Description: A one semester interdisciplinary course integrating mathematics and science investigations in a mathematical modeling setting. Students, working in cooperative groups, investigate real world science problems, formulate model solutions to the problems, and then develop methodology for presenting their solutions in a classroom setting using various technological aids. The course is team-taught by faculty from the mathematics and science departments.
Audience: The course can serve as a lower level math or science elective and can be particularly useful as a math/science enrichment course for students intending to teach at the elementary or secondary school levels.
Prerequisites: Two semesters of college mathematics including college algebra and two semesters of lab science.
Text: Berry & Houston. Mathematical Modeling. London: Edward Arnold, 1995.
- Involve students in current real world problems and issues in math and science
- Expose students to math and science processes through investigative experiences
- Engage students in active critical inquiry and evaluation of information and data
- Show the interconnectedness between science and math disciplines
- Have students learn to solve problems in cooperative group settings
- Develop the ability to effectively communicate results of investigations
- Involve students in the use of current technology to aid in problem solving
- Teach and reinforce basic math and science principles and skills
- Have students to understand the importance of ethics in math and science
Course Objectives: Each student will
- Learn the basic principles associated with developing math models
- Develop model solutions to at least two real world science projects
- Participate in the effective written and oral presentation of two projects
- Integrate knowledge and skills across disciplines in cooperative problem solving
- Demonstrate basic understanding of all projects presented
- Use technological aids (calculator, computer, projector) in project investigations
- Show the effectiveness of the multi-disciplinary approach in real world problem solving
- Demonstrate knowledge of core concepts foundational to math and science inquiry
- Show how ethics concerns are relevant to issues contained in the project modules
Course Methodology and Grading:
The course begins with a brief introduction to math modeling and ethics considerations presented in a full class setting. Students then subdivide into small groups. Each group works on parts of each of the investigatory modules outlined below and selects one of the modules for a semester project. Members of the teaching team introduce each module along with guides and suggestions. After the modules have been introduced, students work together in the small groups and develop model solutions which are typed on a word processor, submitted in term paper or lab report format, and presented orally to the entire class. These solutions should include expositional, tabular, graphical, as well as symbolic elements developed in a computer-based setting. Faculty team members provide leadership and direction in the small groups. Each student is expected to demonstrate knowledge of the basic math and science principles underlying each of the modules.
Course grading is as follows:
Development and Presentation of Module Projects 50%
Cooperative Group Participation 25%
Two Exams on Modeling Principles & Math/Science Content 25%
TOTAL 100%
The course uses written module outlines developed under a grant from the Department of Education (Fund For The Improvement of Postsecondary Education) by a faculty curriculum development team representing the math and science disciplines. Each of the modules contains background material and additional text references.
I. Introduction
1. What is Math Modeling? (Chapters 1 and 2 of Berry and Houston)
- Definition and classification of Models
- Uses and Limits of Models
- Illustrative Examples and Tutorials
2. Ethical Considerations in the Sciences (Fuller, DeLoatch)
- Ethics definitions applied to science professions
- Ethical theories: Relativism, Utilitarianism, Deontological
- Standards of behavior, professional standards, codes of ethics
- Applications to selected case scenarios/Internet Search (Lab Assignment)
II. Investigatory Modules
1. The Quality of Water (McNeil, Green)
- Causes and remedies of water pollution (Chesapeake Bay Foundation Rep)
- Chemistry of water pollution and cleansing
- Search for pollutants in water samples collected in the area
- Water treatment (Visit to Water Treatment Plant)
2. Epidemics and the Spread of Diseases (Smith, Fuller, McNeil)
- Epidemic Models (SIR)
- Virus Hunters: Ebola Example
- HIV/AIDS and Viral Loading
- Site visit to Epedemiolgy Lab
3. Heat Loss and Gain (Ferguson and McNeil)
- Basics of Heat Flow
- Newton's Law of Cooling Investigation
- Modeling the insulation of a house
- A strategy for cost effectiveness
4. Genetics (Smith, Fuller, DeLoatch, McNeil)
- Genetics basics: alleles, genotypes, Hardy-Weinberg Principle, etc.
- Genetic diseases; blood types
- Human Genome Project (Video Tape)
- Ethics and genetic determination
- Site visit to Genetics Lab
III. Final Ethics Considerations (DeLoatch, Fuller)
- Examine fundamental ethics questions across the disciplines
- Discuss specific ethics concerns associated with each module project
I.D. Huntley and J.G. James, ed. Mathematical Modeling: A source Book of Case
Studies. New York: Oxford University Press, 1992.
Sheldon P. Gordon, et. al. Functioning in the Real World: A Precalculus Experience. Reading: Addison-Wesley, 1997.
James Trefil and Robert Hazen. The Sciences: An Integrated Approach. New York: John Wiley & Sons, Inc., 1995.
R.N. Jones and G.K. Richards. Practical Genetics. New York: John Wiley & Sons, 1990.
M.A. Tribe, I. Tallan, and M.R. Eraut. Basic Biology Course: Unit 5 Aspects of Heredity, Book 12 Case Studies in Genetics. New York: Cambridge University Press, 1978.
L.L. Cavilli-Sforza. Elements of Human Genetics. Reading: W.A. Benjamin, Inc., 1977.
Necia Grant Cooper, ed. The Human Genome Project: Deciphering the Blueprint of Humanity. Mill Valley, CA: University Science Books, 1994.
Teresa and Gerald Audesirk. Biology: Life on Earth.Upper Saddle River, NJ: Prentice Hall,
4th Ed., 1996.
Robert Weaver and Philip Hedrick. Genetics. Dubuque, IA: Wm. C. Brown, 2nd Ed., 1992.