Final - 4/11/11
Periodic Review: Department of Mathematics Self Study -- 2010
I. Context. Give a brief overview of the history of the department and describe the mission of the department.
The Mathematics Department is reaching the end of a long transition from a purely teaching mission to a mission that balances teaching and research. Until 1987 all faculty were full time teachers. Research was not required for promotion or tenure. Scholarly activity, if any, was self-motivated and largely unrewarded.
Beginning in 1987 the department’s new assistant professors were hired with the expectation that they produce publishable research. The research expectation came with a lighter teaching load than that expected of pre-1987 hires. Tenure and promotion guidelines changed, but it was still possible to achieve tenure and forge a successful career based on teaching alone. For assistant professors hired with an initial research expectation foregoing research meant a return to the historical teaching load. From 1987 to the present the department has had two distinct classes of professor - those whose duties formally include research and those whose duties are exclusively teaching and service.
By the early 1990’s the department was no longer hiring assistant professors without a research requirement for tenure and promotion. Existing faculty continued to conduct their careers under the older guidelines, but from this point on non-research faculty were effectively barred from promotion to full professor. Retirements and new hires had changed the mix of research and non-research faculty to roughly equal numbers. Although half the faculty were spending significant time on research, historical precedent and department leadership kept a strong focus on the teaching mission. Teaching success remained the dominant component of tenure and promotion decisions.
At about this time the department committed to a pair of strategic objectives: one to create salaried, full time teaching positions to be filled by long serving adjuncts, and the other to build and maintain research groups of at least three faculty with common interests in some sub-discipline. A group in Set Theory was already established. Topology, Numerical Analysis and Computer Science were nascent. Plans were made to start a Statistics group and revive the Mathematics Education group.
Over the next decade these plans were largely accomplished. By 2004 the department had achieved working research groups of at least 3 productive scholars in all the target areas except Mathematics Education. (This was still a work in progress, with two active researchers). Computer Science grew so successfully that it became a separate department. The Set Theory group included two full professors with international prominence. Other groups were younger and still building their reputations. Our conversion from a purely teaching mission was well underway, but throughout the transition we retained our insistence that teaching success figure prominently in tenure and promotion decisions. We had also established seven full time lecturer positions.
Today we are a department of 23 professors and 10 full time lecturers. All of the research groups projected in the late 1990’s have been formed and achieved a reasonable level of stability. We are nearly at the end of the era in which professors were either "research" or "non-research". We continue to hold tenure track professors to the historical teaching standards but more and more emphasis has been placed on their research activity. Looking forward, the department will continue to expand its research profile while maintaining its commitment to teaching.
The department's mission has evolved along similar lines. Once solely focused on teaching and service, we have added more and more emphasis on research. This parallels the development of the university and fits perfectly with the institutional plan to become a metropolitan research university of distinction. However, no matter what level of emphasis is placed on research we are and intend always to be a department committed to excellence in teaching. Broadly, then, our mission is research, teaching, and service.
The nature of research varies by discipline. For a pure mathematician it means proving theorems. For a numerical analyst perhaps the same, perhaps devising new numerical algorithms, certainly implementation in the form of efficient code. Research in mathematics education could be clinical studies and statistical analysis or observational studies and narrative descriptions. Across all disciplines the department's mission is to actively support and encourage research, and to ensure that it forms a significant part of every professor's career.
The teaching mission must accommodate an enormously varied clientele. The department offers Mathematics and Applied Mathematics bachelor's degrees and a master's in Mathematics. We provide training and professional certification with a Mathematics, Secondary Education degree, and we offer a master's degree in Mathematics Education to practicing teachers. We deliver the foundational mathematics instruction for all the sciences and engineering; we provide the mathematical training for all elementary school teachers; we provide the core mathematics courses required of every degree program in the university; we provide (until recently, exclusively in our region) developmental mathematics instruction for all those whose prior training has not prepared them for college level work. Across this vast range our teaching mission is to serve the needs of each group while maintaining appropriate standards of content and rigor.
Service activity is an essential part of each faculty member's career but highly variable in nature and quantity. Every researcher is expected to contribute to the functioning of the international community in which research is produced and disseminated. Every teacher is expected to provide guidance to students as they move along their educational paths and to collaborate in the successful execution of the department-wide teaching mission. Every faculty member is expected to contribute to the healthy functioning of the university and its colleges and departments. The departmental service mission is to deliver our fair share of all this work as it arises and as it is needed.
II. Previous Reviews
Our last program review was conducted in 2001-02. The external review was strongly positive regarding our research activity. It was also positive about our teaching effectiveness, both within the major and in service to other programs, with the exception of developmental Mathematics. This was their only major concern, although they noted several smaller items. The self study, external review report, action items, and 2005 progress report are attached.
Since that review the department has struggled with the delivery of developmental mathematics. At the time of the review we had just launched an entirely new hybrid course design. In every subsequent year concerns about student success have led to significant adjustments in course delivery with varying levels of improvement. In the last three years we have seen significant gains. The recent successes, including the creation of a full time position for a director of developmental mathematics, appear to have brought us to the end that period in our history. Although developmental mathematics remains an intrinsically challenging area of departmental operations it does not dominate discussions as it once did and it is not likely to be singled out as a departmental weakness.
The department offers one professional degree, Mathematics, Secondary Education, that is reviewed by the National Council for Accreditation of Teacher Education (NCATE). The Idaho State Department of Education conducts a simultaneous review. The most recent review occurred in 2008-09. Both reports address teacher education as a whole, so our program is subsumed in a much larger review process. Assessment was noted as an area of concern across all teacher education programs at the institution. We are addressing assessment issues within the department as a matter of departmental planning and policy. NCATE and Idaho DoE reports are attached.
I and II. Background and Previous Reviews 1
Final - 4/11/11
III. Undergraduate Programs
A. What do you do? Please describe the undergraduate programs you offer.
We offer three major programs: BA or BS in Mathematics, BS in Applied Mathematics, and BA or BS in Mathematics, Secondary Education. We also offer a Math minor, an Applied Math minor, and a newly designed Math Teaching Minor.
The Mathematics degree requires core courses in Calculus, Discrete Math, Real Analysis, Linear Algebra, and Probability and Statistics, together with several more advanced courses in these or other areas. Advanced electives can be chosen to suit a student’s particular interests in various areas of pure and applied mathematics. This degree is designed to prepare the student either for more advanced study in mathematics or for careers in any of the increasingly wide variety of areas where mathematical tools and thinking play an essential role. In addition to mastering specific mathematical content, mathematics majors develop excellent general skills in problem solving and precise analytical thinking.
The Applied Math degree requires similar core courses, but emphasizes computational and applied work in areas where the department has significant expertise: Cryptology, Statistics, Computational Math, Numerical Analysis and Differential Equations. The degree prepares students for jobs in areas such as statistics, mathematical modeling, computational science, business management and consulting. It also provides a strong foundation for graduate school in applied mathematics.
The Math Secondary Ed degree fulfills Idaho teacher certification standards and prepares students to teach mathematics in junior and senior high schools. Students acquire a solid background both in mathematics and in the education courses required for certification. Students gain practical knowledge and teaching experience through the department's secondary mathematics methods course and a semester of student teaching in local secondary schools.
A Math minor consists of the full Calculus sequence, at least two proof writing courses, and an additional upper division math elective which could be applied or abstract. As a credential it speaks highly of a student’s motivation and gives evidence of strong problem solving and analytical skills.
An Applied Math minor is the Calculus sequence, a course in Computational Mathematics, and two electives chosen from the more applied upper division offerings. The Computational Math requirement is a recent change, so students matriculating prior to 2009 can still graduate with a third elective instead. The required math sequence for most science and engineering majors is within one course of an Applied Math minor so the program has been structured to include attractive course options for those majors.
The Math Teaching Minor is a new creation designed to meet Idaho Certification requirements when paired with a secondary education major from any of the science programs. It has not yet passed through curriculum approval.
B. Are you successful at what you do? Please demonstrate that each of your programs achieves the following:
1. Your program prepares your students to successfully be able to move to the next phase of their lives.
Evidence is limited to (1) Alumni survey of employment, (2) Alumni Satisfaction Survey, (3) Idaho Dept of Labor employment information, and (4 ) feedback from individual students who stay in contact with faculty members.
Recent surveys are attached. The data are too sparse to be very meaningful, but this snapshot suggests our graduates successfully enter the workforce, earn respectable salaries for the region, regard their degrees as important to their careers, and were largely satisfied with their educational experience. Of note:
a. Very few Applied Math majors were surveyed. This is because the degree program is fairly new and has not had many graduates.
b. The employment survey combined all programs, but the satisfaction surveys broke them out. In the older survey Math Secondary Ed majors were much happier with their experience than other Math majors. In the later survey satisfaction was more even, with slightly more positive results for Math and Applied Math.
c. There is insufficient volume of data to warrant action or changes at this time, but the information revealed in these surveys is of great interested to the department. Much more should be done to collect this data, including data from participants in the minor programs.
Anecdotal evidence is mostly from Secondary Ed majors teaching in the region and from Math majors who have gone on to graduate programs. This includes several who are or were in the two master’s programs in the Math Department. All anecdotal evidence is strongly positive, although clearly subject to availability bias. Department plans include the intent to set up a social networking site to better stay in touch with our alumni.
2. Your students perform well on professional exams or other standardized examinations (as applicable).
Math and Applied Math majors take the ETS Major Field Test in their final semester. In our assessment reports (see III.B.3 below) we rate graduates as meeting our outcome goal if they score in the 70th percentile or higher. That last 4 years of reports show that this occurs much more often than not.
Math Secondary Ed majors take the Praxis II content exam. This threshold has been met consistently every year within recent memory.
Improvements in future assessments will include storage of MFT and Praxis results in a database for better data analysis.
3. Your students achieve the learning goals of your program(s).
In 2006 the department adopted a Program Assessment Plan (PAP) based on measurement of learning outcomes for the three majors. Measurement occurs at various points in the curriculum. Annual (and sometimes semi-annual) reports detail the results for each cohort of graduates. Annual at regular intervals, but less than annually, we have revisited the PAP, making some small changes and noting larger changes that we would like to implement. The original PAP, the reports on changes or suggested changes to the PAP, and each individual report on outcomes are attached.
Since reporting began we have had not had terribly many instances of a graduate failing to meet a significant number of outcomes. The goal most likely to be reported as not met is proof writing, which fits with anecdotal evidence that this is a possible area for improvement. Partly in response to PAP data, and partly from other motivations, the department has recently restructured its introductory proof writing course. The course cap has been lowered to allow instructors more time to coach writing, and the outcomes of the course are more tightly specified to include specific proof writing skills. These changes are too recent for us to have data on their efficacy.
4. Your students are retained by your program(s) and by the university. Your students proceed smoothly through your program(s) and then graduate, without unnecessary impediments.