Modeling and Quantitative Skills

Since natural systems are so complex, using models is often the only way to quantitatively study them. So it is important for students to understand something about models and how to use them effectively. (For extensive information on the what's, why's and how's of using Models in teaching entry level geoscience, see the Starting Point Teaching with Models module.) Further, students should realize that much of modern research relies heavily on devising and improving upon models of natural systems. A major virtue of models is that they may be used to simulate "what if" scenarios, promoting intuitive understanding of complex systems.

Things to keep in mind:

A Model is a simplified representation. They generally try to describe some specific aspect of a natural system, such as atmospheric CO2 content or the temperature in a cooling magma body. Models focus on a set of causal factors that is manageable and can substitute for real situations that are too complex to deal with in their entirety.

Models are built for a specific purpose. Particular issues such as ideal gas behavior (pV=nRT) or classical mechanics (F=ma) are modeled by ignoring parameters which are not considered to have an impact on those issues. Usefulness in a particular situation generally depends on how well the results conform to real world, but what passes for "good" conformity is highly variable and depends on the problem or situation.

Models foster and test the intuition. Students can gain insight into the behavior of complicated systems by running model simulations. Also, designing a model requires students to figure out what parameters affect the phenomena they are trying to model.

Models have Limitations. Models only approximate natural phenomenon and their limitations need to be taken into account.

Models have input and output. Models generally enable study of variations in the behavior of a system (output) when other factors in the system are varied (input). A model's output can then be used to vary the model's performance characteristics through feedback.

Models have temporal and spatial characteristics. Change in a variable over time is a common issue addressed with models. Alternatively, models can look at look at a set of parameters at a particular instant in time. Many models, especially in the geosciences, deal with the spatial distribution of some characteristic either across a temporal range or as a snap-shot at a particular instant.