BACKGROUND

    The purpose of this NSF sponsored project (see NSF link below for additional details) is to begin to develop a new mathematics curriculum to serve the Biosciences. The objectives of the project are largely a response to recommendations and findings of the BIO2010 and CRAFTY Reports. Some excerpts from the reports as well as links to the full findings are provided below.

    This project focuses on the beginning mathematics requirement for biology majors at both Farmingdale State and SUNY Suffolk. The overall goal is to create a new mathematics sequence for biology majors that is more relevant to their requirements and needs.

BIO2010: Transforming Undergraduate Education for Future Research Biologists

http://www.nap.edu/catalog/10497.html

RECOMMENDATIONS:

1. Given the profound changes in the nature of biology and how biological research is performed and communicated, each institution of higher education should reexamine its current courses and teaching approaches to see if they meet the needs of today’s undergraduate biology students. Those selecting the new approaches should consider the importance of building a strong foundation in mathematics and the physical and information sciences to prepare students for research that is increasingly interdisciplinary in character. The implementation of new approaches should be accompanied by a parallel process of assessment, to verify that progress is being made toward the institutional goal of student learning.

2.Concepts, examples, and techniques from mathematics, and the physical and information sciences should be included in biology courses, and biological concepts and examples should be included in other science courses. Faculty in biology, mathematics, and physical sciences must work collaboratively to find ways of integrating mathematics and physical sciences into life science courses as well as providing avenues for incorporating life science examples that reflect the emerging nature of the discipline into courses taught in mathematics and physical sciences.

3. Successful interdisciplinary teaching will require new materials and approaches. College and university administrators, as well as funding agencies, should support mathematics and science faculty in the development or adaptation of techniques that improve interdisciplinary education for biologists. These techniques would include courses, modules (on biological problems suitable for study in mathematics and physical science courses and vice versa), and other teaching materials. These endeavors are time-consuming and difficult and will require serious financial support. In addition, for truly interdisciplinary education to be achieved, administrative and financial barriers to cross-departmental collaboration between faculty must be eliminated.

4. Laboratory courses should be as interdisciplinary as possible, since laboratory experiments confront students with real-world observations do not separate well into conventional disciplines.

5. All students should be encouraged to pursue independent research as early as is practical in their education. They should be able to receive academic credit for independent research done in collaboration with faculty or with off-campus researchers.

6. Seminar-type courses that highlight cutting-edge developments in biology should be provided on a continual and regular basis throughout the four-year undergraduate education of students. Communicating the excitement of biological research is crucial to attracting, retaining, and sustaining a greater diversity of students to the field. These courses would combine presentations by faculty with student projects on research topics. (page 91)

7. Medical school admissions requirements and the Medical College Admissions Test (MCAT) are hindering change in the undergraduate biology curriculum and should be reexamined in light of the recommendations in this report.

8. Faculty development is a crucial component to improving undergraduate biology education. Efforts must be made on individual campuses and nationally to provide faculty the time necessary to refine their own understanding of how the integrative relationships of biology, mathematics, and the physical sciences can be best melded into either existing courses or new courses in the particular areas of science in which they teach.

SUMMARY

It is generally agreed that research in biology has become more quantitatively oriented than in the past. At the same time, it is 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 panelists 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.

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 proposed actions of the MAA in assisting their client colleagues with possible changes and emphasis in the mathematics curriculum could serve not only to increase the quantitative literacy of biologists, but also act as a catalyst for needed changes in the undergraduate biology curriculum. Some common themes that emerged during the workshop were:

1. New areas of biological investigation together with advances in technology have resulted in an increase in quantification of biological theories and models.

2. The collection and analysis of data that is central to biological investigations inevitably leads to the use of mathematics.

3. Mathematics provides a language for the development and expression of biological concepts and theories. It allows biologists to summarize data, to describe it in logical terms, to draw inferences and to make predictions.

4. Statistics, modeling and graphical representation should take priority over calculus.

5. The teaching of mathematics and statistics should use motivating examples that draw on problems or data taken from biology.

6. Creating and analyzing computer simulations of biological systems provides a link between biological understanding and mathematical theory.

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.

1. College Algebra: 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.)

2. 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.

3. Statistics: It is here where the list of necessary topics is the longest and encompasses descriptive statistics, conditional probability, regression analysis, multivariate statistics, probability distributions, simulations, significance and error analysis.

4. 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.

IMPLEMENTATION

There is a variety of ways to implement curricula containing the recommended mathematical topics. It should be noted that responsibility for student competence with mathematics should not rest solely in the hands of the mathematics faculty. The biology faculty must incorporate the use of mathematics into their courses in order to reinforce and verify the importance of mathematics to their students. To this end, the quantitative courses must be taken early so that the topics introduced can be used in subsequent courses in biology. Collaborative efforts to design and deliver the quantitative courses should be encouraged. Some possible curricular options considered by the panel include:

1. Mathematical requirements may be completed in a one-semester course. The panel does not recommend this option, however if only one course in mathematics is required, they suggest that the emphasis of this course be on statistics.

2. Mathematical requirements may be completed in a two-semester sequence. In this scenario, the panel recommends that one course focus on topics in statistics and the other course include topics from calculus and mathematical modeling. A yearlong course integrating these three topics would be preferable.

3. Mathematical requirements may be completed in a three-semester sequence. This option would include a course in statistics and a course integrating topics from calculus and mathematical modeling. The third course might come later in the curriculum as a project-based course oriented toward modeling applications and could also include topics from matrix algebra and discrete mathematics.

4. Mathematical requirements may be completed by an integrated approach. An interdisciplinary approach could be used to embed mathematical modules into biology courses. This approach has the advantage of teaching the mathematical concepts in the context of biological applications. The challenges to this approach are the usual difficulties that arise in the design and delivery of interdisciplinary courses.

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