Tag Archives: mental model

Day 1 in Physics - Models vs. Explanations

One of my goals has always been to differentiate my job from that of a paid explainer. Good teaching is not explaining exclusively - though it can be part of the process. This is why many people seek a great video or activity that thoroughly explains a concept that puzzles them. The process of learning should be an interactive one. An explanation should lead into another question, or an activity that applies the concept.

For the past two years, I've done a demo activity to open my physics class that emphasizes the subtle difference between a mental model for a phenomenon and having just a good explanation for it. A mental model makes predictions and is therefore testable. An explanation is the end of a story.

The demo equipment involves a cylindrical neodymium magnet and an aluminum tube of diameter slightly larger than the magnet. It is the standard eddy current/Lenz's law/electromagnetic induction demo showing what happens when a magnet is dropped into a tube that is of a non-magnetic material. What I think I've been successful at doing is converting the demo into an experience that opens the course with the creation of a mental model and simultaneous testing of that model.

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I walk into the back of the classroom with the tube and the magnet (though I don't tell them that it is one) and climb on top of a table. I stand with the tube above the desk and drop the magnet concentrically into the tube.

Students watch what happens. I ask for them to share their observations. A paraphrased sample:

  • The thing fell through the tube slowly than it should have
  • It's magnetic and is slowing down because it sticks to the side
  • There's so much air in the tube that it slows down the falling object.

I could explain that one of them is correct. I don't. I first ask them to turn their observation into an assertion that should then be testable by some experiment. 'The object is a magnet' becomes 'if the object is a magnet, then it should stick to something made out of steel.' This is then an experiment we can do, and quickly.

When the magnet sticks strongly to the desk, or paper clips, or that something else happens that establishes that the object is magnetic, we can further develop our mental model for what is happening. Since the magnet sticks to steel, and the magnet seems to slow down when it falls, the tube must be made of some magnetic metal. How do we test this? See if the magnet sticks to the tube. The fact that it doesn't stick as it did to the steel means that our model is incomplete.

Students then typically abandon the magnet line of reasoning and go for air resistance. If they went for this first (as has happened before) I just reverse the order of these experiments with the above magnetic discussion. If the object is falling slowly, it must be because the air is slowing it down. How do we test this? From the students: drop another object that is the same size as the first and see if it falls at the same speed. I have a few different objects that I've used for this - usually an aluminum plug or part from the robotics kit works - but the students also insist on taping up the holes that these objects have so that it is as close to the original object as possible. It doesn't fall at the same speed though. When students ask to add mass to the object, I oblige with whatever materials I have on hand. No change.

The mental model is still incomplete.

We've tried changing the object - what about the tube? Assertion from the students: if the material for the tube matters, then the object should fall at a different speed with a plastic tube. We try the experiment with a PVC pipe and see that the magnet speeds along quite unlike it did in the aluminum tube. This confirms our assertion - this is moving us somewhere, though it isn't clear quite where yet.

Students also suggest that friction is involved - this can still be pushed along with the assertion-experiment process. What would you expect to observe if friction is a factor? Students will say they should hear it scraping along or see it in contact with the edges of the tube. I invited a student to stare down the end of the tube as I dropped the magnet. He was noticeably excited by seeing it hover lightly down the entire length of the tube, only touching its edges periodically.

Students this year asked to change the metal itself, but I unfortunately didn't have a copper tube on hand. That would have been awesome if I had. They asked if it would be different if the tube was a different shape. Instead of telling them, I asked them what observation they would expect to make if the tube shape mattered. After they made their assertion, I dropped the magnet into a square tube, and the result was very similar to with the circular tube.

All of these experiments make clear that the facts that (a) the object is a magnet and (b) the tube is made of metal are somehow related. I did at this point say that this was a result of a phenomenon called electromagnetic induction. For the first time during the class, I saw eyes glaze over. I wish I hadn't gone there. I should have just said that we will eventually develop some more insight into why this might happen, but for now, let's be happy that we've developed some understanding of what factors are involved.

All of these opportunities to get students making assertions and then testing them is the scientific method as we normally teach it. The process is a lot less formal than having them write a formal hypothesis, procedure, and conclusion in a lab report - appropriate given that it was the first day of the class - and it makes clear the concept of science as an iterative process. It isn't a straight line from a question to an answer, it is a cyclical process that very often gets hidden when we emphasize the formality of the scientific method in the form of a written lab report. Yes, scientists do publish their findings, but this isn't necessarily what gets them up in the morning.

Some other thoughts:

  • This process emphasizes the value of an experiment either refuting or supporting our hypothesis. There is a consequence to a mental model when an experiment shows what we expected it to show. It's equally instructive when it doesn't.I asked the students how many times we were wrong in our exploration of the demo. They counted more than five or six. How often do we provide opportunities for students to see how failure is helpful? We say it. Do we show how?
  • I finally get why some science museums drive me nuts. At their worst, they are nothing more than clusters of express buses from observation/experiment to explanation. Press the button/lift the flap/open the window/ask the explainer, get the answer. If there's not another step to the exhibit that involves an application of what was learned, an exhibit runs the risk of continuing to perpetuate science as a box of answers you don't know. I'm not saying there isn't value in tossing a bunch of interesting experiences at visitors and knowing that only some stuff will stick. I just think there should be a low floor AND a high ceiling for the activities at a good museum.
  • Mental models must be predictive within the realm in which they are used. If you give students a model for intangible phenomena - the lock and key model for enzymes in biology for example - that model should be robust enough to have students make assertions and predictions based on their conception of the model, and test them. The lock and key model works well to explain why enzymes can lose effectiveness under high temperature because the shape of the active site changing (real world) matches our conception of a key being of the wrong shape (model). Whenever possible, we should expose students to places where the model breaks down, if for no other reason, to show that it can. By definition, it is an incomplete representation of the universe.