Using Models to Reason and Infer New KnowledgeLet me ask you a question: How many windows are in your house or apartment? It's entirely possible that nobody's ever asked you this before. At least, that's what I'm banking on. If you've never been asked "How many windows are in your home?", then that means you aren't answering from memory. Instead, the question requires that you compute a value on the spot. How did you accomplish this task?
My prediction is that you visualized your home, and then started a walk-through, counting each window as you moved from room to room. In other words, you used a mental simulation, or a mental model, to answer my question. As it turns out, mental models are great for more than just answering random questions. They are just one instance of a class of mental representations that we use everyday. Mental models are simulations or images that we use to reason about the world and/or infer new knowledge.
What do toilets and light beams have in common?Consider another example of a mental model: the flushable toilet. If you know how a toilet works, then you can use your mental model to debug it when things go wrong. For example, a well-constructed mental model will help you figure out why the water keeps running (i.e., the filler float is stuck or the flush valve is stuck in the open position). Or why nothing happens when you depress the handle (i.e., the chain that connects the handle to the flush value fell off or is broken).
In addition to reasoning about the world, mental models are also useful in generating new knowledge through the process of inference. In a previous post, we talked about the power of inheritance to derive new information. This is similar in the sense that you infer new facts by "running" a mental model.
One of the more famous examples of this is Einstein's claim that he used a mental simulation of riding a beam of light and asking all sorts of questions about what he might observe at that speed. Good thing he interrogated his mental models because it gave birth to the special theory of relativity!
A STEM ExampleThere are so many examples of mental models in science and engineering that I won't even attempt to catalog them here. In fact, one could argue that STEM education is primarily focused on helping students build detailed and accurate mental models. Here are a couple of illustrative examples.
First, the astute reader probably noticed that a recent post, entitled "Midnight in the Garden of Encoding and Retrieval," attempted to create a mental model of memory. That model proved to be useful when we started asking questions about what happens during encoding, storage, and retrieval. The answers to those questions helped us debug potential reasons why a student might fail to learn a new fact or skill.
Another example, that I've used in my own research, is the human circulatory system. In one of our studies, we asked about the thickness of the muscle for the right ventricle versus the left ventricle of the heart. If you know that the right side of the heart sends the blood to the lungs, and you know that the lungs are proximal to the heart, then you know it doesn't need to pump very hard; therefore, the muscle in the walls of the right ventricle do not need to be as thick as the muscles in the left ventricle. This is useful knowledge that doesn't need to be taught directly. Instead, it can be inferred by the student through a series of leading questions.
The final example I will give is one of my favorites . It has to do with the development of the mental model for the Earth. When kids are little, they know, via observation, that the Earth is flat. Later on, they learn that the Earth is round. To make the observation compatible with the authoritative knowledge that they hear from adults, children then reason that the Earth must be round, like a pancake. If you ask them leading questions, such as, "What will happen if you walk for days and days?", they will answer that you will come to the edge of the Earth.
If the goal of education is to help students develop accurate and complete mental models, then there is a pretty interesting implication for assessment. It is difficult and time-consuming, but developing generative questions is a excellent way to evaluate your students' mental models. Generative questions ask the student to reason about his or her model model. The "muscle thickness of the ventricles" and "walking the Earth for days and days" are good example of generative questions.
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