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WHAT IS DIMACS BioMath Connection (BMC)?
BMC is a pioneering project linking biology and mathematics in the high schools. It provides an opportunity for high school teachers, writers, researchers, and others to get in on the ground floor of developing innovative classroom materials. The materials will consist of modules that can be flexibly adapted for use in a variety of courses at a variety of grade levels in both biology and mathematics. The project is run by DIMACS at Rutgers University in collaboration with the Consortium for Mathematics and its Applications (COMAP) and Colorado State University (CSU). DIMACS has become recognized as a world leader in research and education in bioinformatics, computational biology, and mathematical epidemiology; COMAP has become the recognized leader in the production of cross-disciplinary educational materials; CSU faculty have become internationally known for their evaluation of educational programs.
Specifics of the Program Increasingly, many biological phenomena are being viewed as involving the processing of information. Modern computer and information science have played an important role in such major biological accomplishments as sequencing the human genome, and are of fundamental importance in the rapidly-evolving concept of "digital biology." On the other hand, biological ideas can inspire new concepts and methods in information science. More and more, undergraduate and graduate students are being exposed to this interplay between the mathematical and biological sciences.
High schools, however, have done little to develop interconnections between the biological and mathematical sciences. Introducing high school students to these interconnections will enhance the study of both disciplines. Students interested in biology will realize the importance of understanding modern mathematics and computer science. New horizons will be opened for those who find mathematics interesting, but wonder how it might be useful. Rapidly developing opportunities for further study will be revealed and new career opportunities will be suggested. To achieve these ends, it is critical to have available for teachers to use in their classes curricular materials that highlight the interconnections between the mathematical and biological sciences. That is the principal goal of the BMC program. Moreover, we need to train teachers to use these new materials, and this will involve exposing them to the interface between the disciplines. Teachers from different disciplines need to learn each others' language, open lines of communication, and develop new approaches for introducing cross-disciplinary topics. Bioinformatics and computational biology (CompBio), constitute one of the three major areas of emphasis in BMC. Such topics as global and local string alignment algorithms; the BLAST algorithm; FAST algorithms; PAM matrices; phylogenetic trees and tree parsimony; phylogenetic tree reconstruction and phylogenetic footprinting; and genome rearrangement use mathematical methods that are easily accessible to high school students and do not require sophisticated mathematical background. The basic mathematics required involves graph theory, counting principles, the basics of probability, and the notions of string, substring, and superstring from computer science. The biological background for the topics involves the basics of genomes, sequences, genes, introns and exons, the genetic code, transcription, and translation, and is readily explained.
A second area of emphasis in BMC will be mathematical epidemiology (EPI). Epidemiological models of infectious diseases go back to Bernoulli's mathematical analysis of smallpox in 1760 and since then mathematical models have been developed for key pathogens such as influenza, malaria, gonorrhea, tuberculosis, and HIV. Mathematical modeling provides insights into drug-resistance, rate of spread of infection, and effects of treatment and vaccination, and is being used today to help us deal with emerging disease threats such as SARS or pandemic flu. While much of traditional mathematical epidemiology uses more advanced mathematical tools such as differential equations, a growing body of methods that use tools accessible to high school students is being developed. These include graph-theoretical models of spread of disease and combinatorial group testing to test for AIDS and other sexually-transmitted diseases. The biological background required to understand these topics is minimal and requires only some understanding of hosts, pathogens, incubation periods, etc.
In ecology and population biology (ECO), there is also a long history of mathematical methods that study populations. Indeed, the famous Lotka-Volterra models for growths of interacting populations are well known to most students of differential equations. Matrix methods of population biology are readily accessible to high school audiences and we will concentrate our materials on appropriate topics in this area of ecology. The Fibonacci numbers, a fundamental topic in combinatorics, underlie a whole gamut of ecological topics, ranging from understanding population growth to modeling the whorls on a pineapple and the arrangement of leaves around a stem. These topics, too, are appropriate for high school audiences in both the biological and mathematical sciences. So too are simple optimization models of the movement of populations of social insects such as bees or termites or ants. The mathematics needed for the ECO topics involves matrices, counting, properties of functions, and in some cases elementary calculus topics involving rate of change, max-min problems, and exponentials. Simulation programs can be helpful here, making these ECO topics even more accessible to students. The report Bio2010 recognizes that there is little room in the curriculum and recommends developing modules of self-contained material that could be inserted into existing courses in biology or mathematics. The report suggests organizing summer programs around preparing teaching modules for mathematics and biology courses. These recommendations have led us to make such modules a central part of BMC and to concentrate on smaller units and lessons that can be tested and implemented with little change in the curriculum.
It is our goal in developing modules to take advantage of the unique opportunities for interactive learning that are provided by the web. Web-based materials provide opportunities for quick feedback, greatly extend the number of teachers and students who can access a module, allow modular material to be used outside of formal courses, and allow us to develop materials that are more interactive.
The modules we produce are self-contained text and problem material that can be used for class meetings in high school mathematics or biology courses or both, individually or team taught. They cover up to 10 or more class meetings of 40 minutes each. However, we are producing a small number of modules (one each in CompBio, EPI, and ECO) that cover just one lesson that can be inserted into an already-crowded curriculum. Our feeling is that it is vitally important to start exposing students (and teachers) to the bio-math interface, and so even such a small "foot in the door" is important. Each module starts with a preface that explains the general topic and its interest; the mathematics required (e.g., algebraic operations, matrices, deductive and inductive reasoning, etc.); the biology required (e.g., elementary genetics, DNA, RNA, etc.); whether calculators or computers are necessary and/or desirable; and what is provided in the module (e.g., assessments, transparencies, etc.). The next section, "How to Use the Module," discusses grade levels appropriate for the material, level of student background, format of module, references, expected number of days and amount of material per day, where to implement it within existing mathematics or biology material, relevant mathematics and science standards, etc. The main body of the module is based on lessons assumed to take approxi-mately 35 minutes plus questions from the preceeding lesson. It has an introduction, giving the history of the problem/area, application interests, basic definitions needed and preparation reading required. The lessons include sections that set the stage, motivation (e.g., with a short activity or game), guidance for the teacher as a sidebar, questions and extensions for advanced students, and a homework assignment. The emphasis is on setting up models and working through them. The module closes with extensions, generalizations, wrap-up assignments, references and a glossary. Teacher guides are also available.
Go Back to Specifics of the Program A COMAP Module Development team (MD team) has responsibility for preparing modules. Each MD team consists of high school mathematics and biology teachers, mathematics and biology content experts, and a curriculum writing expert, ideally included among the first four. People previously involved with COMAP and DIMACS programs form the nucleus of these teams, with others added as needed. In the summer, we produce initial drafts of new modules in a 1-week writers workshop on one of the scientific topics. All MD teams will meet again several times during the academic year. They get input from pilot testers and from a Project Editorial Board, prepare the modules for careful field testing, and prepare the final products. Modules are piloted by teachers who have gone through prior DIMACS programs involving CompBio, EPI, and ECO and others who express interest (see How to Participate). There is no particular training and the pilot testers depend upon teacher user instructions contained in the modules. The goal of the Field Tester Workshops is to prepare teachers to use, and more specifically, to field test modules. These workshops are interdisciplinary and emphasize use of the modules in mathematics and in biology classes and ways in which teachers from different disciplines might collaborate/coordinate in the implementation of the materials. We evaluate the process, both during the workshops, and during and after the field testing, in order to gain information that will help us prepare documentation as to how teachers can be trained to use the modular materials we develop. In the process, we seek to gain an understanding of which of the modules can be used with only written teacher materials as background (without formal training).
Each Field Tester Workshop is organized around a main theme, Computational Biology (2007), Epidemiology (2008), or Ecology (2009). We develop programs that give teachers a more general introduction to the math-bio connection in the area specific to that year and the materials in the specific modules to be field-tested. The program is aimed at both biology and mathematics teachers. The participants are invited, to attend, but others may apply as well. Preference is given to pairs of teachers from the same school, a biological sciences and mathematical sciences teacher. Teachers from the same school greatly enhances the opportunities for teachers to collaborate in field testing the materials. We seek a diversity of participants, representing school districts with different learning styles and representing different population groups. This guarantees that the materials can be used in a variety of settings.
Each workshop features a principal instructor, an expert on the topic and on classroom implementation. The emphasis is on hands-on activities, problem-solving, and discovery experiences: working with data, making conjectures, extrapolating from special cases. A computer lab session introduces participants to relevant software, for example Biology Student Workbench. "Homework" sessions, during which paired teachers will be encouraged to assist each other, is important in reinforcing basic concepts.
The workshop is also enhanced by the participation of lead teachers. These are high school teachers, veterans of other programs at DIMACS, who act as mentors/guides for the teachers, teach the tutorials, assist with homework and in the computer lab, advise teachers in need of extra attention, and run classroom implementation sessions in connection with specific modules, including demonstrations of "model" activities.
Alignment with Curriculum Standard
We will ensure that materials developed in BMC connect to state and national content standards in mathematics and science with discipline-specific material. Clear evidence is emerging that implementation of standards-based cross-disciplinary curricula improves student achievement in problem solving, conceptual understanding and computational skills while mitigating performance differences between non-minority and underrepresented minorities. The biology content will incorporate National Science Education Standards, Benchmarks for Science Literacy: Project 2061, and Science for All Americans; mathematics content will be based on NCTM Principles and Standards for School Mathematics and Professional Standards for Teaching Mathematics.
The external evaluation of BMC will focus on the quality, integrity, efficiency, timeliness, and utility of the modules from a formative evaluation perspective. We will also be evaluating the pilot testing of the modules, the field testers workshops, the teacher guides, and the use of project materials in instructional settings - again from a formative evaluation perspective. The instruments to be used to assess these issues have been used extensively in the past by the project evaluators and are ideally suited for this project. Finally, we will be using a pretest-posttest design to evaluate the impact of the project on teachers' students who implement the modules during the field-test process.
The completed modules will be made available in both print and electronic formats, to high school mathematics and biology communities, free in years 1-3 and at cost in years 4 and 5. We will develop materials aimed at parents, explaining the importance of the bio-math interface, and usable by school districts to encourage widespread implementation of our materials. We plan to work with potential textbook writers and to involve curriculum developers in our project. We
recognize that there is no one set of modules that can summarize all important interfaces between mathematics and biology. It is a crucial aspect of this project that we set the stage for continued production and dissemination of new modular material. Our plans call for the founding at COMAP of a Journal to contain new teaching modules and articles about the interaction between mathematics and biology.
If you would like to ask questions specifically about the content of the program, please e-mail Christine Spassione for a list of prior DIMACS Education Program Participants who are willing to answer questions.
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