The field of urban ecology is a hybrid of ecology, the earth sciences, and the social sciences. Similarly, urban ecosystems can be thought of as hybrids of purposeless natural ecosystems and purposefully managed systems. Natural ecosystems are governed by the dynamics of populations and materials, while managed ecosystems, like physiological systems, seek some goal within the constraints of these dynamics. Each of these components requires a different type of quantitative method, and the temptation in an Urban Ecology course is to avoid mathematics entirely. Our pilot version of such a course succumbed to this temptation. I will discuss that experience, and some preliminary thoughts about the challenges of incorporating mathematical methods in the increasingly important environmental sciences.
We will present several computer laboratory projects used in the biocalculus courses at Benedictine University. Two important goals of these projects the are the integration of mathematical and biological reasoning through the understanding of biological models and the development of skills to use appropriate computational software to analyze and solve biological problems. We will discuss how and why we use a combination of Excel, Derive, Berkeley Madonna, and MATLAB to achieve these goals.
Reports like the NRC's Bio 2010 and Microsoft's Towards Science 2020 have changed the landscape of discussion about the reform of undergraduate biology education. Funding organizations like NSF and HHMI have responded by issuing RFP's that reflect the recommendations of these reports and some significant grants have been awarded. Nonetheless, few biology programs are making revolutionary changes. Despite major changes on research fronts of biology, education suffers from both resistance and neglect. What will it take to make significant change? While we might not be able to change some socio- cultural-institutional traditions that do not professionally and financially reward educational scholarship, we as mathematical biologists can catalyze change by developing curricular materials, sharing an interdisciplinary language, and providing professional opportunities for biology and mathematics educators to convene. The data avalanche of contemporary high-throughput biology has challenged the traditional methods of biological inference construction because multidimensional visualization, simultaneous consideration of multiple variables, and multi-disciplinary analyses are required. While mathematics has played exceptionally important roles throughout the history of biology, too frequently it has been unappreciated in biology curricula because textbook authors, and many of the professors who adopt them, assume that biology students have an inadequate mathematical preparation. Recently, computer science and mathematics have completely transformed the practice of biology. Thus, the neglect of both in practice deskills many biology, computer science, and mathematics students, misrepresents contemporary biological research to them, and doesn't prepare them to collaborate on significant problems. We will share successful initiatives in learning through quantitative problem solving by the BioQUEST Curriculum Consortium, in teaching calculus such as by Project CALC, in teaching computational science such as by NCSI and the Shodor Foundation, in teaching chemistry such as by ChemLinks, and in teaching physics such as by Workshop Physics. Each of these curricular reform initiatives has generated a great deal of relevant materials. These reform efforts have empowered thousands of American undergraduates to become proficient in the use of wet labs, field work investigations, case studies, and software packages that could be used to explore the behavior of many famous mathematical models in biology, collect and mine complex data sets, and evaluate their hypotheses with multidimensional visualizations. When the NRC and Microsoft recommendations are examined in light of current research and available resources, numerous progressive alternatives exist for proceeding to develop curricula that address these challenges.
The traditional undergraduate curriculum for a biology major is limited to one year of calculus (or less). This does not prepare biology students adequately for the data rich biology of tomorrow. Instead of adding new mathematics and statistics courses to the already busy four-year plan of biology majors, I suggest integrating mathematics, statistics, and computation directly into biology courses. With funding from the Howard Hughes Medical Institute, I have been developing quantitative course materials suitable to be integrated into biology courses, in addition to a "statistics appreciation" seminar for biology freshmen.
Contemporary research in biology is a collaborative interdisciplinary endeavor. Since 1986, multiple projects from the BioQUEST Curriculum Consortium have supported the use of simulations, tools, data, and other resources for problem posing, problem solving, and peer review in undergraduate biology. These projects are community based and involve educators, scientists, and specialists from multiple disciplines. In this session, resources from Biological ESTEEM(Excel Simulations and Tools for Exploratory, Experiential Mathematics), Microbes Count!, and the BioQUEST Library will be presented. Pedagogical strategies to support inclusivity and open-ended inquiry such as the use of investigative cases and problem spaces will be discussed briefly.