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Lecture: I Saw a Mammoth

When models matter, try this.

In teaching chemistry the use of models is epidemic as it needs to be.  We can’t see much of what we expect our students to understand (atoms, molecules, electrons, protons, neutrons, bonds etc.) so the next best thing to seeing is often a model.  Many years ago my good friend Dr. Jon Barber and I were asked to give a short talk to a group of elementary teachers on the construction and use of models in teaching science.  These teachers were filling a need for in-service credit and I’m sure they dreamed this up because Jon and I were known not to bore folks. So they were thinking time with the two of us was a better choice than time doing something else planned by the district administration. We of course wanted to believe that our expertise in the use models was the motivating factor for the time we were going to spend together, but I’m quite sure that was just wishful thinking.

Jon started the discussion about the need to construction models from things that our students know and understand.  They may be actual objects, but could also be mental in nature or what is sometimes called a “thought experiment”.  Of course each student is different and what works for one may not work for someone else.  This brings to mind all those studies that show that the more anyone knows and understands (on any set of topics) the easier it is to learn new things.  Each “new thing” we try to learn is never completely new unless we don’t know anything about anything to start with.  Second, we need to pick from the things we know carefully because the similarities that connect to the new concept need to be as strong as possible for our model to be all that it can be.  In making this point Jon told the following story.

A few months ago a student came into my class very much excited about an animal he had just seen out back of the school coming out of the swamp. Behind Mounds View High School there is a small lake and a fair amount of low boggy area and that is where the supposed critter was seen. The student did not know the animal and due to his excitement everyone wanted more information about the strange beast. (Now, I want you to know what is was but of course you must not tell anyone or you will ruin the lesson in this story. He had just seen a Wooly Mammoth!!) The student said well it was like and alligator. It’s nose was longer and flexible and a couple of teeth had grown very large and stuck out on either side of its mouth. Its legs were longer and stockier and the body was hairy not scaly. The tail was shorter, more round, with a tuft on the end and hung down instead of sticking straight back. The picture was quite funny and our group was having a good laugh. They all agreed that an elephant would have been a much better starting point for trying to explain a mammoth. Of course and elephant is not a mammoth, but more about that in a minute. Think of all we know as a tree, our personal tree of knowledge. In making a model we need to find the right branch that is most similar to the thing we are trying to understand and tie our rope (model) to that branch. However, no matter how good our model is it cannot have all the properties of the real thing because if it did it would be the real thing! And this brings us to the rub. In the end we must abandon our model or it will lead us astray. The following is a little story to illustrate this point.

A knowledge tree is growing near the edge of a cliff and far below is a wonderful lake filled with the clear blue water of understanding. To get to the water we select the right branch in our tree of knowledge (an elephant not a crocodile) where we will tie our model rope that will hopefully propel us out over the understanding water. Of course we could just run and jump off the cliff and take our chances at making the water, but we may suffer the pain of being dashed on the rocks of poor grades. We may still make the water, although we might be bloodied and bruised. If we choose to swing on the rope model we must pick the right branch, we must hold on and trust till we clear the bad grade rocks and still we must let go of the model rope at just the right moment in order to make a graceful dive into the understanding water. If we let go too early we may hit the poor grade rocks and if we hang on too long we will surly be dashed back on the stones. It is unfortunate that all models are flawed and in the end will always lead us to incorrect ideas about that witch we are trying to understand, but that is the nature of models. The keys are to pick the right branch, tie the rope securely, swing with gusto, and remember to let go at the right moment. After these stories students often say to their classmates when certain questions are posed “let go of the rope” or ”it’s an alligator”.