Maryland Virtual High School of Science and Mathematics
Silver Spring, Maryland 20901
Printed in 1999 in MAST Rapper, 24 (2), 30-33.
The Maryland Virtual High School of Science and Mathematics, funded under a National Science Foundation Research in Educational Policy and Practice grant, is using and creating modeling activities to help students reach the expectations of national and state standards in science and mathematics. Through a software language called STELLATM, students are able to represent the components of a problem with symbols, equations and graphs. Teachers and students have reported enhanced student understanding of graph interpretation, algebraic representation of relationships, feedback in systems, the scientific process and science content as a result of the modeling experience.
Data collection and analysis have always been an integral part of the high school science curriculum, but some problems are too complex for a simple lab experiment. How do we deal with large problems? One excellent example is a computer simulation of the carbon cycle. Students go through a step-by-step process of building a concept map, translating it to a computer model, testing it with data, adding a disturbance, modifying the model to account for more factors, and testing it again. The students see that theory and data must be used together to validate the model they have created. For example, the initial model is in equilibrium because the inputs and outputs to the various parts of the system are set as constant flows which counterbalance one another, but which do not include feedback of any kind. When the students introduce fossil fuel emissions to the system, they observe that the only part of the system affected is the atmospheric carbon. This leads to a discussion of proportional change and the realization that processes like photosynthesis depend on the amount of carbon that has cycled through other parts of the system. Adding feedback shows the students the complexity of the change to the system. At that point, they can add other changes to the system like deforestation. Although the model is a gross simplification of the complex processes in the cycle, the students report that the act of building the model and running the simulations gives them a deeper understanding of the sensitivity of the cycle to outside disturbances and reinforces the concepts underlying the model.
One boy reported that as a visual learner, he found that building the model dramatically increased his understanding. The computer model clarified the reading from the book by making the problem dynamic and hands-on. Examples of other topics for which thorough data collection is difficult include glucose/insulin regulation, alcohol metabolism, evolutionary changes, enzyme catalysis and population dynamics. All of these topics lend themselves to computer models.
In environmental science, the hydrology and ecology of watersheds is an important topic for which students can collect data from their local stream and from databases available on the web. But, students often only collect and plot the data, but go no further. Important questions such as the impact of a new housing development on their watershed are usually beyond their reach. The building of a computer model encourages students to look at mathematical correlations between variables and to research the likely effects of a development. The process of finding the relationships needed to build a model involves the students in a real world problem solving activity.
Computer models are also quite valuable in the study of physics. In spite of a multitude of lab experiences and paper-and-pencil problem solving exercises, physics students often have difficulty mastering the central concepts in kinematics and classical dynamics. Often, because they fail to understand the relationships underlying the problems, they simply memorize techniques for the problems they have seen and are unable to apply those techniques to different, yet related, problems. Computer models provide students with another means of expressing the relationships among the concepts. When the diagram for one model is visably similar to another model, the inherent structure of the problem becomes apparent. In addition, having the ability to manipulate the values in a model to represent a variety of scenarios and to create graphs as the model runs gives the student an efficient and dynamic way to test a variety of hypotheses, leading to richer problem solving experiences. Through models, students even have the opportunity to solve problems which they could not solve mathematically or for which they are unable to collect real data.
Models are also useful in the study of chemistry and earth science. Physical events such as volcano eruptions, earthquakes and hurricanes are exciting to see on television and through web pages, but students have no opportunity to experiment with the forces behind the event. Representing these phenomena through computer models allows students to control variables to see their impact on the severity of the event under study. Creating models of the hydrologic cycle and the rock cycle gives the students a deeper understanding of the concepts and processes underlying those systems. The study of gas laws, kinetics and equilibrium in chemistry comes alive when students are able to manipulate models and compare model results to theory and lab results.
Students who are engaged in the model-building process must pull together science content, math skills, and logical problem-solving skills in order to create a meaningful model. After validating their model through data and theory, they may use their model to test what-if scenarios. This hands-on approach to constructing knowledge about a system results in the reinforcement of math skills, science concepts and the scientific process.