know it'll come back to me once I'm in class."
Throughout the year, the coordinator monitors the number of students placing at each level, assists other academic advisors with placement issues, and distributes information to outside groups, such as high school counselors and teachers. At the end of each year, an analysis is made of the success of the various placement procedures. Adjustments may be made and monitored during the following semester.
Although our tests assess skills, we do not base placement on the correct performance of these skills. For example, we do not give questions which a student must answer entirely correctly. The minimum or cut-off scores, that were used initially were based on the data of students when the test was optional, in the early 80s. These cut-off scores are monitored periodically and adjusted if needed. We do not have a particular goal set for the percentage of students passing courses at each level. Our goal is to set a cut-off score that minimizes the errors on either side of the cut-off; i.e., we do not want to set an unreasonably high cut-off score that would deny registration to a student with a reasonable chance for success. The tables below give some information on our students.
|Percentages of new students placing at various levels in Fall 1996:|
|Placing above the college algebra/trigonometry level||33.9%|
|Placing at the college algebra/trigonometry level||46.4%|
|Placing at the non-credit, beginning algebra level||19.7%|
|Failure/withdrawal percentages for first time freshmen in Fall 1996:|
|Above college algebra/trigonometry||Failure 12%,||Withdrawal 9%|
|College algebra/trigonometry level||Failure 14.4%,||Withdrawal 4.8%|
|Calculus I*||Failure 5%,||Withdrawal 5%|
|(*Approximately half of the students participating in our pilot program for placement into calculus based on RSAT and ACT scores also took the MRT. Of those, 91% placed into calculus.)|
Use of Findings
The data we gather, as well as the periodic studies provided us by the Office of Research on Undergraduate Curriculum, allows us to monitor the effectiveness of our program.
Currently, we are generally pleased with the success rates above. However, we are about to embark on a significant change, due to higher university requirements and the consolidation of our two-semester algebra sequence into one. We are presently trying to determining the "best" cut-off for placement into our new college algebra course. During Fall 1996, we experimented with lower cut-off scores for entry into the new algebra course. The preliminary analysis of the data shows that these borderline students in fact were at significantly higher risk than students who met our regular cut-offs. More analysis and experimentation will be done before we settle on a cut-off score.
Another use of the data is to support the chemistry and biology departments as they determine the mathematics prerequisites for a few of their entry level courses. Both departments independently looked at their pass/fail rates for entry level courses. Chemistry studied their two-semester sequence for all science majors and minors. They found that students testing above the college algebra level or completing college algebra did significantly better. In fact, the students who placed lower, or only completed intermediate algebra received only D's and Failing E's. Biology studied their two-semester sequence for all science majors, minors, and health-related professions. The students who did not place above intermediate algebra had a 90% chance of receiving a D or E.
One important outcome of the data analysis is that there is no room for flexibility with regard to mandatory testing and forced placement. An optional test would be completely ineffective with the 5000 students in our entry-level courses. We have found that the majority of students taking the test are freshmen who have difficulty determining their own readiness for course work at a university.
Several features of the MRT program are essential to its success. Strong support by the department and university is crucial. The move from an optional program to the current one required the cooperation of administrators, faculty, and even students. Continuing communication is also important. Misinformation or lack of information can undermine the credibility of the program. It is imperative that this communication extend to the high schools and local colleges.
Funding and manpower are major obstacles. Until two years ago, the test was free. Now a $5.00 charge is automatically billed to the student's account. This offsets the costs of administering the test through the Testing Office, proctoring, reproduction, and scoring. The mathematics advisors and coordinator are funded through the department. The coordinator also receives a one-course reduction in teaching load during each semester. The commitment of the advisors and coordinator is essential.
Another significant factor for success is the ability to analyze the program and make adjustments. Here are some examples of the types of questions that come up: When the department phases out intermediate algebra next year, will we be able to place some of these students at the next level? Is it necessary to test all transfer students? When the new university entrance requirements of 4 years of mathematics begin in 1998, will Test A be necessary? Flexibility also extends to the appeals process. Although there are guidelines to follow, such as test scores, prerequisite courses, and GPA, a more subjective set of guidelines may be necessary to handle individual cases. In any case, continuity is important.
1 RSAT are recentered SAT scores. SAT did this recentering a few years ago. "RSAT" gives a way to distinguish between "new"
SAT scores and "old" SAT scores.