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By Stanley L. Haan
We physicists can be sticklers for correctness. It grates on us when we see scientific errors in books, movies and so forth. It especially grates on us when we see errors in educational materials. I remember my first encounters as an assistant professor with elementary school science materials. I was appalled at the errors and wrote letters to publishers to get them corrected. I also made a very conscious effort in my first years of teaching to avoid teaching anything I knew to be wrong. If a concept was too complex to be completely understood by beginning students, but the material was unavoidable, I'd teach them just part of the concept.
Now, I regularly teach things that I know are incorrect. And I'm even admitting publicly that I do it. Among other things, I teach that planets travel in elliptical orbits around the sun. I teach that mass is conserved. I teach that force equals mass times acceleration. I teach that warm air holds more moisture than cold air. I even teach that electrons orbit atomic nuclei somewhat like miniature planets orbiting a sun.
Planetary orbits around the sun are not perfectly elliptical. The interactions between the plants (and occasional asteroids or meteors) perturb them. Each of the things listed is incorrect — but in some ways is "almost correct," and even useful. In fact, I submit that each person should learn that these things are true before he or she can appreciate that they are not true. The equivalence of mass and energy, for example, becomes significant only if one already understands the classical idea that mass and energy are conserved separately.
Am I dishonest with my students when I teach them ideas I know are incorrect? If I am teaching an introductory course in classical mechanics, do I have a responsibility to go beyond teaching "mass is conserved," or "F=ma" to include a disclaimer that it really isn't so? I've tried including disclaimers in the past, but feedback from student journals and exams has led me to conclude that more often than not, my disclaimers just confuse them.
Happily, I have found a way that I can teach incorrect ideas with integrity. I teach my students models, and tell them I am doing so. I don't teach that electrons orbit nuclei like miniature planets orbiting the sun as if it were the final word on atomic structure. Instead, I teach a model of the atom. My goal is that when I've finished, they will understand the model and also recognize that what they have learned is just that, not the "final word."
Of course, for this approach to be effective, students need to understand what models are. Consequently, I spend some class time specifically discussing models. Some models can be physical constructions — e.g., a globe as a model of the earth — while others are sets of analogies or ideas that are intended to help us understand intrinsically complex systems. For example, the "particle model" of matter postulates that all matter is composed of indestructible particles called atoms, whose masses are conserved and which can be rearranged in a host of ways to form different molecules. I'm still very careful to try and get the facts — i.e., the data itself — correct. It's only in the explanatory principles that I allow for "mistruths" to arise. I don't feel obligated to tell my students everything I know about a topic.
Since students must construct a scaffold of understanding in order to learn physics, I have come to the conclusion that it is dangerous to try to avoid teaching something that is wrong by distilling out only certain concepts from complex systems. For example, if we want to teach about atomic structure and only teach that electrons are bound to atomic nuclei and that various atomic states can be described in terms of energy, then as far as I know we haven't said anything wrong. But what have the students learned? Perhaps empty verbalism. Or perhaps they have constructed their own model of an atom and have somehow grafted our teaching onto it. I think they'd be a lot better off learning the Bohr model of the atom in its entirety, including its popular extension into multi-electron atoms that makes my rigorous side cringe. Then, when students are ready, we can refine the model or teach them a new one.
Using models in our teaching is consistent with the historical development of science. Our scientific theories themselves are in many ways just models that have grown in complexity and depth with time, or been replaced by superior models. A hundred years ago someone could teach F=ma and believe it to be fully correct. I believe we should still teach it today without obfuscating it in a cloud of relativity. We just need to let our students know that what we're teaching — and all our scientific theories — should not be considered the "final word" on a subject.
Stanley L. Haan is professor and chair of the Department of Physics and Astronomy at Calvin College in Grand Rapids, Michigan. A longer version of this article appeared in the Spring 1999 newsletter of the APS Forum on Education.
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