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Evaluating Mathematical Models
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Purpose
To use the Internet to evaluate a variety of mathematical models.
Context
Because mathematics plays such a central role in modern culture, scientifically literate students must develop a basic understanding of the nature of mathematics. It is important for students to realize that mathematics, like science and technology, incorporates both finding answers to fundamental questions and solving practical problems. The ideas in this lesson are also related to the following benchmarks: - 8E Information Processing: Computer Modeling
- 11B Common Themes: Models
Planning Ahead
Materials:
The website provides all the details for this activity.
Motivation
Run the WebBeePop Model on the GEARS website. This is a simulation model to study how honeybee population dynamics depends on the weather. Run the model for each of the five cities using the same starting population. Then, allow the students, working in groups, to explore different starting population sizes for the five cities. At this point, students should not move on to the WebBeePop: Death and Destruction model. This can be explored later. After students have had an opportunity to explore the effects of different starting population sizes, have students discuss what they have learned from the models and pose possible reasons for the differences in the growth of the bee populations among the five cities.
Development
Students will study different mathematical models on the Internet. For each model, they will write a paragraph in response to the following questions: - A) What is the system being modeled? Describe it and its parts.
- B) What is the behavior or activity being simulated?
- C) What are the instructions, data, and possible consequences of the model?
- D) How would you evaluate the model's usefulness in a real-life application. What kinds of decisions could it help you make?
Divide the class into groups of three or four and assign one of the mathematical models on the Measure for Measure website.
Suggested models include the following:
Assessment
Have the groups report on the computer models that they investigated. Students should try to estimate how long it would take to perform some of the calculations and simulations without a computer.
Extensions
WebBeePop: Death and Destruction This program continues the simulation of bee populations on the GEARS website. In this simulation, students can compare what happens when. (Note: this model can only be run from the screen displaying the results of the preliminary settings.) This simulation examines the effects of critical or catastrophic events on bee populations.
Students can explore The Stock Market Game, in which K-12 students discover the risks and rewards involved in decision-making, the sources and uses of capital, and other related economic concepts. Over a 10-week period, participants invest a hypothetical $100,000 in Nasdaq, Amex, and NYSE-listed common stocks. They research stocks, study how the financial markets work, choose their portfolios, manage budgets, follow companies in the news, and make decisions on whether to buy, sell, or hold. They can also compare their portfolios’ performance to peers on a weekly basis.
Created :09/06/2000
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