Model-based Learning

We construct every-day mental models by interacting with the world. Already as babies we are constantly trying things out and seeing what happens. Mental model construction is an active process.

Scientists learn about nature by creating models of reality. This is also an active process of questioning, investigating, analyzing, and model building. It is similar to constructing every-day mental models but more rigorous and includes external representations. The process also requires interacting and experimenting with the external representations themselves. You can gain intuition about an equation by graphing it, rearranging it, modifying it, etc.

Luckily for us in the 21st century, computational models can bridge the intuitive and the formal. Computer code is a formal representation, but it can be used to create interactive visualizations. This can be extremely useful for developing intuitive mental models about phenomena that cannot be directly observed.

We will learn in this course by using and modifying various kinds of models. We will engage in all four processes of scientific inquiry: modeling, questioning, investigating, and analyzing. There will be a focus on developing strong mental models, often through interacting with computational models that include visualizations, like the forest fire model above. But we don’t want to stop at intuitive mental models. We want to link those mental models with formal computational and mathematical represenations, because they allow us to do things that are impossible for the unaided mind. Both aspects are important. Learning how to manipulate the symbols in a equation without knowing what they mean is not very useful. That makes you like a robot manipulating someone else’s model without understanding what it is all about, and you won’t be able to use the formal representation to do new things. But, by developing intuitive mental models and linking them to formal external representations, you gain the type of deep understanding that has enabled us to build things that would have been considered magic just a few generations ago.