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Instructional Materials and Approaches for Interdisciplinary Teaching

RECOMMENDATION #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.

Outstanding textbooks such as Linus Pauling’s General Chemistry and James Watson’s Molecular Biology of the Gene have enriched and transformed undergraduate education in the past. These innovative works defined new areas of science and made them accessible and exciting to future scientists at a crucial formative stage. The need for works that sculpt science in ways that inform, enlighten, and empower the next generation of researchers is even greater today. First, new architectures that encompass the highly interdisciplinary character of biology can accelerate the learning process and enable students to exercise their talents earlier in their careers. Second, new technologies provide exceptional opportunities for enhancing the learning process. The potentialities of computers and computer graphics have barely



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Bio 2010: Transforming Undergraduate Education for Future Research Biologists 3 Instructional Materials and Approaches for Interdisciplinary Teaching RECOMMENDATION #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. Outstanding textbooks such as Linus Pauling’s General Chemistry and James Watson’s Molecular Biology of the Gene have enriched and transformed undergraduate education in the past. These innovative works defined new areas of science and made them accessible and exciting to future scientists at a crucial formative stage. The need for works that sculpt science in ways that inform, enlighten, and empower the next generation of researchers is even greater today. First, new architectures that encompass the highly interdisciplinary character of biology can accelerate the learning process and enable students to exercise their talents earlier in their careers. Second, new technologies provide exceptional opportunities for enhancing the learning process. The potentialities of computers and computer graphics have barely

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Bio 2010: Transforming Undergraduate Education for Future Research Biologists been tapped. They need to be integrated into traditional teaching and developed as distinctive media that stand on their own. This chapter highlights some opportunities, starting with interdisciplinary modules. The physical science and mathematics background of life science majors should be markedly strengthened by bringing principles and examples drawn from these disciplines into the teaching of biology courses. No longer should these disciplines be regarded merely as courses to be “taken” by life science students. Rather, they should be woven into the teaching of biology itself to better illustrate the integrative and interdisciplinary nature of the life sciences. The next section presents examples of ways to integrate two or more sciences together into one course. The ideas presented here may be helpful in designing courses for the curricular ideas and arrangements presented in Chapter 2. MODULES FOR COURSE ENRICHMENT The purpose of this section is to provide some of the best examples identified in the course of this study as models for faculty who may want to incorporate some of the ideas into their own teaching. A step toward interdisciplinary teaching can be taken by using modules that focus on important principles of mathematics and the physical and information sciences in order to demonstrate their relevance to biology. A module could be presented in a single lecture or laboratory session, or over several sessions. For example, a module on allosteric interactions in hemoglobin could enrich the teaching of respiratory physiology. Students could explore the following questions by carrying out interactive computer simulations: How does the cooperative binding of oxygen to hemoglobin increase the efficiency of oxygen transport? How much oxygen is released from hemoglobin when the pH is lowered? How is oxygen transport affected by high altitude? Modules have been developed and integrated into science curricula with success at some institutions, but this approach has not been widely adopted at a majority of institutions nationwide. The use of biological examples as modules in courses on chemistry, physics, computer science, and mathematics could help make those courses more relevant to future biological research scientists. Well-chosen examples that vividly present the biological pertinence of the physical or mathematical concepts under study can help students draw connections between material taught in different courses. Faculty from different disciplines should get together to prepare a series of interdisciplinary modules and associated teaching materials

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Bio 2010: Transforming Undergraduate Education for Future Research Biologists such as computer simulations and animations. Several examples of topics in biology that could be effectively taught using modules that present concepts from mathematics and the physical and information sciences are given at the end of this section. The mathematics, physics, chemistry, or engineering background needed for each module could be succinctly developed in the context of a biological question. Adaptable modules for course enrichment that take full advantage of interactive computer programs and multimedia educational tools are a very attractive complementary means of strengthening undergraduate biology education. They can be designed for class use or independent study. Highly focused modules conveying connections between disciplines could be presented in a single teaching session or over several days depending on their scope and their role in the course. The NSF has launched the National Science Digital Library ( http://www.smete.org/) as a gathering place for resources in science education. The idea is to provide a virtual gathering spot, a peer-reviewed library on education, and tested resources for teaching science. The NSDL is being assembled in parts. An example of a fully functioning component is the library for earth system education (http://www.dlese.org/). The biology component, BioSciEdNet (BEN), is still under development (www.biosciednet.org/), but could be a valuable resource if the community embraces it. Numerous independent groups have published modules or resources that could be used to enhance the teaching of undergraduate biology students. One group that has developed numerous modules for biology courses and laboratories is the BioQUEST Curriculum Consortium (Case Study #2). Examples of problem-based learning can be found at the University of Delaware’s clearinghouse (http://www.udel.edu/pbl/). Case studies are collected by the National Center for Case Study Teaching in Science at SUNY Buffalo (http://ublib.buffalo.edu/libraries/projects/cases/case.html). The Consortium for Mathematics and its Applications has a project, Intermath, that works to foster the creation of interdisciplinary courses that demonstrate the interdependence of mathematics and science. They have produced supplementary modules in a searchable database at http://www.comap.com/undergraduate/ and also publish The UMAP Journal. A sample module is presented here (Case Study #3); it was designed for a course in organic chemistry. The premise of the module is that studying the infectivity of the influenza virus is an effective means of engaging student interest in carbohydrates and teaching principles of molecular recognition and rational drug design in a stimulating context.

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Bio 2010: Transforming Undergraduate Education for Future Research Biologists CASE STUDY #2 BioQUEST Curriculum Consortium BioQUEST designs, develops, and publishes teaching materials to support investigative, student-centered learning. The BioQUEST Library is a peer-reviewed publication of computer-based curricular materials for biology education. The current volume (VI) contains more than 75 software simulations and supporting materials from diverse areas of biology, such as Biota (modeling and simulating population dynamics), Evolve (population genetics), Isolated Heart Laboratory (pressure-volume relationships in a variety of physiological states), Epidemiology (simulation of the spread of an infectious disease), and Diffusion Laboratories (models of pattern formation in development). These modules include quantitative approaches to the study topics. The consortium also provides opportunities for faculty development in the form of nine-day summer workshops at Beloit College. For example, one BioQUEST Curriculum summer workshop focused on change in introductory biology courses. Participants had the opportunity to experience, as a student would, the use of research strategies to pose and explore biological problems. These investigations were built around the use of several BioQUEST modules including Genetics Construction Kit, Environmental Decision Making, BIRRD, Demography, EcoBeaker, Evolve, Wading Bird, and others. Materials developed collaboratively, such as LifeLines Online cases and bioinformatics problems from the Workbench Users’ group, were also featured. Their co-developed curriculum materials also include an Internet-based suite of bioinformatics tools and databases, a database and tools for exploring evolution via multiple data resources, investigative cases for introductory biology in two-year institutions, and multimedia resources for the American Society for Microbiology video series Unseen Life on Earth. For more information: http://bioquest.org

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Bio 2010: Transforming Undergraduate Education for Future Research Biologists CASE STUDY #3 Carbohydrates in Organic Chemistry In his organic chemistry course Jerry Mohrig integrates material on carbohydrates by having a capstone to his yearlong course. This capstone is called “Why do we get the flu every year?” It treats the basic chemistry of carbohydrates, proteins, and molecular recognition in a modern context, and it provides a story line that runs through the whole course. Information on glycobiology, molecular recognition, and cell-cell interactions is integrated throughout both semesters as a story line. Originally, he tried to use multiple isolated biological examples, but the relevance did not connect for the students. This example about the flu was chosen instead of details on how egg and sperm bind because more is known about the viral system. Although the basics of carbohydrate and amino acid chemistry are taught as part of most second-term organic chemistry courses, many students would be hard pressed to recognize or appreciate the great importance that carbohydrates have in biochemical recognition. The structures of oligosaccharides and their binding to protein recognition sites are straightforward enough to teach in the second-semester organic course. The flu module focuses on the recognition by the influenza virus of two crucial proteins with sialic acid units attached to cell surfaces. The viral hemagglutinin binds to neuraminic acid residues on the surface of the respiratory tract and the viral neuraminidase cleaves these residues. The interactions allow viral invasion of cells, and understanding these interac Some other ideas for modules to enrich the teaching of biology include the following: What determines whether an epidemic waxes or wanes? In a simple model, a population consists of susceptibles who can contract a disease, infectives who can transmit it, and removals who have had the disease and are neither susceptible nor infective. Given an infection rate, a removal rate, and initial sizes of the three groups, one can calculate how the population evolves. Mathematical treatments, illuminated by examples of plague, flu, and AIDS epidemics, are given by Murray (1993, pp. 610-696) and by Hoppensteadt and Peskin (1992, pp. 67-81).

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Bio 2010: Transforming Undergraduate Education for Future Research Biologists tions has also led to the development of neuraminidase inhalators that serve as therapeutic agents. The module ends with the neuraminidase inhibitors that are available to fight flu symptoms. One question on the final exam is an x-ray picture of a monosaccharide bound to a protein recognition site. The students are asked to describe the noncovalent interactions that are responsible for the binding. Dr. Mohrig believes that it is not enough to teach future biologists the organic chemistry of small molecules if they never see how this knowledge can be applied to biological molecules of consequence. It is important that students see that they can make sense of how to relate complex organic molecules to biological questions and develop the confidence to do so. Since he has been teaching the flu module, he has seen a significant increase in the interest in organic chemistry of the many biology students in the course. He also designed a carry-forward questionnaire on the value of the module to students who subsequently enroll in an immunology course. He asked students one or two years after the flu example to answer a question on immunological aspects of influenza. Student opinion on the value of the module increased if they later took a biology course in which the professor discussed the chemistry of carbohydrates. The biology faculty had to communicate to their students that chemistry was essential to fully understand the biological system. For more information: http://mc2.cchem.berkeley.edu/modules/flu/ What accounts for the all-or-none character of nerve action potentials? The classic Hodgin-Huxley model of action potentials is presented by Hille (2001, pp. 45-60). A module on the Hodgkin-Huxley model of nerve action potentials would deepen students’ understanding of how information is transmitted over long distances in the nervous system. Students can explore the following questions by carrying out interactive computer simulations: What gives rise to the all-or-none nature of action potentials? What accounts for the threshold in generating action potentials? What factors govern their frequency? The molecular properties of two kinds of channels account for this fundamental signaling process. The interplay of cooperativity, positive feedback, deactivation, and delayed reactivation can

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Bio 2010: Transforming Undergraduate Education for Future Research Biologists be vividly demonstrated by interactive simulations. For more information: http://pb010.anes.ucla.edu/nervelt/nervelt.html How can chance events markedly alter gene frequencies in small populations? Consider an allele initially present at a frequency of 0.5. As was shown by Kimura, the allele will, on average, become fixed or lost after 2.77 N generations, where N is the population size. Genetic drift is akin to diffusion, as discussed by Hartl and Clark (1997, pp. 267-313). How do leopards get their spots and zebras get their stripes? In 1952, Alan Turing published a seminal paper showing that an initially homogeneous distribution of chemicals can give rise to heterogeneous spatial patterns by reaction and diffusion. Animal coat patterns and other applications of reaction diffusion mechanisms are discussed by Murray (1993, pp. 434-480) How can topology and knot theory help us understand the packing of DNA in the cell nucleus? DNA can be visualized as a complicated knot that must be unknotted by enzymes in order for replication or transcription to occur. A mathematical knot is a closed curve. This can be visualized as a closed loop of string. If the string had a knot in it, it would be impossible to unknot without slicing through the loop. This analogy can help students understand the actions of topoisomerase enzymes on DNA. For more information: http://www.tiem.utk.edu/~harrell/webmodules/DNAknot.html Exploring the Nanoworld. Vivid explorations of many facets of materials at the nanoscale can be made at the Exploring the Nanoworld Web site. LEGOÒ bricks are used to build models demonstrating pertinent physical and chemical principles. This site also demonstrates how a laser pointer and an optical transform slide can be used to show how Watson and Crick deduced that DNA is double helical. For more information: http://mrsec.wisc.edu/edetc/ INTERDISCIPLINARY LECTURE AND SEMINAR COURSES In addition to modules, interdisciplinary lecture and seminar courses can give students a better and more realistic picture of how connections between different areas of science are made in research. Because research is becoming increasingly interdisciplinary, such courses should be made available to students beginning in their first year. There are several possible formats for courses that extensively combine the teaching of physical sciences, mathematics, and/or engineering with the teaching of life sciences. One example is presented in Case Study #4. Such courses could be pre-

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Bio 2010: Transforming Undergraduate Education for Future Research Biologists sented at various times during undergraduate study. The courses could be distinguished by purpose and the number of prerequisites. At one end of the spectrum could be a truly interdisciplinary course used as an introductory first-year seminar with relatively few details and no prerequisites. It could serve as a “whet the appetite” course to introduce students to many disciplines in their first year, and to hold the interest of first-year students who are taking disciplinary prerequisites prior to starting courses in biological sciences. This course could have a single theme; an example of a first-year seminar on plagues that draws on different disciplines is described in Case Study #11. An alternative format could feature a series of faculty or guest speakers who present case studies on a wide range of topics exemplified by genomics, environmental science, infectious disease epidemiology, medical statistics, computational biology, mathematical biology, toxicology, and risk assessment. Such a course would serve a dual role: biology students would see that mathematics and computation play an important role in their future work, and mathematics and computer science students would get a taste of how quantitative methods (statistics, applied mathematics, computer science) can be fruitfully applied in biology and medicine. At the other end of the spectrum could be a capstone course for seniors with substantial educational experience in multiple disciplines. With extensive prerequisites in these disciplines, an interdisciplinary course organized around a topic could be presented at an advanced level. On the Mechanics of Organisms, an upper-level course at the University of California at Berkeley, effectively brings biology and engineering together (Case Study #5). Engineering principles pertinent to particular biological processes are presented first, followed by their place in biology. This is only one example, and many other upper-level courses can be imagined that would vividly illustrate the interplay of biology with the physical and mathematical sciences and engineering, such as Three-dimensional Structure Determination (x-ray diffraction, nuclear magnetic resonance spectroscopy), Sensory Signaling Systems (vision, smell, taste, hearing, and touch), Biological Imaging (fluorescence microscopy, confocal imaging, evanescent wave microscopy, two-photon imaging), and Medical Imaging (functional magnetic resonance imaging, positron emission tomography, ultrasound). At intermediate levels, a variety of course plans could incorporate material from the physical sciences, and the mathematical concepts and skills that subtend these disciplines, into biological courses. Possible examples are a course in quantitative physiology (blood circulation, gas exchange in the

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Bio 2010: Transforming Undergraduate Education for Future Research Biologists CASE STUDY #4 Quantitative Education for Biologists University of Tennessee This course sequence provides an introduction to a variety of mathematical topics of use in analyzing problems arising in the biological sciences. It is designed for students in biology, agriculture, forestry, wildlife, and premedicine and other prehealth professions. The general aim of the sequence is to show how mathematical and analytical tools may be used to explore and explain a wide variety of biological phenomena that are not easily understood with verbal reasoning alone. Prerequisites are two years of high school algebra, one year of geometry, and half a year of trigonometry. The goals of the course are to develop the students’ ability to quantitatively analyze problems arising in their own work in biology, to illustrate the great utility of mathematical models to provide answers to key biological problems, and to provide experience using computer software to analyze data and investigate mathematical models. This is accomplished by encouraging hypothesis formulation and testing and the investigation of real-world biological problems through the use of data. Another goal is to reduce rote memorization of mathematical formulae and rules through the use of software including Matlab and MicroCalc. Students can be encouraged to investigate biological areas of particular interest to them using a variety of quantitative software from a diversity of biological specialties. In many respects, this course is more difficult than the university’s science/engineering calculus sequence (Math 141-142) since it covers a wider variety of mathematical topics, is coupled to real data, and involves the use of the computer. Although the course is challenging, it has been designed specifically for life science students, and includes many more biological examples than other mathematics courses. It, therefore, introduces the students to quantitative concepts not covered in these other math courses that they should find useful in their biology courses. The main text is Mathematics for the Biosciences by Michael Cullen, which is extensively supplemented by material provided in class. Each class session begins with the students generating one or more hypotheses regarding a biological or mathematical topic germane to that day’s material. For example, students go outdoors to collect leaf size data. They are then asked: Are leaf width and length related? Is the relationship the same for all tree species? What affects leaf sizes? Why do some trees have larger leaves

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Bio 2010: Transforming Undergraduate Education for Future Research Biologists than others? Each of these questions could generate many hypotheses, and students can then go on to use Matlab to analyze the data sets they collect in order to evaluate the hypotheses. Some hypotheses do not relate to a biological area and are based on mathematics alone. For example, after linear regression is introduced, students are asked whether this regression can be reasonably used to determine the y-value for an x-value for which there are no data. This leads naturally to a discussion of interpolation and extrapolation. As each topic is introduced, the instructor includes a brief description of how it relates to biology. This is often done by having a background biological example used for each main mathematical topic being covered, which can be referred to regularly as the math is developed. For example, in covering matrices, the material can be introduced with this example: “Suppose you are a land manager in the U.S. West, and you have satellite images of the land you manage taken every year for several years. The images clearly show whether a point on the image (actually a 500 m x 500 m plot of land) is bare soil, grassland, or shrubland. How can you use these to help you manage the system?” From this, the students develop the key notion of a transition matrix; the professor can then go on to matrix multiplication, and eigenvalues and eigenvectors for describing dynamics of the landscape and the long-term fraction in bare soil, grass, and shrubs. Attempts are made to include real, rather than fabricated, data in class demonstrations, project assignments, and exams. For example, data of monthly CO2 concentrations in the Northern Hemisphere can be used to introduce semi-log regression, and allometry data can be used for studying log-log regressions. Students are encouraged to collect their own data for appropriate portions of the course, particularly the descriptive statistics section. Scientific journal articles that use the math under study are also provided. Syllabus Math 151: Descriptive statistics—analysis of tabular data, means, variances, histograms, linear regression Exponentials and logarithms, non-linear scalings, allometry Matrix algebra—addition, subtraction, multiplication, inverses, matrix models in population biology, eigenvalues, eigenvectors, Markov chains, ecological succession Discrete probability—population genetics, behavioral sequence analysis

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Bio 2010: Transforming Undergraduate Education for Future Research Biologists Sequences and difference equations—introduction to sequences and limit concept Syllabus Math 152: Difference equations, linear and nonlinear examples, equilibrium, stability and homeostasis, logistic models, introduction to limits Limits of functions and continuity Derivatives and curve sketching Exponential and logarithms Antiderivatives and integrals Trigonometric functions Differential equations and modeling Students are graded through weekly 10-minute quizzes, assignments based on the use of the computer to analyze particular sets of data or problems (some done in groups), three in-class exams, and a comprehensive final exam. The exams are generally not computer-based, focusing rather on the key concepts and techniques discussed in the course. Extra-credit opportunities require students to evaluate one of a wide variety of software programs available involving some area of biology. This requires becoming very familiar with the program, and writing a formal review of the software, in the same format as might appear in a scientific journal. For more information: http://www.tiem.utk.edu/~gross/quant.lifesci.html lung, control of cell volume, electrical activity of neurons, renal countercurrent mechanism, muscle mechanics) or a course in population biology (epidemic and endemic disease, ecological dynamics, population genetics, evolution). Such interdisciplinary courses could provide excellent opportunities to learn important mathematical skills, such as deriving equations, using computer simulations, and working in teams. Many topics could be taught at an elementary or more advanced level, depending on the ways in which the mathematics is treated. For example, ordinary differential equations can be made tractable via Euler’s method without the need for a for-

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Bio 2010: Transforming Undergraduate Education for Future Research Biologists CASE STUDY #5 Seminar on the Mechanics of Organisms University of California at Berkeley This upper-level interdisciplinary course brings biology and engineering together. It teaches functional morphology in terms of mechanical design principles. The basics of fluid and solid mechanics are covered along with examples of their biological implications, stressing the dependence of mechanical behavior on the structure of molecules, tissues, structural elements, whole organisms, and habitats. Organisms are introduced as “Living Machines” and their abilities to fly, swim, parachute, glide, walk, run, buckle, twist, and stretch are evaluated in the context of physics and engineering principles. Students learn about the different types of fluid flow (laminar, tubular, large and small scale), the fluid dynamic forces of drag and lift, and how organisms live on wave-swept shores. They consider other biological issues such as life at low Reynolds number (the sticky world of small organisms), benthic boundary layers and flow microhabitats, and fluid dynamics of filters including suspension feeding. They evaluate stress distribution in structures, including tension, compression, shear, beam theory, buckling, twisting, kinking, and strain. They learn about the biomechanics of bone, muscle, and cells, and the idea of molecular motors. They consider issues of size and scaling of organisms, how mechanical properties change during the life of an organism, the physics of shape changes in morphogenesis, viscoelasticity, resilience and plasticity, as well as fracture and the evolution of safety features. For more information: http://ib.berkeley.edu/about.html mal background in differential equations. Euler’s method provides a simplified method for obtaining an approximate numerical solution to a differential equation. Simulations involving random numbers can be done with only an intuitive introduction to probability and the use of a random number generator. A computer language such as Matlab makes it easy to write programs that implement Euler’s method (and other similar methods), and also provides easy access to graphical output, including animations.

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Bio 2010: Transforming Undergraduate Education for Future Research Biologists TEACHING MATERIALS Making biology education more interdisciplinary and representative of how biological research is actually conducted is critically dependent on the availability of new and innovative teaching materials. Teaching materials are not solely textbooks; they also include computer-based materials, instructor guides, modules, and case studies. Textbooks that bridge different disciplines and provide a coherent framework for study and learning can play a vital role in achieving the objective of more interdisciplinary and relevant biology education. Many high-quality biology textbooks are available, but publishers could do more. For example, it is especially rare to find detailed mention of physical science or mathematical principles in introductory biology texts. The committee is not aware of any comparative analysis of biology textbooks for the college level; however, two different groups, the American Association for the Advancement of Science and the American Institute of Biological Sciences, have evaluated biology textbooks used in high schools. Both groups conclude that the books provide massive quantities of information, which may result in sacrificing depth and conceptual understanding as teachers attempt to cover the material (http://www.project2061.org/newsinfo/research/textbook/hsbio/about.htm) Some of the suggestions made in these reports may prove useful to those writing or revising college textbooks. Representative texts that emphasize interdisciplinary aspects of science are given in the box at the end of the chapter.1 Although the list is not comprehensive, many more are needed. In selecting these titles, the committee looked for books that drew connections between multiple scientific disciplines. Although not all the books listed reflect recent scientific advances, they do illustrate exemplary approaches to their topics. Educational institutions, professional societies, private and public foundations, and publishers should work together to ensure that interdisciplinary materials are produced. The National Institute for Science Education’s College Level One team at the University of Wisconsin-Madison has been active in developing teaching materials as well as promoting and conducting research on learning, teaching, and assessment. Their five-year funding cycle from NSF has ended, but it is hoped that this will not be the end of the innovative work they have done. 1   These textbooks are listed for illustrative purposes, and this list does not constitute an endorsement of their content by the National Research Council.

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Bio 2010: Transforming Undergraduate Education for Future Research Biologists Interdisciplinary Textbooks: Some Examples Berg, H.C., 1993. Random Walks in Biology. Princeton University Press. Written to sharpen the intuition of biologists about the statistics of molecules. The book focuses on diffusion. Topics range from the one-dimensional random walk to the motile behavior of bacteria . Cavalli-Sforza, L.L., 2000. Genes, Peoples, and Languages. North Point Press. A view of the last hundred thousand years of human evolution based on combining information from three disciplines—genetics, archaeology, and linguistics. Denny, M.W., 1993. Air and Water: The Biology and Physics of Life’s Media. Princeton University Press. Presentation of the basic principles of physics as they apply to air and water, followed by many interesting biological illustrations (e.g., Why are eggs so fragile?). Edelstein-Keshet, L., 1988. Mathematical Models in Biology. Birkhauser. Summary of modern mathematical methods currently used in modeling, and examples of applications of mathematics to real-life problems. Hoppensteadt, F.C. and Peskin, C.S., 1992. Mathematics in Medicine and the Life Sciences. Springer. Presentation of topics drawn mainly from population biology (e.g., demographics, population biology, epidemics) and physiology (e.g., blood flow, gas exchange, renal countercurrent mechanism, biological clocks and neural control) that have benefited from mathematical modeling and analysis. Howard, J., 2001. Mechanics of Motor Proteins and the Cytoskeleton. Sinauer. Presentation of physical principles (mechanical, thermal, and chemical forces) underlying biomolecular mechanics, followed by a detailed exposition of the structure, mechanics, and force-generation mechanisms of the cytoskeleton and motor proteins. Murray, J.D., 1993. Mathematical Biology (2nd ed.). Springer. Presentation of mathematical models that provide insight into biological processes. Topics include population biology, biological oscillators and switches, pattern formation, biological waves, and infectious disease dynamics. Taubes, C.H., 2001. Modeling Differential Equations in Biology. Prentice Hall. Based on a differential equation course at Harvard designed for life science students who have had only the basics of calculus. In each chapter, mathematical principles pertinent to a biological problem are developed and applied. Each chap-

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Bio 2010: Transforming Undergraduate Education for Future Research Biologists ter also contains several biological research articles illustrating the power of differential equations and analysis in gaining a deeper understanding of biological questions. These papers deal with topics such as Scope of the AIDS Epidemic in the United States, Experimentally Induced Transitions in the Dynamic Behavior of Insect Populations, and Thresholds in Development. Vogel, S., 1998. Cats’ Paws and Catapults: Mechanical Worlds of Nature and People. Norton. An introduction to biomechanics. Compares nature’s solutions with those arising from human technology. It should be noted here that preparation of such modules is no small task and will require a major commitment of time and effort. The collaborating faculty do not all need to teach at the same institution, especially if financial support is provided by foundations, agencies, or societies. Because of the huge commitment, it is efficient for two or more faculty to collaborate in development, and for the results to be widely disseminated. This is only possible if they receive adequate support from their own institution and other organizations that fund biology education. Issues related to the creation of additional teaching materials and the design of new approaches are further discussed in Chapter 6: Implementation.