Why I teach my students things that are incorrect
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 I wrote letters to publishers to try
to get the errors corrected. I also made a very conscious effort in my
first years of teaching to avoid teaching anything that 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 my students just part of the
Now I regularly teach things that I know are incorrect. Without bashfulness.
I'm even admitting publicly that I do it.
What are some examples of things I teach that are incorrect? 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
Planetary orbits around the sun are not perfectly elliptical. The interactions
between the planets (and occasional asteroids or meteors) perturb them;
variations in the orbit of Mercury provided important tests of general
relativity; and so forth. 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 to my students when I teach them ideas that 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 the students.
Yet I do admit that I find it somewhat unsettling to hammer on a concept
that I know is incorrect, or at best is only a partial truth. Happily,
I have found a way that I can teach incorrect ideas with integrity. What
I do is to teach my students models, and I tell my students what I'm doing.
I don't teach that electrons orbit nuclei like little miniature planets
orbiting the sun as if it were the final word on atomic structure--instead
I teach a model of the atom, and I tell my students that I'm teaching
them about a model. My goal is that when I've finished, they will understand
the model and also recognize that what they have learned is a model and
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. We discuss that some models can be physical constructions--e.g.,
a globe as a model of the earth--while other models 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.
So I'm actually quite selective about what I teach that's "incorrect." I'm
still very careful to try to 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 try to tell students everything I know
about a topic.
In some ways, my teaching hasn't changed much. But one very important
change is that in the past I rarely made a conscious effort to tell my
students when I was teaching a model or theory, so I don't think they were
as prepared for learning refinements or revisions as my present students.
When students know that what they have learned is a model, they will be
naturally inquisitive about the limitations and shortcomings of the model.
Since students apparently must construct a scaffold of understanding in
order to learn physics, I have come to the conclusion that it is very dangerous
to try to avoid teaching something that is wrong by distilling out only
certain concepts from a complex system. For example, if we want to teach
about atomic structure and we 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 that is wrong. (Note that
I avoided saying that electrons could only have certain prescribed energies,
since I know that would be incorrect--states which are coherent superpositions
of energy levels are quite possible.) 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 whole new model.
In many ways using models in our teaching is consistent with the historical
development of science. Our scientific theories are themselves in many
ways just models that have grown in complexity and depth with time, or
perhaps have been replaced by superior models. Our theories may themselves
need additional refinement in the future. 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.
By the way, I still try my hardest to stamp out factual errors. There's
no excuse for teaching facts that aren't facts--such as that the Coriolis
effect causes water in sinks to spin counterclockwise in the Northern Hemisphere.
Or making movies that have noises on the moon or in space. Or ...
Stanley L. Haan is Professor and Chair of the Department of Physics and
Astronomy at Calvin College in Grand Rapids, MI