Although the statistics program at this large Ph.D.-granting university in the Midwest is not housed within a mathematical sciences department, the wide variety of measures used to assess the statistics program can serve as one model for assessing the mathematics major. All of the assessment measures used are described with particular emphasis on surveys of graduates and surveys of employers of graduates.
Background and Purpose
Iowa State University (ISU) is a large land-grant institution with a strong emphasis in the areas of science and technology. It was, in fact, designated the nation's first land-grant college when Iowa accepted the terms of the Morrill Act in 1864. It is located in Ames, Iowa, near the center of the state about 30 miles north of Des Moines. The current enrollment is about 24,000 students and about 20,000 of these are undergraduates, eighty-five percent from Iowa. The B.S. program in statistics began with the establishment of the Department of Statistics at ISU in 1947. It was one of the first universities in the U.S. or elsewhere to offer a curriculum leading to the B.S. degree in statistics. The first B.S. degree in statistics was awarded in 1949, and through 1997 over 425 individuals have received this degree. The enrollment in the major has remained reasonably stable over the period 1975-1997 in the range of 30-40 students. The current curriculum for the B.S. statistics degree includes:
In addition, the College of Liberal Arts and Sciences (LAS) has a variety of distribution requirements in the arts and humanities, foreign language, communication, the natural sciences and the social sciences.
The goals of the B.S. program in statistics had been implicitly considered as early as 1947 when the curriculum for the B.S. degree was established. However, the aims of the program had not been written in explicit form. A memorandum in September 1991, from the Office of the Provost, required each department and college to develop a plan for assessing the outcomes of undergraduate instructional programs. In response, in spring 1992 the Department submitted a document entitled "Student Outcomes Assessment for the B.S. Program in Statistics," to the Dean of the LAS College, which summarized the intended outcomes for our undergraduate major as follows:
Students completing the undergraduate degree in statistics should have a broad understanding of the discipline of statistics. They should have a clear comprehension of the theoretical basis of statistical reasoning and should be proficient in the use of modern statistical methods and computing. Such graduates should have an ability to apply and convey statistical concepts and knowledge in oral and written form. They should have the technical background and preparation to assume an entry level statistics position in commerce, government or industry. Academically talented and strongly motivated B.S. level graduates should have adequate background to pursue study towards an advanced degree in statistics.
With the idea of finding suitable measures of program performance, the 1992 plan also included the following abilities, knowledge and/or skills expected of B.S. graduates in statistics.
The following measures and procedures have been used over the period 1992 to date to assess the success in achieving the goals or knowledge/skills for students in the B.S. program in statistics at ISU. A brief description of these methods is presented here together with an indication of which goal(s) or knowledge/ skills(s) mentioned in Section 1 they are designed to measure or reflect.
1. A distribution of B.S. level statistics graduates grades (without names) has been maintained for the following categories of courses:
Grade data is summarized annually by the Director of Undergraduate Studies and is included in an annual Outcomes Assessment report to the LAS Dean. This information is also available to students interested in majoring in statistics.
These grade records provide information about the goals of B.S. graduates having a clear comprehension of the theoretical basis of statistics and being proficient in the use of modern statistical methods and computing. They refer directly to assessment of program and student success mentioned in the first three knowledge/skills categories in the first section.
2. A record of the performance on Actuarial Examinations 100 (General Mathematics) and 110 (Probability and Statistics) has been kept.
While taken by only a small number of our graduates these standardized examinations assess a B.S. student's knowledge of the mathematical and theoretical basis of statistics.
3. The Department keeps a record of summer undergraduate internships involving statistics in the Statistical Laboratory Annual Report, which receives wide distribution.
4. A record of the first positions or activities of our graduates is maintained. The names of the corporations, governmental bodies, or other institutions employing B.S. graduates together with the positions our students have obtained are listed. These positions or activities are grouped as commercial, governmental, manufacturing, graduate school and other.
The success of our graduates in obtaining internships and first positions in statistics reflects the goal of preparing our graduates to obtain entry level positions in commerce, government and industry. Additionally, the later hiring of statistical interns in permanent positions and multiple hiring by well established corporations or other institutions indicates the success of these graduates in meeting the general goals of our program.
5. A record of graduate degrees obtained by B.S. graduates (and the institution from which these degrees have been received) has been kept since 1974.
Most of our graduates who continue to graduate school do so in statistics. A record of the success of our graduates in obtaining an advanced degree (usually the M.S. in statistics) indicates the success of the program in providing an adequate background for academically talented students to pursue graduate study in statistics.
6. During the period July-October 1992 a survey of employers of two or more of our B.S. graduates in statistics since 1980 was conducted to obtain information about the opinions of supervisors of our graduates about their educational background. Respondents were encouraged to give their views on the strongest and weakest abilities of our graduates and make recommendations for improvement of our B.S. program.
This survey was valuable in providing the viewpoint of the employers of our graduates on all aspects of the B.S. program. Questions were asked relating to all the goals and knowledge/skills mentioned in Section 1.
7. A questionnaire was sent in the academic year 1992-93 to 111 B.S. graduates of the Department of Statistics receiving their undergraduate degrees in the period 1981-1991. Of these surveys 55 (50 percent) were returned. The survey was developed by Professor W. Robert Stephenson with assistance from the Survey Section of the Statistical Laboratory at ISU. The survey was aimed at determining the current employment and graduate educational experience of our B.S. graduates. Questions were also included to determine these graduates' evaluation of their educational experience at ISU. Additional questions were included to determine how well graduates of our program thought individual courses offered in the undergraduate statistics program prepared them for further education and employment. Open-ended questions about strong and weak points of the undergraduate program and an opportunity to make suggestions for improving the undergraduate statistics program were also included. This survey was also valuable in providing responses from our B.S. graduates concerning all aspects of the B.S. program in statistics at ISU.
1. Distribution of B.S. level grade point averages by categories.
For the 62 graduates of the program over the period from fall 1990 to spring 1997 the average GPAs were calculated for the categories defined in Section 2 and are presented below.
|(a) mathematical and theoretical courses||2.84||0.69|
|(b) statistical methods courses||3.30||0.56|
|(c) computer science and statistical
|(d) statistics courses||3.25||0.56|
|(e) all courses||3.06||0.56|
The information concerning grades reinforced our general perception that statistics majors have most difficulty with theory courses and least with statistical methods courses. No trends over this relatively short period of time in these GPAs have been observed.
2. Actuarial Examinations 100 (General Mathematics) and 110 (Probability and Statistics).
During the 1991-97 period three students took the 100 Examination, all during the current (1996-97) academic year. Two passed and one did not.
3. Summer Internships.
As an example, in the summer of 1996 four students held such positions. Companies employing these students were John Deere Health Care in Davenport, IA, the Mayo Clinic in Rochester, MN, the Motorola Company in Mount Pleasant, IA, and the Survey Sampling Section of the Statistical Laboratory at ISU. The first of these students was hired permanently by his internship company upon his graduation in spring 1997. The second was rehired by the Mayo Clinic this summer before he begins graduate school in statistics in fall 1997 at ISU. The third has an internship with the 3M Corporation in Minneapolis, MN this summer before she begins graduate school in statistics at the University of Minnesota in the fall. The last is working for the Statistical Laboratory again, prior to his senior year at ISU. It is generally true that it is possible to place only our better students in these rewarding positions.
4. First Positions or Activities.
Of the 62 graduates from fall 1990 to spring 1997, 15 have gone to graduate school, 27 to positions in commerce (in banking, health services, insurance, research and similar organizations), 2 to positions in manufacturing, 7 to governmental positions and 11 are in other situations.
5. Graduate School in Statistics.
Eight B.S. graduates since 1990 have received M.S. degrees in statistics, four are currently in M.S. degree programs in statistics, and one (in a Ph.D. program in statistics) has completed the M.S. degree requirements.
6. Survey of Employers of B.S. Graduates.
The purpose of this survey was to obtain an evaluation of the strengths and weaknesses of graduates of our program as seen by employers of these graduates and to make suggestions to improve our program. The average overall response (on a scale of Poor=1 to Excellent=5) of respondents to the questions concerning the overall quality of the education of our B.S. graduates was 4.21/5.00, received with some gratitude by the current authors. The strongest abilities of our graduates noted by their supervisors were in general statistical background and in an area best described as "having a good work ethic."
Employers expressed concern about the following
areas of the background of our graduates:
a) Knowledge of "real world" applications of statistics.
b) Ability to communicate statistical ideas well orally and in writing.
c) Having substantive knowledge in a specific field of application.
7. Survey of Graduates of the B.S. Program in Statistics at ISU.
Of the 55 individuals returning a survey 30 (54.5 percent) had continued to graduate school with 26 of 30 (86.7 percent) either having completed a graduate degree or continuing in graduate school. This probably indicates that this group was more likely to respond to the survey, as other information indicates that 35-40 percent of our B.S. graduates continue to graduate education. Almost all of the respondents have been employed since receiving the B.S. degree, with 87 percent of the respondents having taken a position in statistics or a related field.
B.S. graduates did indicate some areas of concern with our program. They indicated, as did employers, that there is a clear need for strong oral and written communication skills. This was particularly evident in the responses of individuals who went directly to positions in commerce, government or industry. Secondly, B.S. graduates reported a need for improved background in two topics in statistical computing computer simulation and graphical display of data. Finally, the course on survey sampling was the lowest rated of the core (required) courses in the student survey.
Readers who wish to obtain copies of the survey instruments and/or a more complete summary of the results of the survey of B.S. graduates may contact W. Robert Stephenson via email at: email@example.com.
Use of Findings
Explicit action has been taken regarding the findings under the headings 1, 6 and 7 in the previous section. Firstly, noting that the courses in probability and mathematical statistics are the most difficult core courses for our students, additional efforts have been made to provide regular problem sessions and review lectures prior to examinations in these courses in probability and mathematical statistics.
The Department has recognized the need for better communications skills and has for many years required a Junior/Senior level writing course (Business Communications or Technical Writing) in addition to the one year Freshman English sequence. We have also required a speech course, typically Fundamentals of Speech Communication. Both of these courses were ranked highly by students in response to the question: "How valuable has this course been in relation to your current employment?" As a result of the continued emphasis placed on communications by our graduates and their employers, we now incorporate writing projects in the statistical methods sequence required of all majors. These cover a wide range of topics and styles. At the beginning of the sequence students are asked to write short summaries of statistical results they obtain on weekly assignments. Later, they are asked to write a short newspaper-like article describing a scientific study that explains statistical analyses and concepts. The students also participate in group data collection and analysis projects that result in five to ten page technical reports. The Department now has a requirement that a sample of the technical writing of each graduate be evaluated and placed in their departmental file prior to graduation.
Concerning computing, the Department received an National Science Foundation (NSF) supported Instructional Scientific Equipment Grant (1992-94) which has permitted the acquisition of 22 Digital Equipment Corporation (DEC 5000/25) workstations in a laboratory in Snedecor Hall where the Department of Statistics is located. This has permitted substantial improvement in the teaching of computer graphics and simulation in many of the required courses in the B.S. program. For example, in the multivariate analysis course, students can now look at several dimensions simultaneously. It is now possible to rotate the axes of these plots to visually explore interesting patterns in multidimensional data. In the statistical computing courses, students are not only able to simulate sampling from populations, but they are able to visualize sampling distributions and statistical concepts such as the central limit theorem and confidence intervals.
Recognizing that computing is becoming extremely important for practicing statisticians, the Department has received funding from NSF (1997-99) to upgrade the equipment available to our undergraduates. All of the workstations described above will be replaced by high performance DEC Alpha workstations. This equipment will also allow faculty members to develop instructional modules that will go beyond traditional statistical methods. The modules will be developed around real world problems and will implement new statistical methods (often computationally intensive) to solve those problems. It is our intent to expose our students to these new methods so that they will be better prepared as statisticians.
Responding to the suggestions of our B.S. graduates, the survey sampling course has been redesigned by two new faculty members. They have introduced hands-on experience in designing surveys and analyzing their results utilizing a simulation package on the work-stations. The recent (S95 and S96) student evaluations have shown substantial improvement in student reception of the redesigned survey sampling course.
The documentation of summer internships achieved, first positions obtained, and graduate degrees received by B.S. graduates under headings 3, 4, and 5 in the previous section give a method of monitoring the success in achieving the goals of preparing graduates for entry level positions in commerce, government and industry and of preparation for graduate school stated in Section 1.
To implement a program of outcomes assessment of this
type requires substantial effort on the part of all faculty
associated with the B.S. program. It is important that a program
of Student Assessment have support at a high
administrative level (i.e., the presidential level) and the support of
the Faculty Senate (or equivalent group). There must also
departmental support to provide adequate financial
and secretarial aid to maintain records and carry out surveys.
In our opinion this will take time equivalent to at least
one course per year for a faculty member. Such an
individual should be assigned to maintain such records and carry
out and analyze appropriate surveys. We feel that this duty
should be assigned over a period of years (about four). Such
a program needs administrative support and understanding
that improvements in undergraduate education require
effort, resources and time. We believe that improvements in
our B.S. program have justified these expenditures.