What mathematical experiences and knowledge should all Health and Life Sciences students gain during their first two years of study? And what can Mathematics Departments and colleagues in Life Sciences Departments do to interact productively to provide these experiences?
These issues were addressed by the Curriculum Foundations Conference on the Mathematics Curriculum for Health and Life Sciences students, held in May 2000 at Virginia Commonwealth University in Richmond, Virginia. Conference participants represented both mathematics and the life sciences. The summary report of the conference is a statement of the common ground discovered through the conference discussions, along with some general recommendations for the mathematics community from the life sciences participants. The summary report is available at the Bowdoin College web site at http://academic.bowdoin.edu/math/faculty/B/barker/index.shtml.
This article highlights two major issues that generated interesting discussion at this conference. On both issues there was a general consensus on basic requirements. These two issues are the need for a core mathematics curriculum for life sciences students, with an emphasis on mastery of mathematical concepts, and the need for flexibility in the curriculum of all life science disciplines, to allow all students access to this core mathematics curriculum.
A Core Curriculum: The consensus on the need for a core mathematics curriculum was reached very quickly. The essential requirement, on which the participants agreed, was that mastery of a mathematical concept means conceptual understanding combined with understanding of implementations/computations involving that concept. To achieve mastery, the conceptual discussion of mathematical concepts must be integrated with relevant computations in problem-solving. This requirement is currently being addressed by calculus courses using texts that give equal time to algebraic, geometric, and numerical aspects of mathematical concepts. However, conference participants from the life sciences were generally unaware of mathematics education reform efforts. The core curriculum should emphasize modeling discussions, and life scientists observed that modeling “requires a solid mathematical background in techniques and structures.” Although mathematics in biology frequently uses discrete models, life scientists affirmed the importance of standard introductory courses in the continuous models of calculus and its extensions, as in differential equations. In addition, there were frequent calls for an emphasis on the use of statistics and data analysis.
Here are some additional statements that addressed the quest for mastery:
Graphing and visualization skills, including the use of log scales, and all aspects of the linear equation y = mx + b should be mastered.
Some participants observed that “chemistry students tend to think more visually than physics students, who tend to think in terms of formulae.” These habits, or inclinations, as the case may be, represent trade-offs in the overall mastery of concepts.
Students should master computer use and statistics for problem-solving, through use of a high level software package. The specific software package is less important than mastery of the concepts common to each class of package.
Mastery requires that theoretical understanding and computational skill be considered two sides of the same coin, the overall understanding of concepts. The desired balance between these aspects can be problem/question dependent. Some participants noted that biology students in the first two years “might not necessarily know how to solve a differential equation, but they should understand qualitatively what the various terms in the equation mean.” This emphasizes basic conceptual understanding at some expense to the implementation aspect of understanding.
Flexibility: Life scientists observed that the value of mathematics is not restricted to the specific content of any particular course. Life sciences students should be permitted and indeed encouraged to take more mathematics courses even at the expense of some lesser amount of life sciences coursework. Thus, life sciences students might be offered a program structure that includes substantial mathematics courses. In the words of one participant, the flexibility needed for the benefit of life sciences students is that “the content of specific courses is not as important as the whole package of courses that the student is allowed to take.” Some students might want and need to take additional courses beyond the recommended core material. One scientist commented on the needs of students with ambitions beyond the basic undergraduate level: “The current areas of biological interest will branch into further areas and mathematical issues will be crucial in forming links between these areas.” The reader of this article can view the “most likely optional list” of additional mathematics topics as discussed by conference participants, by going to the web site given earlier in the article.
On the other hand, flexibility is needed on the part of Mathematics Departments, to offer program tracks with substantial life science courses for students with interests in those areas, even at the expense of taking some lesser amount of mathematics credits.
How do we all benefit? Successful interdisciplinary work often involves overcoming the difficulties of language or academic culture differences. Administrations must realize that instructors and researchers working across traditional academic boundaries need support and encouragement. The reward will be the realization of the creative potential that lies at these boundaries.
William J. Terrell is Associate Professor of Mathematics at Virginia Commonwealth University. Thomas F. Huff is Vice Provost for Life Sciences at Virginia Commonwealth University