Who Learns the Most in a Science Class?

I’m back, after two weeks of teaching non-experts in a short course covering particle physics, the Higgs field, and the discovery of the Higgs particle.  (The last third of the course, on the politics and funding of particle physics and science more broadly, is wisely being taught by a more disinterested party, an economist with some undergraduate physics background.)  And I’ve been reminded: One of the great joys (and great secrets) of teaching is that the teacher always learns more than the students do.

At least, this is generally true for a new class that the teacher hasn’t taught before. In many university physics departments, and elsewhere, there is an informal requirement that professors teach a class no more than three years in a row. [Let us ignore for the moment that all of this will be overturned in the coming years by the on-line revolution; we can discuss the possible consequences later.] After the third year, they are expected to switch and teach something else. Now you might think that the benefits of the division of labor would suggest a different approach; after all, shouldn’t each professor perfect a course, become the expert, and teach it year in, year out? This usually doesn’t work (though there are exceptions) because each professor’s interaction with a new course has a natural life cycle.

The first time a professor teaches a course, he or she has to review material learned long ago, and sometimes learn it anew. You might think this is only difficult for advanced classes, but that’s not the case. Advanced classes can indeed be difficult to teach because the material is intrinsically complex. But beginning classes are also difficult to teach because the material, while less complex, is just as complex for the students, and meanwhile the teacher has to remember how to think like a beginner, which is an experience long forgotten. If you can’t put yourself into your students’ heads, you can’t teach them very effectively… and this is extremely challenging.

Typically, this initial year of a course is quite exhausting, with the professor spending many more hours in preparation than in class. (I personally found it typical to spend 3 to 5 hours of preparation for each hour in front of students.) But the benefits are also considerable. I have often found myself learning several different ways of explaining a concept — my students only get to learn one, because that’s all the time we have, but I learn them all. And along the way I’ve often discovered links between disparate concepts that I hadn’t previously realized were related, or filled in a surprising gap in my understanding, or learned an application of a concept to a real-world phenomenon that I hadn’t previously known about. Often my students don’t get the immediate benefit because what I’ve learned is beyond the scope of the course. So they struggle to learn some fraction of what I teach them, which is typically much less than what I’ve learned myself.

Year two in the life cycle is the opportunity to fix everything that went wrong in year one, and it is usually the best year. I have usually found myself completely rewriting the first year’s notes, streamlining them, re-ordering them, and improving everything from the overall course structure to the details of how I explain certain subtle points. And I find I still learn quite a bit in the process, particularly about little loose ends that I didn’t have time to tie up during the frantic class preparations of the previous go-round.

But by year three, the whole thing is becoming routine. There isn’t much left for the professor to learn about the class material, and the struggle to master the content and perfect the presentation is no longer so severe. Sure, there’s always more that can be done to help the students deal with the technical material more effectively, but diminishing returns are setting in; any particularly creative ideas for how to convey the most problematic concepts have probably already appeared. So year three is not quite at the point of boredom… but beware year four.  And you do not want to be taught anything by a bored professor.

And so the professor is sent on to begin the cycle anew, to re-learn another subject, and to struggle to find the words and means to explain it clearly.

Two years ago, when I first wrote the Higgs FAQ (here’s the old 1.0 version and the new 2.0 version) I didn’t do a very complete or satisfying job of explaining the most important conceptual issues in particle physics: what are particles and what are fields? One really can’t understand modern physics, and the current notion of what ordinary matter actually is, what forces are, what mass is, etc., without these basic concepts. I promised a full article on the matter, but didn’t really deliver. I had done something brief in the my Secret Science Club presentation, but I didn’t feel it was as good as I wanted.

Then a bit under a year ago, having learned a great deal from writing articles for this site, from encountering and attempting to answer readers’ questions, and from preparing and delivering a number of public lectures on the search for the Higgs particle, I wrote a set of articles entitled “Fields and Their Particles (with math)” and “How the Higgs Field Works (with math)“, which boiled the issues down to the point that they could be understood by a first-year undergraduate college physics student. At the time, I promised a set of articles without the math, yet found myself unable to find the right strategy to do it. In particular, I did not want to make compromises that would require me to lie. Sure, some amount of compromise is necessary when explaining a difficult concept to someone who’s never seen anything like it. But that shouldn’t go as far as telling someone something they will later have to un-learn, or that will confuse them because it is actually false. (For instance: saying “the Higgs field is like molasses; it gives mass to things by slowing them down” is a lie. [As one of my students pointed out last week, you'll find this lie right at the top of http://simple.wikipedia.org/wiki/Higgs_field.] Molasses exerts drag, like air resistance; the Higgs field’s effect is obviously not a form of drag, because it affects stationary objects as well as moving ones.)

I believe I finally found a workable strategy while preparing a one-hour public lecture this March, and in preparing my recent course, which I described to the students as “non-technical” (i.e. no use of math except very simple and conceptual equations, such as E = m c² and E = h f) “but sophisticated” (i.e., you can’t tell the truth and yet make everything as simple and effortless as breathing).  In four 9o-minute lectures, I managed to describe the known particles and forces, explain how both arise from fields (which are the fundamental ingredients of nature), clarify what particles really are and what a particle’s mass really means, and finally, explain how the Higgs field gives mass to particles; then it wasn’t that hard to explain how the Higgs particle was discovered and how that discovery convinces us the Higgs field really exists.  And I don’t believe I lied once, though I should check that…

As usual, my students’ questions taught me a lot about all of the issues I’d forgotten to explain, and about little loose ends in my presentation that I hadn’t tied off.  Though they may not realize it, I owe them a big thank you!  Because now, given what I learned from preparing and teaching the course, I think I can finally begin planning the promised set of articles: “Fields and Their Particles (without math)”, to be followed by “How the Higgs Field Works (without math)”.

And meanwhile I hope I’ll get to teach that course again soon — since the second time around is when you fix what you messed up the first time…

25 responses to “Who Learns the Most in a Science Class?

  1. kashyap Vasavada

    Nice article as usual. In general, I agree with your statement that the professor should not teach the same course for more than three years. This would be ok if you teach only 3-4 hours a week as in major universities. However, in smaller universities there are practical limitations. In addition to limitations due to smaller number of faculty, the capitalist system has taken over American universities’ administration. Unless you get grants you must teach 9 hours or more!! If your work is good someone must be willing to pay for it!!! This belief puts lot of constraints on faculty desiring to do research in basic physics and of course do good teaching at the same time. I do not know if this is true in Europe (probably not). But in smaller American universities this is certainly true. Even in midsize universities, there is an enormous pressure to get outside funding. States do not give any research funding and as you mentioned previously federal funding sources are drying out. In a typical small university the chance for getting research funding for a proposal are less than 10%. One reviewer saying that the proposal is “very good (rather than excellent)” is already enough to kill the proposal!! As has been discussed in this blog
    before, this will eventually result in decline of research in U.S.

  2. Matt: I think there’s a lot in the old Einstein saying “You do not really understand something unless you can explain it to your grandmother”. So what I’d like to see is your explanation of how gamma-gamma pair production works. But beware, it isn’t as easy as you might think, and it opens up all sorts of problems.

    • “Beware”. Thanks for the warning. I’ve done this at least a dozen times (though I’m not sure if you are referring to e+e- –> gamma gamma or if you are referring to gamma gamma –> e+e-, from your wording.) What sorts of problems do you think I’m overlooking?

  3. It is interesting this “statute of limitations” concept applied to the life cycle of courses. In the IT industry there is no need to worry about such limitations, because it happens by default, with no need to manage anything at all: the entire industry is controlled by an empirical law, Moore’s Law.

    In fact, Moore’s Law is a natural consequence of the economics of chip fabrication: this law drives the entire industry, from hardware, to software, to tools, to certifications, to courses.

    I have been teaching IT certification courses on a continuous basis for the last 10 years, and the life cycle of such courses is just about 2 to 3 years, give or take no more than a couple of months, depending on the kind of software tool the certification is based on.

    Software development tools on average have a life cycle of 2 years for a give version. A clear example of this is Microsoft’s Visual Studio.NET, just in perfect synchro with Moore’s Law.

    Server tools on average have a life cyle of 3 years for a given version. A clear example of this is Microsoft’s SQL Server, lagging behind Moore’s Law by a full year.

    Technical obsolescence is a driver so strong that there is no need to manage the life cycle of courses.

    Kind regards, GEN

  4. Weinberg angle is the angle (theory) by which spontaneous symmetry breaking rotates the original W0 and B0 vector boson plane, producing as a result the Z0 boson, and the photon.

    In the early days of quantum field “theory”, massive vector particles didn’t seem to make any sense! In mathematical consistency, It seemed like, massive vector particles just weren’t allowed. The coupling constant determines the strength of the force exerted in an interaction – From abstract Lagrangian or the Hamiltonian, which are dimensionless, i.e., are pure numbers.

    Cabibbo’s idea originated from a need to explain two observed phenomena:
    the transitions u ↔ d, e ↔ νe, and μ ↔ νμ had similar amplitudes.
    the transitions with change in strangeness ΔS = 1 had amplitudes equal to 1/4 of those with ΔS = 0.
    Cabibbo’s solution consisted of postulating weak universality to resolve the first issue, along with a mixing angle θc, now called the Cabibbo angle.
    The rotation of vectors in three dimensional space is a linear transformation.
    So cabibbo angle explains the observerd parameters of transformation from linear momentum to angular momentum in concrete geometrical terms ?

    Weinberg angle is a parameter, after angular momentum, determines the position of vector bosons in that concrete geometry ? – by spontaneous symmetry breaking ?

    /The difference between massless force particles (like the photon and gluon) and massive force particles (like the W and Z) is the longitudinal degree of freedom./
    Force particles naturally appear in “theories” as massless particles. From above, we know that the difference between a massless and a massive particle is a single, extra longitudinal degree of freedom.

    Somehow we need to find extra longitudinal degrees of freedom to lend to the W and Z – in this concrete geometry ?

  5. Tienzen (Jeh-Tween) Gong

    Matt: “In particular, I did not want to make compromises that would require me to lie. Sure, some amount of compromise is necessary when explaining a difficult concept to someone who’s never seen anything like it. But that shouldn’t go as far as telling someone something they will later have to un-learn, or that will confuse them because it is actually false.”

    This article is truly a great report of personal experience. But, I am a bit surprised that you still need to make compromises (even to the edge of lying) sometimes. I fully agree with John Duffield’s quote, ” … Einstein saying ‘You do not really understand something unless you can explain it to your grandmother’” . In addition to simply agree with Einstein 100%, I would like to give it a theoretical support with the following points.

    A. Whatever the “foundation” of this universe is, this universe evolves via the self-similarity transformation from that foundation. However complicated a “physics law” is, it is always only a “foundation” of the higher tier manifestations. That is, the essence of that physics law is expressed in every piece of the higher tier “expression”. If we cannot use a “story” which is easily understood by the old grandmother, we did not truly understand that complicated physics law, period. Absolutely no compromise is needed. Furthermore, if a physics law can be told with two different folklores, the old grandmother will and can be the “judge” to decide which one is a good story while the other is the hallucination.

    B. In general, people view the linguistics as languages. I will define the linguistics universe with three parts.
    a. A meta-space — it encompasses the events and objects in the physical universe.

    b. Languages — they try to describe the stories in that meta-space.

    c. A meaning-space — the meaning of the meta-space story is understood by people.

    In general, a meta-space story could be understood differently by different people who have different world views. However, we could exclude the culture element and deal the issue strictly linguistically, that is, in terms of translation among languages only. Then, the meaning-space for all languages is identical.

    Now, for all languages (including mathematics), they share two identical continents (meta-space and meaning-space). That is, “all” languages are permanently linked among one another by these two continents. And, every language can be “translated” to any other language. Math is the “simplest” language in linguistics. When one cannot translate a math equation to a nature language, he does for sure not truly understand that math equation.

  6. When I write popular science articles, my target is teen-agers who are not particularly interested in science, so I try to add a note of humor to what I say, but I don’t lie! My motto is: no math necessary beyond first year high school algebra.
    A physicist friend said she wished her kids had read articles like mine when they were growing up. I don’t think she would have said that if she had detected any fibs.

  7. Matt– You said “In particular, I did not want to make compromises that would require me to lie. Sure, some amount of compromise is necessary when explaining a difficult concept to someone who’s never seen anything like it. But that shouldn’t go as far as telling someone something they will later have to un-learn, or that will confuse them because it is actually false.”

    I’m not sure that a pedagogic lie isn’t sometimes useful. The classic example is the Bohr atom. It is what most students first learn, and it does give an idea of the basic structure of the atom and even the idea of quantization of energy levels, using the idea of a deBroglie wavelength to introduce quantization. But it is wrong…completely wrong (no L=0 orbits). And yet most of the general public thinks of the atom in this way. Is this such a bad thing? The truth would simply be beyond them, and the Bohr atom is an excellent model for the non-scientists. When I teach it (to sophomores/juniors who have had chemistry), I certainly tell them that it is technically wrong but has some important features, so I’m not lying. But for non-majors?

    • Tienzen (Jeh-Tween) Gong

      Teach an incomplete theory is definitely not lie. Standard Model is definitely not complete, and it is definitely not a lie by teaching it.

      Bohr’s atom is definitely not a final model. But, it is historically important. Teaching with steps is not lie. Teaching a very important history (an incomplete model) in the development of a better model is definitely not lie, not even a pedagogic lie.

    • Yes, Marc, for non-majors *especially* I try not to lie, because they will have no opportunity to have the lie corrected. Majors will learn the truth, so lying to them temporarily has short-term consequences. Not so for the public.

      If I lie to them, I try to tell them that’s what I’m doing. More often I skirt an issue rather than lie about it. I don’t have a problem telling them something is more complex than I can explain in a particular context, and that what I’m going to tell them is wrong but gives the right idea. That’s what I would do with the Bohr atom — and in fact I’m always careful to say the Bohr atom was an early, and not actually correct, view of how atoms work.

      In my experience with non-experts — especially highly motivated non-experts who want to understand as much as they can — I find they do not want to be lied to. They would rather be told “this is too complicated to explain” than be told a story that makes them feel good until they learn they were sold a bill of goods. And I also find that those who’ve been lied to then have trouble understanding other things later. That’s the most common type of question I get when I lecture to non-experts: “How can what you are saying be true”, the student asks, “since it contradicts X, which I read on Wikipedia/read in someone’s book/saw in a video online?” Inevitably, it happens that in fact X is false, and so I have to convince them that I’m right and that what they learned previously is just wrong. I don’t think learning “X is true”, without any caveats, was helpful.

      • I generally teach pre-meds, and they’ve had chemistry so I certainly tell them that the Bohr model is a useful analogy, but not correct (they mostly know about electron “clouds” anyway). Now that I think about it, when I teach non-science majors, I do go through (qualitatively) the Bohr model, show how it leads to energy levels and most of spectroscopy, and then always tell them that this model was shown in the 1920′s to be incorrect, but the quantization concept still carried over. So the “lie” is only for a few lectures…..

  8. P.S. Have you really never described (to a lay audience) the cosmological redshift by starting out with the Doppler shift? That’s also wrong, but is a good analogy for the lay audience.

    • No, I have never lied to anyone that cosmological redshift is a Doppler effect. Because not only is it a lie, it is a very very boring lie. [It also leads to serious misunderstandings, which is very bad, but not as bad as being boring.] Indeed, the fact that it isn’t a Doppler effect is the main reason for caring about it.

      • Indeed, that is the kind of misleading and not-easier-to-understand kind of thing that really has no place in physics. I only just got a proper explanation of it this week.

  9. I personally am quite fond of lies. they’re a necessary evil of sorts. There will come a point in many lessons, especially to those involving youngsters, where you simply cannot impart any useful information without constructing a simple, if incorrect, model.

    My favorite example is the rainbow where the default basic explanation is that sunlight passes through raindrops that split the light like a prism. Another I like is classical mechanics or even basic physics itself (This is true… for a point mass experiencing no friction or gravity.)

    I’ve always taken a positive view to being informed that I was ‘lied’ to previously, seeing it not as wrong but as less accurate. (Yes I learned this back then, but this is a more accurate model I am able to use now.)

    The only times that being lied to annoys me is when the original lie was not in fact simpler, just more wrong. Is telling someone that small things ‘sometimes act as particles, sometimes as waves; oooh mysterious!’ any simpler than simply saying they’re 100% wave, just a special wave? (A tank of water can be used to illustrate a number of ‘particulate’ properties.)

    Simply saying you can’t explain\it’s hard to understand\you’ll be told later is ok in many cases (if deeply unsatisfying to many people who tend to see it as a cop-out.) but sometimes a good lie can do so much more.

  10. Mathematics is as old as Man.– (Stefan Banach).

    We use…numbers in all of our theories, but we don’t understand them—what they are, or where they come from. I believe that from a fundamental point of view, this is a very interesting and serious problem.
    —- Nobel Laureate Richard Feynman.

    These are lies or not lies ?

    • Tienzen (Jeh-Tween) Gong

      Feynman’s comment is not lie but is a sincere statement about not only his understanding but about the entire mainstream physics community’s understanding on “numbers” relating to the physics laws. Of course, no part of physics laws can be “outside” of the “essence” of “numbers”. But, this is an off topic for this article.

      • John Duffield

        Not really, because Feynman also said “The first principle is that you must not fool yourself, and you are the easiest person to fool”. I hope we will shortly see a stunning example of that.

  11. Being one of your permanent readers , i would like to tell you about my reflections concerning micro-physics , when i try to imagine the solid ground of ” what are out there ” i find it impossible to reach a final clear-cut picture , you always say that what physics present as reality is just our imagination of it ,……fields , particles , forces , interactions…..violent ocean of activity …..all of that MAY NOT be what is really out there , we have equations , data , concepts…..but all of this may by the year 2100 be obsolete , i , frankly , find this very “” painful “” ,…. human spirit always search for ultimate reality ,…..
    Well my dear teacher of physics ; what in your opinion may be the ultimate physics ?

  12. I read all of your posts , i started believing that the most fundamental building blocks are fields and interactions , now i am not sure of that , now i am inclined to see unity in all that vast ocean of activities where there are no identity /essence / solid substance but mere rules ….constant , permanent , and ruling rules……….or what else ?

  13. The professors at my physics department alternate years for some courses, or teach the same thing year after year, indefinitely. Three years preceeded and followed by a long fallow period sounds utopian to me.

  14. Pingback: You can only teach a course three times | Andraz Tori Blog

  15. Awesome things here. I’m very glad to look your article. Thanks so much and I am taking a look ahead to contact you. Will you kindly drop me a mail?

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