Debriefing Presentations

We worked together to produce a model of an orchard for a senior graduate level biology course. Our model incorporates a number of the factors that can affect marketable yield, including percent of optimal rainfall, temperature and soil nutrients, percent of diseased trees, and whether pesticides were sprayed. We have designed two different levels to this model: One to get the students to think about how things can be represented mathematically, and one for the students to build upon by researching the scientific literature and designing experiments.

We have investigated several modeling "toolboxes" and have built several models to take back with us to use in our classes. We envision using the computational modeling approach in many of our courses, including calculus, differential equations and mathematical modeling.

We have developed a model of a bacterial growth curve that will be used in a community college setting, in general biology, human anatomy and physiology, and microbiology courses. While it is still being developed, it will eventually allow students to specify a particular bacterium, set the generation time (doubling time), produce a graph of the growth curve for that organism, change organisms, and compare the two curves. If the model were enlarged to include the effects of varying amounts of antibiotics, or other factors affecting the bacterial growth, it could be used as versatile tool in other courses as well. We hope that this model will become a part of a lab in which students grow bacteria in nutrient broth, measure the amount of bacteria using a spectrophotometer, enter this information into the model, and determine generation times for different species experimentally. Other lab applications that might make use of this model include: measuring the effect of various antibodies on bacterial cultures, effects of other environmental resistance such as competition, and projections on the carrying capacity of different environments.

Hugh Sanders, Mathematics and Computer Science, Georgia College and State University:

I have learned about the limitations that computers have with regards to having only a finite set of numbers, and the problems that can occur due to the accumulation of round-off errors. I learned how to use modeling in classes and gained experience in modeling with various software, concentrating on working with modeling in a probability and statistics course. I also plan to use modeling in other classes that I will be teaching, such as calculus and mathematics education courses.

I have looked at two models during this workshop. Using Stella for the first time, I was able to create a visual model of a rocket that could be used to allow students to investigate projectile motion. A number of factors, such as initial height and velocity, wind resistance, the launch angle and the use of a parachute could be varied and effects of the changes could be seen on both graphs and tables. In a classroom setting, this allows students to investigate and explore the important "what if" questions interactively. I also looked at queues. Queues are important data structures in computer science and are a difficult concept for students to understand and program abstractly. There are several introductory animations available on the web to illustrate queues, and I have discovered that Stella software had many of the queuing functions built into it. As a result I am in the process of building several small queuing models that can be used in data structures to introduce a queue, operating systems to study the behavior of various kinds of queues, and in a networking course for analysis.

I work with pre-service and in-service elementary school teachers, helping them to create unit themes in aerospace education. Introducing modeling into the classroom allows for several objectives to be met: (1) They see and adopt a positive view of today's technology and the possibility of tomorrow's technology; (2) Some of the best resources for developing scientific inquiry are on the computer. All of the physical laws that have been taught in the past through static models can easily be replaced using the dynamic models with an aerospace theme.

I built a model to find the bias (DC) current in a transistor. The model allows the user to vary four different resistors to study the effects on the model. I would be using this in an introductory circuit design course as a supplement to actually building the transistor.

Here are some of the ways I foresee using mathematical modeling in physical education: To teach and examine finite skills, to stress the importance of control, to teach angles in skill execution, to create mental images of motor programs, to correct motor programs and for coaching demonstrations. I have developed a model of how arm angle, stance and ball velocity affect the success of a volleyball pass.

Lesley College offers the course 'Microworlds, Models, and Simulations' to candidates for a Masters degree in Educational Technology in sites across the country. The students are themselves teachers, collectively spanning all subjects in K-12 schools. The MMS course introduces students to modeling, and dynamic and complex systems thinking, thereby requiring a diversity of relevant resources, with varied levels of mathematical sophistication. The Lesley College team has conceptualized a strategic plan that includes the development of a MMS resource web site comprising client-model archives available for ftp, and web-accessible client-server and java models available from the Shodor foundation. Through a partnership with Shodor, Lesley students will have the opportunity to contribute models for conversion to client-server form, and which will then be made available on the Shodor server.

We are developing a sociological model of children killing children in schools. We have included the effects of drug use, gun availability, comprehensive educational programs, drug intervention programs, and poverty in our model. We have a qualitative model for which we are working on studying the literature to quantify the factors. We hope to have a model that students can use to experiment with various scenarios mimicing actual communities.

Ibrahim Salama, Business, North Carolina Central University, and Sahar Zaghlou, Food Sciences and Nutrition, University of Arkansas at Pinebluff:

We investigated building a model of weight gain/loss which took into consideration gender, caloric intake, resting metabolic rate, and level of physical activity. This model can be used to mimic eating behaviors of various kinds, including binge dieting. Students can investigate the affects of changing caloric intake versus changing physical activity simply by changing the settings in the user friendly Stella interface.