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At a large, research university in the West, a major effort over the past 10 to 15 years has been underway to reform the entry level mathematics courses which the department offers. Assessment has been at the heart of this process. Focusing on all first year courses through assessment has had a positive effect on the undergraduate mathematics major and the courses in that major. This article describes the process and the ongoing assessment of student learning.
Background and Purpose
During the 1970s the University of Arizona, like many other colleges and universities, experienced a large growth in enrollment in beginning mathematics courses. This growth was coupled by a loss of faculty positions over the same period. The resulting strain on resources forced the department to make some difficult decisions in order to meet its teaching obligations. Notable among these was the creation of a self-study algebra program and the teaching of finite mathematics and business calculus in lectures of size 300 to 600. The situation reached its lowest point in the early 1980s when the annual enrollment in the self study algebra program exceeded 5000 students and the attrition rates (failures and withdrawals) in some beginning courses reached 50%. Before we describe the turnaround that began in 1985 we give some data about the department.
Currently the Mathematics Department has 59 regular faculty, 8 to 12 visiting faculty from other universities, 20 to 25 adjunct faculty, 6 to 8 visiting faculty from high schools and community colleges, 2 research post-doctorate faculty, and 2 teaching post-doctorate faculty. Each semester the Department offers between 250 and 300 courses serving about 10,000 undergraduate and graduate students. (The enrollment of the University is around 35,000.) Sixty to seventy percent of mathematics students take freshmen level courses in classes of size 35. There are approximately 350 majors in mathematics, mathematics education and engineering mathematics. In the past five years the Department has secured external funding at an average of 2.5 million per year.
The overarching goal of the Mathematics Department at the University of Arizona is to provide intellectual leadership in the mathematical sciences. It spans the areas of research, undergraduate and graduate teaching, outreach, and collaboration with other University units. The Department's goals include:
Method
The assessment of the freshman mathematics program began in 1983 with a Provost appointed University committee consisting mostly of faculty from client departments with three representatives from mathematics. This was followed by an intensive departmental review in 1984. The review included an examination of the department by an Internal Review Committee and an External Review Committee of distinguished mathematicians from other universities. The committees reviewed reports on enrollment, pass/failure rates in lower division courses, interviewed faculty members individually or in small groups, met with graduate teaching assistants, mathematics majors, representatives of client departments and the University Administration.
In the 1992/93 academic year the Department went through its second review to check on its progress to meet its goals. This included departmental committees on Faculty and Research, Undergraduate Education, Graduate Program, Academic Outreach, Collaboration with other University Units, Space, the Computer Environment, Library Facilities, and the Departmental Administration. In addition, there was a University Review Committee consisting of faculty from hydrology, chemistry, philosophy and biology and an External Review Committee with mathematics faculty from MIT, Rutgers, Wisconsin, Nebraska, and Texas.
Other reviews of the program are conducted regularly. One in particular that is worthy of mention is done by the Mathematics Center in the form of exit surveys of mathematics majors. The surveys cover three main areas. The background section covers such topics as why the student became a mathematics major and whether the student worked while in college. The mathematics experience section covers such areas as the courses and instructors the student appreciated and whether the overall educational experience met the student's expectations. The future plans section inquires into the student's immediate plans such as graduate school, employment or other options. Exit interview data is reviewed by the Associate Head for Undergraduate Programs and the Department Head. Comments and suggestions by students are considered in making changes in the undergraduate program and in continuing to find ways to support our undergraduates.
Findings
These reports documented several important findings. The following are three quotations from the 1983 and 1984 reports indicating the dismal nature of things at the time. Provost Committee: "Although other factors need to be considered, it is difficult to avoid the conclusion that many of the problems in freshman math can be traced to inadequate allocation of resources by the University Administration." Internal Review Committee: "The most important course in the lower division is calculus and this course is not a success ...the success rate is less than 50% ..." External Review Committee: "One of the best ways to help the research effort ... would be to tame this monstrous beast (precalculus teaching) ... it seems essential for everyone's morale that the pass/fail ratio be increased, section size reduced, ..."
The situation was different in 1992. The findings by the review committees showed that substantial improvements were accomplished since 1984. The following are some quotations from these reports. University Review Committee: "The Department of Mathematics has made tremendous strides since its last review in 1984. Its faculty has grown and established a firm scholarly reputation in key areas of pure and applied mathematics. Undergraduate education has improved greatly due to a reduction in entry level class sizes, the introduction of desktop computers in the classroom, and the vibrant activities of the mathematics education group that has evolved into a national leader ..." External Review Committee: "Since the last external review (1984), the Department has addressed the problems of entry-level instruction responsibly, effectively, and efficiently . . ."
Use of Findings
These reports led to the appointment of two significant committees: an Ad Hoc Intercollegiate Committee on Calculus and a Departmental Entry Level Committee with the charge to draft a plan to address the problems in beginning mathematics courses. The result was a five year implementation plan together with an estimate of the resources needed in each year. The plan was based on five fundamental premises.
The following are the key recommendations of the Entry Level Committee's action plan. First, reduce class size. Second, institute a mandatory math placement and advising program. Third, institute a new precalculus course. Fourth, introduce a calculus I course with five credit hours. Fifth, replace the self-study intermediate and college algebra courses with a two semester sequence in college algebra to be taught primarily in small classes. (Note: This sequence is currently being upgraded to a one semester four credit algebra course.)
The findings by the various review committees coupled with the action plan of the Entry Level Committee began a process of change in 1985 which resulted in a dramatic turnaround in the educational environment. Over the past twelve years the University has provided mathematics with a dozen new faculty positions and a supplementary budget to improve undergraduate education. (This is currently at $900,000 per year.) These funds, augmented by grant monies from NSF, have allowed the Department to dramatically improve the quality of the undergraduate mathematics experience particularly for beginning students. This was accomplished under the leadership of the Head, a dozen or so faculty, and a dedicated cadre of adjunct lecturers. In sharp contrast to the situation pre 1985, currently all freshman level courses are taught in classes of size 35. Student performance has improved greatly and the passing rate in these courses has increased 30 to 40 percent. We have excellent relations with other departments in the University, with the high schools, and with the local community college.
The number of mathematics majors has increased steadily over the past eight years. In the 1988-89 school year the University awarded 12 BS or BA degrees while in 1996-97 we expect to award 52 degrees. In this period the number of degrees in mathematics education have been steady at around 12 while the number of engineering mathematics degrees has declined from 12 to 4 due to the establishment of undergraduate degree programs in computer science and computer engineering.
The increase in the number of mathematics majors is due to several factors but in particular to the increased time and effort put in to improve their lot. We have created a new Mathematics Center—an office with library materials, a full-time advisor, lockers, and computer facilities. The Center provides special services to mathematics majors including access to an academic advisor during working hours, upper division tutoring, an undergraduate mathematics colloquium, and information about graduate schools, careers, and summer programs. The Center is under the direction of a new position of Associate Head for Undergraduate Programs.
In the last six years the Department has been involved in education reform. It is becoming a recognized national leader in calculus and differential equations reform and the use of technology in the classroom. Its leadership role is evident from the amount of external funding it has received for educational endeavors, for the number of visiting scholars who come to Arizona to learn about our classroom environment, and the participation of faculty members in national meetings and service on national committees.
Success Factors
The Mathematics Department has tackled the challenge of improving the educational experience for students in what we feel is a wholly unique manner. The additional resources allowed the Department to augment its faculty with adjunct lecturers who are dedicated to teaching. This meant several things. First, the number of students who had to take the self-study algebra program decreased in stages to its discontinuation in Fall 1997. Second, our faculty noticed an improvement in the teaching environment. Because of the mandatory mathematics placement test their classes contained students with better mathematical preparation. Furthermore, the addition of adjunct faculty gave the regular faculty opportunities to teach the classes that they preferred, generally in smaller sections. The result is an improvement in faculty morale in the Department. A number of faculty have been involved in curriculum projects to improve undergraduate education. Notable among these is the Consortium Calculus Project, the development of material for two differential equations courses, and a geometry and algebra course for prospective teachers.
We close with a list of some of the ingredients that go into a successful program.
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