Copyright © 2007 jsd
This is a review of the following book:
Author:  Arnold Arons  
Title:  Teaching Introductory Physics  
Publisher:  John Wiley  
Date: ^{1}  1996 or 1997  
ISBN:  0471137073 
This book is a trap. It is superficially attractive, but the more you step into it, the more it reveals itself to be a morass of wrong physics and bad pedagogy. The book contains some good ideas, but they are so diluted by bad ideas that nothing can be relied upon. This makes the book particularly unsuitable for its target audiences, namely preservice teachers and novice teachers (part I) or students (part III).
The book pays lip service to lofty principles, such as the importance of critical thinking, sensitivity to student misconceptions, and the precedence of ideas over terminology. Alas the book byandlarge fails to uphold those principles. An example is its mishandling of the twofluid theory of electrical charge (item 24).
The book is too much in thrall to the “historical approach”, resulting in needless complexity, confusion, and error. See section 4.
The book goes out with a bang. Chapters III3 and III4 are a long discussion of thermodynamics without entropy ... which is like skydiving without a parachute. The book mentions heat, sensible heat, latent heat, caloric, friction, and energy ... without ever mentioning entropy. Ideas such as spontaneity and irreversibility that are intimately connected with entropy are almostexplicitly attributed to energy instead. Also the student is led by detailed historical arguments to a wrong theory, namely conservation of caloric. This will have to be unlearned later. Unlearning is never easy. See item 45.
A relatively minor additional criticism is that the book is inconsistent as to level. It purports to discuss introductory physics, yet it sometimes complains that conventional courses leave students with an incomplete understanding of difficult topics. That’s silly, since incompleteness is natural and unavoidable in an introductory course. For example, see item 32.
Part I of Teaching Introductory Physics spends a lot of time discussing misconceptions. If this were done properly, it would not be a problem, insofar as Part I is addressed to teachers, not to naïve students. The problems lie elsewhere:
For some possiblyconstructive suggestions on how to deal with misconceptions in the classroom, see reference 1.
In what follows, approving comments are marked (+) and disapproving comments are marked (–).
I don’t mind making approximations, especially in an introductory course, but to repeatedly redefine the meaning of a single term, back and forth – not just in the direction of progressive refinement – is a very bad practice. It would be much better to put qualifiers on the various versions, such as the subscripts on g_{I}, g_{L}, and g_{E} as explained in reference 2.
In Teaching Introductory Physics, the definition of mg on page I16 contradicts the definition on page I66 which contradicts the definition on page I126.
The fact is, the laws of physics do not care whether a force is «active» or «passive». There are innumerable examples of forces that cannot meaningfully be classified as «active» or «passive».
Students enter with a qualitative but perfectly correct notion that astronauts are weightless in the frame comoving with the space station. It would be foolish to force them to unlearn this idea in the introductory class, and then force them to relearn it later.
It is a great disservice to students to teach them the equivalence principle one day and then penalize them for invoking the principle another day.
This is an example where the book compounds a misconception rather than dispelling it.
The same issue shows up again on page I185.
(More generally, an introductory physics course must review many ideas that are directly connected to the axioms of arithmetic, and it helps to be explicit about the connection.)
dE = dQ − dW (1) 
which is not a valid equation, because there is no function Q and no function W that could possibly mean what equation 1 requires them to mean.
Furthermore, even if we were to cross out equation 1 and insert something roughly similar that actually means something, such as
dE = T dS − P dV (2) 
this would still be highly suboptimal, because equation 2 is nowhere near general enough to deserve being called the «first law» of anything. It would be much better to formulate the first law of thermodynamics as a simple, direct statement of conservation of energy, as discussed in reference 7.
Compare item 56.
ΔE = ΔE_{therm} + ΔE_{chem} + ΔE_{kin} + ΔE_{pot} + ⋯ (3) 
A similar equation appears on page III128.
Let’s see if we can apply this equation to the mechanisms shown in figure 1. The mechanism on the right side of the figure contains just a simple spring. Any F·dx work done by the applied force will presumably result in macroscopic potential energy stored in the spring, and attributed to the ΔE_{pot} term in equation 3. So far so good.
Meanwhile, the mechanism on the left side of the figure contains a gas of anhydrous acetic acid molecules. If we temporarily (!) approximate this as an ideal gas, any F·dx work done by the applied force will result in kinetic energy in the gas molecules. So arguably this should be attributed to the ΔE_{kin} term in equation 3. But since it is microscopic kinetic energy, not centerofmass kinetic energy, arguably it should be attributed to the ΔE_{therm} term. Furthermore, if we look more closely, we see that the acetic acid molecules undergo a reversible chemical reaction, to an extent that depends on pressure, so this is not really an ideal gas, and some of the F·dx work should be attributed to the ΔE_{chem} term. On the other hand, the energy of chemical bonds is entirely attributable to the potential and kinetic energy of the electrons and nuclei in the molecule, so arguably this should be attributed to the ΔE_{pot} and ΔE_{kin} terms in equation 3.
Overall, I have no idea how to make the RHS of equation 3 meaningful. It appears to be mixing things that ought not to be mixed.
That’s just wrong physics. Charge is not matter, and matter is not charge. Electrons and protons are different kinds of charged particles, but they are not the only kinds of particles, and all together there is only one kind of electrical charge. We know how things would look if there really were multiple kinds of charge, by analogy to the nuclear color charge — and electrical charge definitely does not look like that. See reference 8 for details on this.
This is the height of irony: The book preaches “critical thinking” at every opportunity, yet it repeatedly and emphatically rejects the onecomponent theory, even though there has never been the slightest evidence against the theory.
µ = 

 (4) 
where Δp represents the pressure....»
Molecular mass? Really?
It goes on to say «Although this is certainly not a useful way of measure molecular mass, able students find the exercise in mathematical physics very instructive.»
Calling it not «useful» is beyond an understatement. Equation 4 cannot possibly measure the molecular mass at all. This should be obvious on theoretical grounds. It should also be obvious from an orderofmagnitude estimate for the quantities involved, considering (say) a 1000foothigh column of air subject to a oneGee acceleration.
The book touts the importance of critical thinking, but fails to follow its own advice. The historical tail is allowed to wag the thoughtful dog.
See section 4 for more on this.
There seems to be some dramatic license involved. The approach that works for pressure waves in a tube of air doesn’t work for strings. The calculation on page I243 only works for a particular chosen point on a particular chosen waveform; the main features (e.g. dispersionless propagation) of waves on a string were assumed on page I242. They were assumed without proof, not derived.
This issue comes up again in question 14.8 in the book’s Section II.
Consider the contrast:
There is a scaling argument that goes like this:
 (5) 
Under the conditions of the experiment, the length of the apparatus L is constant, the accelerating voltage V is constant, and the charge of each particle q is the same. Therefore the velocity scales inversely like the square root of the mass m, the time of flight scales like the square root of the mass, and the gravitational deflection d scales directly like the mass.
So I would not be too quick to poohpooh a student who says that the small mass explains the small deflection. Even a student who cannot articulate the details of the scaling argument might have a good “feel” for the right argument … or might simply have correctly identified the mass as the only parameter that could possibly be relevant.
On the other hand, I would be disappointed if the student explained the massdependence in a way that violated the equivalence principle, or who thought the cathode ray velocity was small.
The book’s nonrecognition of this scaling argument is inconsistent with its remarks in Section 1.2 and elsewhere, which properly extol the importance of scaling arguments.
I disagree. It appears that the key idea here is the gauge invariance of electrostatics. Students were not born knowing this idea. Expecting students to reinvent gauge invariance on their own is completely unreasonable. What’s more, depending on how the chassis and vacuumenvelope of the apparatus are constructed, the ΔV in this experiment may not even exhibit gauge invariance. I would say that there are some quite «complex» ideas involved, and furthermore the problem is seriously underconstrained, because the statement of the problem leaves out important information. This goes far, far beyond «lack of practice on the part of the students».
It is always possible, but meaningless, to find a seeminglypathdependent way of calculating a pathindependent quantity. See also item 48.
v→ > 0 (6) 
In equation 6, note that:
We should distinguish bad pedagogy from wrong physics. For onedimensional motion, this example does not count as wrong physics, because in D=1 there is an isomorphism between scalars and vectors. However, it certainly seems like bad pedagogy to emphasize on the LHS that vectors are different from scalars, and on the RHS to treat vectors as indistinguishable from scalars.
This is especially disappointing because better alternatives exist, better in the sense that at little or no cost, they establish concepts that can be generalized to higher dimensions. One zerocost alternative would be to say that one vector is “directed to the right” while the other is “directed to the left”. This makes use of the idea that a vector has magnitude and direction, which is true in any number of dimensions, from one on up. As another alternative, at small cost one could introduce a basis vector γ and say that the first vector is directed in the +γ direction while the other is directed in the −γ direction.
What’s worse, this is a terrible “definition”, and it is immediately contradicted by the examples on page III68, and by the redefinition on page III69. Not until page III124 do we see the usual textbook definition of “heat” (which itself is not a very good definition, either, by the way).
The book introduces the terms “sensible heat” and “latent heat” without ever giving reliable definitions for them.
This misdefinition mentions melting, but fails to mention evaporation, sublimation, demagnetization, et cetera.
On page III71 the book coyly asks the student to explain «Why does Eq. 3.2.4 suggest that the quantity we have invented may be conserved?» Basic pedagogical principles tell us that ideas that students come to on their own are more deeply seated than ideas that are merely told to them. Alas, here the student is asked to form, based on a sizable collection of evidence, his own notion of conservation of heat. It is not until page III116 that there is a clear indication that heat can be created from scratch. It is not until page III122 that there is a clear indication that heat can be converted to motion.
Black believed that “sensible heat” and “latent heat” were state functions. The book does nothing to prevent students from believing the same thing.
This seems like the epitome of bad pedagogy. It practically guarantees that students will come away with deepseated misconceptions about heat.
This is an object lesson in the perils of the twistorical approach as discussed in section 4.
«You can strengthen your insight into these concepts by now returning to the discussion of impulse and change of momentum in Section 1.9. Notice that impulse, like quantity of heat transferred, is path dependent. In order to calculate an impulse, we must know how the force delivering the impulse varied instant by instant (i.e., we must know the "path" of the force with respect to the succession of clock readings). If we have this information, we can evaluate the impulse as an integral (i.e., an area under a graph). The situation with respect to transfer of heat is exactly analogous: Delivery of impulse (which is not a state variable) results in a change in the state variable called "momentum." Transfer of heat (which is not a state variable) at constant pressure results in a change of the state variable temperature.»
The quoted passage has more errors than it has sentences.
One of the central points that this section tries to make is actually valid, if you take it out of context, and reinterpret it in just the right way: It is true that in noncramped thermodynamics, there is no pathindependent value for ∫ TdS.
Alas, Teaching Introductory Physics buries this fact under three layers of wrong physics, plus a few layers of bad pedagogy.
The book does not correctly explain the relationship between TdS (which is a function of state) and ∫ TdS (which is not). This could have been explained using pictures, such as the picture of uncramped thermodynamics in reference 7. See also reference 13.
However, the quoted statement is clearly talking about paths in statespace. That changes everything, because momentum is a function of state ... not a function of position per se, but a function of state. That allows us to carry out the following calculation:
 (7) 
This rule is inconsistent with basic physics in this context; it is simply not true that heat transfers of the kind considered in this paragraph always result in a change of temperature.
Alas, Joule’s hypothesis is not correct. The KE/PE distinction does not parallel the heat/latentheat distinction. Not all kinetic energy is thermal, and not all thermal energy is kinetic. See reference 7.
ΔE=Q+W (allegedly) (8) 
which is not a good idea in general. It wouldn’t be so bad if this formula were advertised as an approximate or introductory idea, but on the contrary, the book utterly fails to recognize the weaknesses of this approach. It says equation 8 «always holds». Counterexamples are easy to find, including a wide range of dissipative phenomena, as in item 57 and in the grindstones discussed in reference 7. Another wide class of counterexamples involves advection, also discussed in reference 7.
Compare item 22.
In previous sections the book defined (after a fashion) W and Q and E, and said that the equation 8 «always holds». Many properties of W were explored, including the work/KE theorem.
Now in section 4.22 an impartial observer would see strong evidence that equation 8 does not hold. Rather than analyzing things impartially, the book brutally redefines W so as to make equation 8 hold. The redefinition is based on the assumption that equation 8 should hold, so the result is a meaningless circular argument.
There is no recognition that the redefinition breaks much of the previous development, including the work/KE theorem.
In any situation where dissipation is involved, this approach invalidates the foundations of classical thermodynamics, and leaves us with nothing. In particular it invalidates the idea that there is a meaningful separation between the macroscopic phenomena (W) and thermal phenomena (Q) as in equation 8. Once you start including “some” unobservable microscopic phenomena in W, it is no longer clear what (if anything) is meant by Q.
As an example of what I mean, consider the skin friction drag on the middle car of a long train, as shown in figure 2. We ignore pressure drag and pressure recovery acting on the front and rear of this car (since they nearly cancel by symmetry), which means skin friction drag is the dominant contribution to the drag. It imparts rightward momentum to the leftwardmoving train (as shown by the red arrow) and the same process imparts leftward momentum to the ambient air (as shown by the blue arrow). It would be nice to have a work/KE theorem that included this drag force, but Teaching Introductory Physics leaves us without one.
The book’s approach is a travesty of science and logic. It is akin to the adhoc arguments attributed to Faust in section 4.23.
This also makes a mockery of the socalled historical approach, since the relationship between work and frictional heating has been known since 1798, and should have been taken into account when Q and W were first introduced. Actually the book recognized this problem in the opening sentences on page IIIiii (item 38). But the problem, having been recognized, is never solved.
There are ways in which this problem could have been solved, but they are not hinted at in the book. In a small sense the work/KE theorems can be rescued as discussed in reference 12. In a much larger sense thermodynamics can be rescued by giving up on work (W) and heat (Q) and instead talking about energy and entropy, as in reference 7.
As far as I can tell, the word “entropy” does not appear in the book. It is definitely not in the index or the table of contents. Does it appear in the body of the text? If so, it is very inconspicuous. That is really quite astonishing.
In many places, this book follows the “historical approach” as a way to motivate and to organize an introductorylevel course. This is not good.
An introductory course should keep things simple and straightforward. Real history is neither simple nor straightforward. The real history of science is a tale of confusion, with much backtracking out of blind alleys. Nobody would be so foolish as to inflict the real history on introductorylevel students.
Examples of what can go wrong include item 30 and especially item 45. One might argue that item 30 (i.e. explicitly uncritical acceptance of Faraday’s field hypothesis) is OK, according to the maxim “no harm no foul”, since we know in hindsight that Faraday’s speculations turned out to be correct. However, there are at least two reasons why we should consider it a problem:
As pointed out by Kuhn (reference 15) and others, the “history” taught in introductory science class bears little resemblance to the actual historical facts. In many cases, folks who advocate the “historical approach” are so ignorant of the real history that they don’t realize how badly they are twisting the facts.
While item 30 is bad enough, when it comes to item 45 things get much worse. The book spends many pages retracing the path to a theory that turned out to be wrong, namely the conservation of heat. Students who follow this path will learn the wrong theory, and will have a hard time unlearning it. The wrong theory is all the more pernicious because it is plausible.
There is no law that says pedagogy must recapitulate phylogeny. In introductory classes we should use the best available evidence, not the most ancient evidence. For more on this, see reference 16.
I have the greatest respect for real history and real historians. If someone really wants to study the history of science, that’s commendable. The history of science is advanced topic, suitable for those who already have a good grasp of science and a good grasp of historical methods. Please do not confuse introductory physics with the history of physics.
Copyright © 2007 jsd