Understanding and Content
Surveys of quantitative skills needed for biologists frequently include college algebra, introductory calculus and statistics. Among these three areas of mathematics, statistics is the most commonly mentioned and the most extensively used. Other content areas that are mentioned include mathematical modeling, discrete mathematics, and matrix algebra. What follows are topics, organized by course, that the workshop participants identified as important in the study of biology.
College Algebra or Precalculus: Biology students need to understand the meaning and use of variables, parameters, functions and relations. They need to know how to formulate linear, exponential, and logarithmic functions from data or from general principles. They must also understand the basic periodic nature of the sine and cosine functions. It is fundamentally important that students are familiar with the graphical representation of data in a variety of formats (histograms, scatter plots, pie charts, log-log, and semi-log graphs.)
Introductory Calculus: The topics from introductory calculus that were mentioned at the workshop included integration for the purpose of calculating areas and average value, rates of change, optimization, and gradients for the purpose of understanding contour maps.
Statistics: It is here where the list of necessary topics is the longest and encompassed descriptive statistics, conditional probability, regression analysis, multivariate statistics, probability distributions, simulations, significance, and error analysis.
Discrete Mathematics and Matrix Algebra: The topics most frequently mentioned were qualitative graphs (trees, networks, flowcharts, digraphs), matrices (Leslie, Markov chains), and discrete time difference equations. Other topics included equilibria, stability and counting techniques.
The pervasive presence of computers, together with their ever-increasing computational power, encourages biologists to apply statistical methods to analyze data that is collected in the laboratory or the field. One important software application used by biologists is the spreadsheet. Increasingly, spreadsheet applications contain sophisticated statistical tools sufficient for use with undergraduate biology majors. The panelists were unanimous in their observation that the graphing calculator is not the tool of choice for biology students. Technological tools must be capable of producing graphs that can be incorporated into printed and presentation documents. They must allow students to apply modeling techniques to large data sets and they must also support simulation of models that are stochastic, discrete or continuous.
The biologists generally agreed that current research areas in biology are more quantitatively oriented. At the same time, they also recognized that the quantitative needs of undergraduate students enrolled in biology courses are diverse and depend largely upon the student audience (e.g., majors versus non-majors) and the variety of disciplinary tracks, ranging from molecular biology to ecology, that students choose to explore. In an already crowded biology curriculum, the biologists agreed that the issue of increasing quantitative emphasis would call for innovative solutions. They suggested solutions ranging from the creation of mathematical courses designed specifically for biology majors to the creation of mathematical modules that could be incorporated into existing biology courses.
One particular challenge facing biology educators is the range of mathematical backgrounds of professors of biology. Many biology educators have completed only calculus and one course in statistics. The limited mathematical background of most biologists is clearly reflected in the correspondingly limited quantitative components of both biology textbooks and curricula. As we begin to expand the quantitative backgrounds of biology students we will also have to provide opportunities for the biology faculty to increase their own facility with mathematics.
To build and require more quantitatively oriented biology courses would be a major, but important, undertaking and would necessitate increased cooperation among biologists and mathematicians. The biologists viewed the proposed actions of the MAA in assisting their partner colleagues with possible changes and emphasis in the mathematics curriculum as a catalyst for needed changes in the undergraduate biology curriculum.
Anita Salem is Professor of Mathematics and Interim Dean, College of Arts & Sciences at Rockhurst University. Judith Dilts is the Dr. Burnell Landers Chair in Biology and Department Chair of Biology at William Jewell College.