**MAA-CUPM CRAFTY Initiative on
Mathematics in Undergraduate Biology Education**

The SMB Educational Committee was asked to officially represent SMB at the Mathematics Association of America (MAA) - Committee on Undergraduate Program in Mathematics (CUPM) special initiative entitled "Calculus Reform and the First Two Years (CRAFTY)'s Curriculum Foundations Workshop in Chemistry and the Biological Sciences". The meeting was held at Macalester College, St. Paul, Minnesota, from November 2-5, 2000. Our host was Professor David Bressoud; he should be contacted for details. The conference was supported by the National Science Foundation and the Howard Hughes Medical Institute. SMB Committee members included Claudia Neuhauser (U Minnesota), Lou Gross (U Tennessee Knoxville), Anita Salem (Rockhurst College), and John R. Jungck (Beloit College). In addition, SMB was well represented by Fred Adler (U Utah), Stephen and Sandra Merrill (Marquette U), Danny Kaplan (Macalester College), Dan Tranchina (Courant Institute), and Eric Marland (Appalachian State). Unfortunately, Hans Othmer (U Minnesota), who planned to attend, was too ill to join us.

After an introductory session led by Lou Gross and David Bressoud , mathematical biologists, biomathematicians, biologists, and half of the mathematicians met separately to develop a set of mathematical expectations for undergraduate majors in biology. Lou's list included seven categories:

- Rate of Change;
- Scale;
- Equilibria;
- Stability;
- Structure;
- Interactions; and,
- Stochasticity.

These provided an excellent jump-start of discussion. In addition, David stressed MAA's post-1981 commitment to mathematical education involving: discovering, computing, modeling, and writing. He described contemporary calculus reform initiatives, which began in 1988, use a rule of six, namely, that each subject should be approached in the following ways: "

- treat key idea symbolically, numerically, and visually-graphically,
- use technology as appropriate,
- use writing to foster critical thinking skills,
- incorporate appropriate applications and interdisciplinary projects [hence, biology],
- encourage cooperative/collaborative learning, and
- find appropriate assessment tools and use them to improve teaching and learning."

Departments of Mathematics were asked two questions:

- What are you doing with your undergraduate community of learners?, and,
- What are you doing to foster relationships with client disciplines?

The relevance of the University of Rochester case as a stimulus to the community of mathematicians to take such issues much more seriously than in the past received considerable attention. The group's conclusion was that each department has to address these issues on their own terms. Danny Kaplan discussed the current state of mathematics in biology curricula. The
median expectation of undergraduate biology majors is one semester each of calculus and statistics. However, many departments required no mathematics and even the most quantitatively rigorous programs rarely required more than three courses in mathematics and/or computer science. The mismatch between these requirements and contemporary opportunities for biologists in bioinformatics, GIS, computational biology, and ecology were earnestly debated. Specific needs of different kinds of biology majors were raised: biochemistry and genetics - physical chemistry and physics of electricity and magnetism, ecology - multivariate statistics, calculus, and discrete mathematics, and neurobiology - differential equations and nonlinear dynamics. Danny said he was particularly struck that there was no program with a multivariate statistics or linear algebra requirement, no oscillations in dynamics, no Markov chains, no saddle point analyses, and no experience with modeling. The most widely adopted textbook in biology, while over a thousand pages, only contained two equations: y = mx + b and p^{2} + 2pq + q^{2} = 1. Hence, current biology majors seldom have to background to handle contemporary research uses of mathematics in biology. An ensuing discussion concluded that situation in computer science might even be worse than in mathematics.

Fred Adler and Claudia Neuhauser both made presentations about their approaches to calculus for biologists based upon the textbooks that they each have written. Eric Marland asked whether we are perhaps teaching mathematics too early to biologists before they realize that they need deeper sophistication in mathematics. Anita Salem emphasized the utility and appeal of teaching calculus to biologists from a data-driven perspective. Bob Blystone, Trinity University, San Antonio, Texas, gave an elegant, well-received survey of the role of digital video microscopy, morphing, 2D and 3D reconstruction, and digital archiving for introducing much more quantitative, computational, and modeling into biology than has previously been taught in a descriptive rather than in an analytical mode. I gave a brief introduction to the computer simulations, tools, databases, and digital libraries of the BioQUEST Curriculum Consortium. Other BioQUEST authors at the meeting included Dan Hornbach, acting president of Macalester College, and Bob Blystone. Several new publishing initiatives in mathematical biology also received attention: Eric Marland showed "Kaiser's Computational Cell Biology," Stephen and Sandra Merrill shared the outline for their new textbook in mathematical biology, which included applications in bioinformatics and molecular phylogenetics. Danny Kaplan shared copies of his book: "Resampling Statistics in MATLAB" with participants. Dick Molnar, Macalester College, showed a draft of a text by John Rhodes, Melinda Harder, and Elizabeth Allman which will cover modeling molecular evolution, constructing phylogenetic trees, epidemic modeling, curve fitting and AIDS modeling.

The meeting concluded with the development of a list of topics and concepts that should be addressed in a new MAA-CUPM initiative on curricula for undergraduate biology students. Each item received a priority score. Bob Blystone issued a minority report that encouraged those present to seriously consider the constraints on undergraduate biology education and to not presume that the number of mathematical prerequisites can realistically change much; therefore, he encouraged mathematicians to look within the constraints of their generously allotted time.

Three conclusions were shared by all:

- These courses should be taken early, so that topics introduced in these courses can be used in (are prerequisites of) later courses in biology;
- Care must be taken in developing and teaching these courses to mesh with being able to take more advanced mathematical science courses with as few gaps as possible; and,
- Collaboration in development between departments is imperative and can include team taught courses, teaching circles, and guest lectures integrated into standard courses.

SMB members in attendance decided that we should continue this discussion next July at the annual meeting when the educational symposium will feature courses team taught by a mathematician and a biologist. Please contact us with additional suggestions.

Finally, please remember that Lee Segel, Editor of the Bulletin of Mathematical Biology, has invited educational manuscripts. Please help us identify high quality work appropriate for the journal as well as criteria for relevant editorial policy.

Respectfully submitted,

*John R. Jungck*

Committee Chairperson