MOVING BEYOND MYTHS
Effective programs teach students, not just mathematics.
—Challenges for College Mathematics, 1990
Responses to the problems facing undergraduate mathematics must occur on many fronts, including faculty members and their departments, colleges and universities, business and industry, professional societies, and government agencies. All those with a stake in mathematics must reassert the vital importance of effective undergraduate education in the mathematical sciences. Over the next decade, the mathematical community must restructure fundamentally the culture, content, and context of undergraduate mathematics education.
No one should underestimate the inertia that must be overcome in order to change the culture that controls undergraduate mathematics. Many agencies and constituencies
must join the campaign, including business and industry, government at all levels (federal, state, local), scientists and engineers, college and university administrators, and public officials. Broad support is necessary if significant improvement is to be possible. But it will require leadership to marshal that support in consistent and constructive directions. Leadership for reform is the responsibility of the faculty—of mathematicians in every institution of higher education, from comprehensive universities to two-year colleges, from liberal arts colleges to research universities.
Producing Mathematics Majors
Clarence Stephens created at SUNY Potsdam an undergraduate mathematics program that is difficult to overlook. For nearly two decades mathematics has dominated this regional public college of 4000 students, both in terms of quality and quantity of students. In 1985 the college graduated 184 mathematics majors, a total exceeded only by two campuses of the University of California. Approximately 24 percent of the bachelor's degrees at SUNY Potsdam are in mathematics and over 40 percent of the college's honor students are mathematics majors.
Mathematics at SUNY Potsdam does not rely on novel use of technology or innovative curricula to attract students. "We focus on the human factor," Stephens says, "to change students' perception that mathematics is an almost impossible subject for students to learn and that only the most gifted can be expected to achieve any degree of success." The atmosphere makes mathematics students feel good about themselves; as a result of a supportive environment, they want to learn.
In particular, mathematical sciences faculty must assume full responsibility for the mathematics education of all students. They must change the way mathematics is taught; increase substantially the participation of women, minorities, and the disabled; and play a more substantial role in the preparation of mathematics teachers. In a world in which productivity depends so heavily on quantitative literacy, everybody does count.
Over half of the freshman class takes calculus as an elective, and post-calculus courses account for 50 percent of total mathematics enrollments. The program recognizes every student's accomplishments and stresses the development of successful role models; faculty present just enough in courses for students to learn essential ideas, not so much as to overwhelm them. Tests are viewed as milestones in learning, not as measures for setting high or low levels of achievement. The program depends on a faculty dedicated to teaching and committed to students. The rewards for faculty are students who learn.
Effective undergraduate mathematics instruction for all students.
Full utilization of the mathematical potential of women, minorities, and the disabled.
Active engagement of college and university mathematicians with school mathematics, especially in the preparation of teachers.
A culture for mathematicians that respects and rewards teaching, research, and scholarship.
AN ACTION PLAN
Develop and Promulgate Effective Instructional Models:
Professional Development Programs
Achievement in mathematics is promoted by offering students an environment that fosters success. The Professional Development Program (PDP) at the University of California at Berkeley was developed ten years ago by Uri Treisman to redress excessive failure rates in calculus of Blacks with strong academic records. The program was developed in response to evidence that social isolation of minority students impeded their learning of calculus. It substituted for remedial efforts an approach to learning based on faculty involvement, academic challenge, collaborative learning, and growth of a student community. This approach to learning, which has always been a central part of the educational philosophy of the Historically Black Colleges and the private liberal arts colleges, has now been replicated in special programs in more than fifty universities.
One example is the Professional Development Program at California State Polytechnic University at Pomona. Another is the Emerging Scholars Program (ESP) at the University of Texas, Austin. In both cases the format is similar to that at Berkeley, with special recitation sections that meet for several two-hour sessions each week. Study groups integrate aspects of students' social and academic lives and encourage independent study habits. Key ingredients include high expectations of competence, strong academic components, capable instruction, cooperative learning, and commitment from students.
Learn about learning • Think as deeply about how to teach as about what to teach • Query unexamined assumptions about education • Explore effective alternatives to "lecture and listen" • Involve students actively in the learning process • Emphasize practices known to be effective with minority students • Teach future teachers in the ways they will be expected to teach • Exploit modern technology fully • Teach the students you have, not the ones you wish you had.
Develop effective programs targeting underrepresented groups • Adapt tested and proven models • Build a team of faculty to carry out experiments, and expose all faculty to the results • Start a departmental seminar on issues of teaching and learning • Assign the best teachers to introductory courses • Employ varied instructional approaches: group methods, writing, investigative assignments, laboratory projects • Recognize and support the extensive special effort required to introduce computers effectively into the curriculum • Use knowledge gleaned from minority projects • Sensitize teaching assistants to cultural impacts in the classroom • Vigorously recruit women, minorities, and disabled students to pursue careers in mathematics and science.
Undergraduate research, in which students experience for themselves the open-ended exploratory nature of mathematical investigation, is one of the proven means of launching students on successful careers in the mathematical sciences. However, during the ten-year hiatus in NSF support of undergraduate research, few institutions managed to sustain these programs on their own.
One exception is the University of Minnesota at Duluth, where Joe Gallian has, since 1977, directed a summer research program for undergraduates in mathematics. Faculty and students are imbedded in an informal, nurturing environment that is conducive to research and provides for necessary special attention. Each student is given a problem that has been carefully selected to meet the student's background and to sustain the student's interest. A publishable result is the stated goal for each experience.
Discussion and interaction are encouraged through weekly meetings in which partial results are presented, and by having the participants share living quarters so that they can communicate and work at home. Outings and weekly luncheons bring students and faculty advisors together on a social basis, but the discussions normally turn to mathematics. Preparation of manuscripts for publication often takes a year or more following the summer session, but in many cases these papers do appear in a mathematical or scientific journal.
Colleges and Universities:
Form an institutional task force in response to Moving Beyond Myths • Work with other institutions of higher education to frame an initial state response • Use both responses to stimulate mathematical sciences departmental efforts • Provide resources for appropriate experimentation • Stimulate use of computers in mathematics teaching • Insist that departments mainstream rather than remediate students • Emphasize effectiveness in teaching • Begin an institutional effort to learn how to evaluate teaching properly • Recognize and reward educational innovation.
Investigate and publicize successful instructional models, especially for underrepresented groups • Launch nationwide programs to promulgate effective instructional models • Intensify efforts to inform faculty of the nature, magnitude, and urgency of the problems in undergraduate mathematics • Send peer consulting teams into departments • Establish a journal of undergraduate educational research and practice • Expand programs to educate the public on harmful effects of popular myths about mathematics • Develop and disseminate information on careers in mathematics-based fields • Encourage dialogue among school, college, and university faculty through joint meetings • Stimulate local, state, and national networks • Establish national mathematics education awards that recognize contributions in innovative curricular design, effective methods of teaching, and understanding of how mathematics is learned.
Give undergraduate mathematics high priority in education funding • Focus first on introductory subjects as a key to opportunity for disadvantaged groups • Support results-oriented experimentation • Invest in dissemination and pro-
mulgation of successful models • Broaden experimentation to encompass the full curriculum • Provide resources to support effective instructional methods • Augment graduate fellowship programs with a program of cash awards to undergraduate departments that produce the students • Expand support for programs that retain women and minorities in the mathematics pipeline, keying on critical transition points • Support efforts that ally groups in support of planned, systemic change.
Making Mathematics Work
During the last decade, as mathematics majors climbed nationally from 1 to 2 percent of baccalaureate degrees, mathematics majors at St. Olaf College in Northfield, Minnesota, rose from 8 to 16 percent of the college's graduates. In the last decade, over 30 graduates have earned doctorates in the mathematical sciences—averaging three per year from each graduating class.
St. Olaf is a liberal arts institution of 3000 students. Mathematics is promoted and taught as an excellent liberal arts major—a subject that opens doors to many disciplines. As a consequence, each year from first year through senior year, the number of intending mathematics majors increases. Faculty enthusiasm for mathematics is conveyed both in the classroom and through various social activities designed to promote an image on campus that it is fun to major in mathematics.
Faculty standards are made clear in a written departmental statement of professional expectations given to every prospective faculty member: teaching is top priority, supported by an active but broad professional record of scholarship or research. Teaching is formally evaluated both by peers and students and contributes significantly to reappointment decisions. Professional activity is defined in broad terms and is supported through a strong sabbatical program and other college funds for professional development.
Mathematics faculty are professionally very active, both in research and in education. In the last twelve years, members of the Mathematics Department have received nearly $2 million in grants for projects related to undergraduate curriculum development, school outreach, faculty professional activity, and computer labs. One recent grant from the Fund for the Improvement of Post-Secondary Education (FIPSE) supports an innovative ''teaching post-doc" program that provides new Ph.D.s with a two-year mentored transition to undergraduate teaching that provides time for research and for seminars on teaching and learning.
Establish and Disseminate National Guidelines or Standards:
Develop and disseminate new advisory national guidelines for undergraduate and graduate programs dealing with curriculum, teaching, and evaluation • Align these with national standards for school mathematics • Focus on critical transitions: lower division to upper division, two-year college to university, undergraduate to graduate • Set specific targets for achieving parity for underrepresented groups • Relate guidelines to college and university accreditation • Conduct an in-depth study of resources for departments • Launch a visionary curriculum project aimed at the early decades of the next century.
Participate actively in professional societies' discussion and development of national goals and guidelines • Support and implement emerging guidelines for undergraduate and graduate mathematics • Become familiar with evidence that all students can learn mathematics • Teach as if each student is a national asset • Reinterpret "high standards" to mean that many students learn rather than that most students don't • Recognize that meeting such standards may require dramatic change in classroom practice • Approach teaching as a profession, not as a task • Set a stringent personal standard—that if my students don't learn, it is I (not my students or their previous teachers) who have failed.
SUMMA's Action Plan
To provide national leadership in addressing problems that result in the under-representation of minorities in mathematics, the Mathematical Association of America has established project SUMMA—Strengthening Underrepresented Minority Mathematics Achievement. SUMMA is designed to stimulate fundamental changes in attitude and practice of the collegiate mathematics community in regard to the education of minority students. The project is organized around five key components:
Develop a five-year plan to transform departmental instruction based on national guidelines • Emphasize mathematics for all • Be results-oriented: increase success rates • Incorporate insights gained from departmental experimentation • Include specific plans for using computers, improving numeracy, teaching teachers, and supporting majors • Use national targets from professional societies for success of women and minorities • Set department targets to reduce dependence on teaching assistants and part-time instructors • Address the need to enlarge the scope of graduate programs in the mathematical sciences to include issues of curriculum, teaching, and learning • Relate the departmental plan to the weak state of research funding and to changes in school mathematics programs • Enlist the aid of professional societies in developing and implementing the departmental plan • Take the departmental plan to the administration • Offer higher success rates in exchange for resources needed to implement the plan.
Colleges and Universities:
Give top institutional priority to effective teaching • Judge teaching by results, not by process • Adopt a broad standard of professional responsibility encompassing teaching and scholarship as well as research • Utilize this broad standard in decisions about hiring, retention, salary, promotion, and tenure • Align institutional admissions and placement practices with contemporary standards for school mathematics • Set high institutional expectations for the mathematics performance of all students • Help develop a five-year state plan for undergraduate mathematics • Involve state mathematics coalitions to ensure close coupling to national and state goals for school mathematics • Help the mathematics department implement their five-year plan, injecting resources in planned stages as results become apparent.
For the past several years the Exxon Foundation has helped Cornell University develop a series of innovative general education courses in mathematics. For example, a mathematician and an artist team-teach a course entitled "Mathematics and Art" that deals with the influence of mathematical ideas on art through concepts such as proportion, perspective, and projective geometry. Another course introduces students to the intellectual history of calculus by helping them read parts of the original classic mathematical treatises of the Greek philosophers, of Newton, and of Gauss, among others.
A third course, "From Space to Geometry," explores the ways in which geometry has been used throughout the centuries to try to explain the universe in which we live. Two other courses integrate the use of personal computers in novel ways. One of these developed a new collection of computer software to enable students to interactively understand important mathematical concepts at their own pace and from their own perspective.
Support the development of advisory national standards or guidelines • As consensus emerges, encourage undergraduate mathematics plans, proposals, and projects based on these guidelines • Develop governmental responses to revitalization of undergraduate mathematics • Coordinate across agencies • Recognize the key role played by professional societies, since changing values must be internalized over time by the mathematics community.
Build and Sustain Supportive Attitudes and Structures:
Minority Access to Research Careers
Since 1975 the National Institutes of Health (NIH) have been administering a program dedicated to increasing the number of scientists in biomedical research who are members of minority groups. The program, Minority Access to Research Careers (MARC), supports biomedical research training for students and faculty members at colleges and universities with substantial minority enrollments. It operates through four programs:
The President and Governors:
Expand efforts to inform the public of the importance of mathematics (and science) education • Retain the national education goal of being "first in the world" • Emphasize that revitalization of undergraduate education is essential for reaching this goal • Highlight mathematics education as a key to opportunity in our time • Designate someone on the senior scientific and educational staff as responsible for implementing this Action Plan.
Congress, State Legislators, Regents:
Insist that plans for reforming mathematics (and science) education encompass the undergraduate level • Put resources behind undergraduate revitalization • Support planned, systemic change, not isolated projects and programs.
Federal and State Agencies:
Create a network of regional centers for excellence in the teaching of mathematics • Support time spent at regional centers by teachers at all educational levels • Initiate major programs of postdoctoral teaching fellowships to enable beginning faculty to develop expertise in curriculum, teaching, and learning • Institute fellowship programs to enable faculty members to enhance teaching effectiveness through time spent at innovative centers and institutions • Increase significantly the numbers of predoctoral fellowships and research assistantships in mathematics • Work to reduce dependency on teaching assistants for undergraduate mathematics instruction • Support effective programs of financial
fees, a stipend of $8,500, and $2,000 respectively for supplies and travel are awarded each year for three years to students who enter Ph.D. or M.D.-Ph.D. programs. In 1989 there were 53 such awards.
Faculty Fellowships: This program provides opportunities for advanced research training to selected full-time faculty at four-year colleges, universities, and health professional schools with substantial minority enrollments. Fellows are nominated by their employing institution and may pursue the Ph.D. degree or obtain postdoctoral research training in the biomedical sciences. In 1989 there were 7 predoctoral and 5 postdoctoral awards.
Visiting Scientist Program: This program provides support for periods of 3 to 12 months to outstanding scientist-teachers who serve as visiting scientists at eligible minority institutions. The intent of the program is to help strengthen research and teaching in the biomedical sciences at these institutions by allowing visiting scientists to draw on the special talents of experts.
incentives for students planning on teaching careers, emphasizing especially minority teachers • Significantly increase support for dissemination and public information activities • Provide sustained financial support for working alliances and networks to implement parts of this Action Plan.
Universities and Colleges:
Fully fund the cost of effective undergraduate mathematics teaching • Provide sufficient computer labs to enable mathematics courses to be taught with full computer support • Speak out about the importance of research funding for healthy undergraduate education • Support the concepts of predoctoral, postdoctoral, and mid-career fellowships for college and university teachers of mathematics.
Faculty and Departments:
Build faculty networks within institutions, linking user departments • Connect to networks of mathematicians committed to educational reform • Develop a strong presence in regional and national meetings of department chairs • Forge professional alliances and initiate collaborative projects with mathematics teachers in local schools • Offer regular enrichment programs that motivate school-age youth, especially minorities, to continue studying mathematics • Speak to needs and accomplishments in a second five-year plan for undergraduate mathematics.
Professional Societies and National Organizations:
Involve the broad constituencies of mathematics education in discussions of goals and standards • Sustain structures built to promulgate targeted minority programs • Support national transformation based on new guidelines • Establish structures linking corporations, minority action groups, and scientific societies to long-term revitalization effort.
• Update this Action Plan regularly and coordinate implementation well into the next century.
Statewide Mathematics Articulation
Approximately every five years, the Illinois Community College Board invites the Illinois Mathematical Association of Community Colleges and the Illinois Section of the Mathematical Association of America to form a joint task force to revise and update the Illinois Curriculum Guide for Courses in Mathematics and Computer Science in Colleges and Universities. This document contains the minimum content, range of credit hours, and suggested prerequisites for transfer-level courses in mathematics and computer science as well as pretransfer-level mathematics courses.
Each joint task force includes a mathematics faculty representative from each major state university and a like number of community college mathematics faculty representatives. The purpose of the Guide is to assist in the articulation of mathematics and computer science courses between community colleges, from any community college to any four-year college or university, and between four-year colleges and universities.