20 Questions Deans Should Ask Their Mathematics Departments
20 Questions that Deans Should Ask Their Mathematics Departments
Deans who wish to improve mathematics education on their campus need to recognize two realities:
- mathematics can be learned by most students
- the cost of failure is often higher than the cost of success.
Armed with these convictions, they can begin the process of self-renewal by posing to their mathematics department a series of critical yet frequently unasked questions, about students, curriculum, faculty and cost:
Who are your students?
Does the department know, systemically and in useful detail, who its students are and why they are in its courses? Students who enroll in college mathematics courses arrive with amazing mixtures of aspirations and anxieties, often exaggerated, always intensely personal; student attitudes toward mathematics frequently have more influence on performance than do remembered skills or school-based learning. A first step toward improved success is a good, up-to-date understanding of the preparation and motivations of the students.
Are you committed to teaching the students you have?
It is all too easy for faculty to cover students who fit an imagined mold of young scholars created in the faculty's image, or to treat every first-year student as a potential mathematics major. Instead, the department's priorities should match the actual student population. Instructional practice based on false assumptions yields disillusionment for both students and faculty. Effective instruction harmonizes the goals of the institution with the expectations of its students.
Do you believe that your department should educate all students?
More concretely, does the faculty believe that all students can learn mathematics? Does the department offer appropriate and appealing courses that meet the needs of all students who enroll in the institution? Does the faculty apply as much creative energy to improving the most elementary courses (those often termed "developmental" or, more derisively, "remedial") as it does to the advanced? In fact, the "simple" courses might be the most important in the long run: Most mathematics used in the world, after all, is just simple school mathematics applied in unusual contexts.
Do you have explicit goals for increasing the number of students from unrepresented groups who succeed with mathematics courses?
Vague intentions without explicit goals are too easily ignored. There are precious few departments of mathematics in the country whose record of success with black., Hispanic, and other under represented groups could not be significantly improved. Any goal must be specific to the institution, but barely one aspiration must be that mathematics becomes a pump rather than a filter for students who have been traditionally under represented in the professional fields that build upon college-level mathematics.
What do your students achieve?
More specifically, how does the department know what its students have really accomplished? End-of-term exams generally reveal only short-lived mastery of procedural skills. Does the faculty have any evidence about broader objectives or longer-term learning? Does the faculty ever ask students to solve authentic, open-ended problems, or to write, read, or speak about mathematics? Do courses provide opportunities for students to learn anything other than textbook-based template exercises? To what extent are course grades based on an examination of these broader goals of mathematics education?
Do you know what happens to students after they leave your courses?
Do students who take mathematics courses go on to use their mathematics in subsequent courses? What mathematics? How well? What about students who drop out or fail: Have they given up on mathematics, or do they return and succeed in subsequent courses? Do students who receive good grades find that what they learned serves them well in subsequent courses? Does the department have a mechanism for adjusting curricular emphases based on feedback from students who have taken its courses?
Do your departmental objectives support institutional goals?
Despite variations in rhetoric, widely shared goals for mathematics education are entirely consistent with broad goals of higher education: to develop students' capabilities for critical thinking, for creative problem solving, for analytic reasoning, and for communicating effectively about quantitative ideas. Yet the implicit objectives of many mathematics departments, as inferred from curricula, exams, and student performance, are often focused on mastering relatively sophisticated yet intellectually limited procedural skills. Departments must express for themselves – and even more so, for their students – how their course objectives advance their institution's educational goals.
Do your courses reflect current mathematics?
Since mathematics is such an old subject, it is all to easy for its curriculum to become ossified. Strong departments find that they replace or change significantly half of their courses approximately once a decade. As new mathematics is continually created, so mathematics courses must be continually renewed. Does the mathematics curriculum reveal to students a level of innovation and attractiveness that reflects the excitement of contemporary mathematical practice?
Are you aware of the new NCTM Standards for school mathematics?
More importantly, is the faculty making plans to provide an appropriate curriculum that builds on the foundation of the National Council of Teachers of Mathematics Standards, following their spirit as well as their content? Colleges must be prepared for students arriving with increasingly disparate backgrounds – many from traditional authoritarian, exercise-based courses, but an increasing number of others fresh from an active, project-centered approach that typifies NCTM's new school Standards. It would be ironic, indeed tragic, if intransigent college mathematics departments were to hold back reform of school mathematics by refusing to adapt to the new reality of a more diverse and powerful secondary school curriculum.
Are calculators and computers used extensively and effectively?
Beginning with placement exams and continuing all the way through senior courses, calculators and computers should be used in every appropriate context. Since the mathematics used in the scientific and business world is fully integrated with calculators and computers, the mathematics taught in college must reflect this reality. Anything less shortchanges students, parents, and taxpayers.
Does your curriculum meet postgraduation needs of yours students?
Does the department know what its majors do after graduation? How many take jobs in which they use their mathematics training? How many enter secondary or elementary teaching? What about graduate school – in mathematical sciences, in other sciences – or professional school? Does the students' mathematics education adequately prepare them for those experiences?
How does your program help students see the ways mathematics connects to broad issues of human concern?
Specifically, does the mathematics faculty and its courses connect mathematics to student aspirations, to liberal education, to other disciplines? Does the program empower students to think and act mathematically in broad contexts beyond the classroom? Unless this happens, students feel cheated by lack of reward commensurate with the effort required.
How does the scholarship of your faculty relate to the teaching mission of your department?
Does the faculty subscribe to a narrow view of research or to a broad perspective on scholarship? Traditional standards of mathematical research make direct connections to undergraduate teaching rather difficult, whereas a "reconsidered" view of scholarship opens doors to constructive engagements in which the faculty can thrive professionally and students can become junior colleagues. Does the department both expect and support professional development in its varied forms? Is the department committed to offering all of its majors suitable professional, scholarly, research, or internship opportunities?
What steps have you taken to be sure your faculty is well informed about curriculum studies and research on how students learn?
Part of the professional responsibility of faculty is to know that scholarship that undergirds college teaching. Everyone has opinions about curriculum and pedagogy, but professionals need to support their opinions with evidence. Since graduate education in mathematics rarely provides any introduction to this arena of scholarship, departments must accept it as part of their responsibilities. Regular faculty seminars on issues of curriculum, teaching, and learning help create an environment of faculty attention that is crucial to students success.
What are your priorities for teaching assignments?
In particular, does the department assign its best teachers to beginning courses? Are courses for nonmajors given the same priority as those or majors? Does the faculty prefer students who learn without being taught, or those who challenge teachers to teach effectively? How do rewards reflect the teaching challenges faculty undertake? Is the quality of teaching measured by the good students the faculty attracts to its courses, or by the learning of all students in those courses?
Is your faculty fulfilling its responsibility for the preparation and continuing professional education of teachers?
NCTM's new Standards for school mathematics include clear expectations for both content and pedagogical style in the mathematical preparation of school teachers at all grade levels. How many members of the mathematics department are familiar with those expectations? To what extent do courses conform to those Standards? What steps are the department taking to ensure that all mathematics courses for prospective teachers meet appropriate professional expectations?
How are faculty resources allocated between courses that serve the major and those that serve general education?
Typically, 80 percent of the students in a mathematics department are enrolled either in service courses or general-education courses. Often more than 80 percent of students command only 20 percent of faculty time and energy. Yet it is those students who will go on to be future policy leaders of society – members of boards of education and city councils, editors of local newspapers, leaders of Chambers of Commerce.
Have you calculated the true cost of the status quo?
Course staffed on cheap (the "cash cow" approach to funding mathematics departments) result in students repeating courses, failing related science courses, or dropping out of college altogether. Students who succeed in their first college mathematics course are far more likely to succeed in college than those who do not. Cheap courses are not necessarily as cost-effective as they appear.
-Lynn A. Steen, Professor of Mathematics, St. Olaf College