Salisbury State College

The Mathematical Competition in Modeling

Purpose of Project:

Undergraduate mathematics is the keystone to research and knowledge in the natural sciences, economics, engineering, computer science and other fields. And yet we live in an era of alarmingly low math proficiency-a situation in which too many students know too little math. To enhance the presence of mathematics on college and university campuses nationwide, the Consortium for Mathematics and its Applications (COMAP) sponsored a Mathematical Competition in Modeling (MCM) each grant year from 1985 through 1987, and it continues today. COMAP is the largest source of materials in undergraduate mathematics application.

Innovative Features:

This mathematical contest differs from the well-established Putnam Competition in the following ways: the math problems are open-ended and do not have a single or clear solution; students work in teams of three for an entire weekend to solve one problem they have selected from a set of two, and may use books, notes, and computers to derive solutions. Over 150 teams of undergraduates from 118 higher education institutions participated in the final grant year competition.

Evaluation:

Four indicators of program success were used: yearly contest participation rates, quality of submitted papers, responses to an opinion questionnaire, and numbers of invited presentations by mathematical associations.

All submitted solutions to the math problems were judged by a chief grader and 10 associate graders from various colleges and universities, who classified the solutions as: "Successful Participation," "Honorable Mention," and "Meritorious." Each year, selected Meritorious papers have been published in national, refereed journals.

Impact Or Changes From Grant Activities:

For each year the project operated and the contest was held, there was a 30% increase in the number of entries over the year before, for example, from 118 team submissions in 1986 to 156 in 1987. Project staff have noted an increase in quality and number over the three-year period not only of submitted solutions but of student presentations of results to regional and national meetings of major mathematical organizations such as the Mathematics Association of America (MAA), Operations Research Society of America (ORSA), and the Society for Industrial and Applied Mathematics (SIAM). A final indication of project impact is the publishing in 1987 of the four top entries in a special issue of an international research journal, Mathematical Modeling (Pergamon Press, Volume 9, Number 10), devoted entirely to this competition, with the project director as guest editor.

Changes in the curriculum to reflect the importance of mathematical modeling represent the most gratifying way the contest might influence mathematics on campuses nationwide. The project staff are more confident about this change now than in years past since MCM has been given backing by both SIAM and ORSA. The latter contributed graders, prizes, and memberships, as well as its endorsement.

The project director concludes that "the 1985, 1986, and 1987 contests suggest there is a good nucleus of budding modelers in [our] schools." In fact, about 40% of the participating teams receive some type of official recognition such as travel funds from their colleges and universities. Some MCM winners have gone on to receive "enhanced" graduate assistantships and two winning teams received cash prizes and fully-paid trips to professional meetings.

What Activities Worked Unexpectedly?

Unexpected yet welcome results were the rapidly increasing interest in this applied mathematics activity; the strong showing by small colleges; and the ease and efficiency with which students can learn to solve problems collaboratively.

What Activities Didn't Work?

Challenges to project staff included designing suitable math problems, recruiting competent graders, and managing the grading process. First and second year experiences with these issues led to third year refinements.

What Do You Have To Send Others And How Do They Get It?

Solutions from all three years of winning teams are available in standard math publications. In addition, MCM announcements describe contest rules and guidelines and include selected MCM questions from previous years. The project director is a regional representative for TEAM, an NSF project that produced six video tape modules on modeling.

For background information on MCM, contact the project director for a 1985 article in Mathematical Modeling, Volume 6.

For these materials, write to:
B.A. Fusaro
Department of Mathematical Sciences
Salisbury State College
P.O. Box 2195
Salisbury, MD 21801
301-543-6470

Cost Effectiveness:

The major context expenses, which vary with the number of contestants, include grading, released time for the project director, and mailing. Special cooperation from Salisbury State has kept two of these costs unusually low by having grading done on campus, using on-campus housing for graders, and subsidizing released time for the project director. Other costs associated with maintaining a contest data base and preparing announcements are covered by COMAP.

What Has Happened To The Program Since The Grant Ended?

The Mathematical Competition in Modelling is being supported in part by several leading applied mathematics organizations and has, to some extent, been institutionalized at Salisbury State College with the primary support coming from COMAP. Currently, special long-term funding is being solicited from other sources to replace COMAP funds. In 1985, the contest involved 70 colleges, with 90 teams. The 1989 contest doubles that initial number of institutions to 143, with 211 teams. Six of the Meritorious solution papers will be published in the Journal of Undergraduate Mathematics and its Applications, a COMAP publication. The 1990 contest was held in February.

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