I was assigned two readings from his book, A Guide to Introductory Physics Teaching, 1 and I was immediately struck by two things. First, I was impressed and frankly, a bit amazed at how deeply he thought about the teaching of topics in physics. Second, as I explored other parts of the book, I was impressed by how many topics he thought so deeply about. As a physics teacher myself, I too had thought about these topics and, of course, about the teaching of them. However, until these readings, my thought process had never been given the type of structure and voice that I immediately found from reading the sections that were assigned for my M.
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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 pooh-pooh a student who says that the small mass explains the small deflection.
On the other hand, I would be disappointed if the student explained the mass-dependence in a way that violated the equivalence principle, or who thought the cathode ray velocity was small. It appears that the key idea here is the gauge invariance of electrostatics. Students were not born knowing this idea. Expecting students to re-invent gauge invariance on their own is completely unreasonable. This just adds to the burdens imposed on the student by item It places far too little emphasis on four-vectors and spacetime diagrams.
The key question is not asked, let alone answered. The question is, what would happen if we chose a different path from state A to state B? The passage imparts quite a serious misconception about what path-dependent means. It is always possible, but meaningless, to find a seemingly-path-dependent way of calculating a path-independent quantity. See also item Of course positive means greater than zero, and negative means less than zero.
The vector v has an arrow over it to emphasize that vectors are different from scalars. On the RHS there is a scalar. In the middle there is an inequality operator that is generally only defined for scalars. Vectors are not well-ordered in two or more dimensions. We should distinguish bad pedagogy from wrong physics. 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. 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.
To all appearances, these are meant to illustrate some property of energy. There is one sentence, buried in the middle of a paragraph on page I, where the second law of thermodynamics is mentioned, and a Philadelphia lawyer might argue that because of this one sentence, the whole section is technically correct.
However, no matter what the technicalities, this section is the epitome of bad pedagogy. It is entirely inappropriate to feature these examples in a chapter on energy. After reading this section, students will be more confused than before This misdefinition mentions melting, but fails to mention evaporation, sublimation, demagnetization, et cetera. 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 III that there is a clear indication that heat can be created from scratch. It is not until page III that there is a clear indication that heat can be converted to motion. 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 deep-seated misconceptions about heat. Specific heat is intensive. It is ironic that the book preaches the importance of scaling laws, but fails to apply the most basic scaling checks and dimensional-analysis checks to statements like this.
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.
If we have this information, we can evaluate the impulse as an integral i. 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. Alas, Teaching Introductory Physics buries this fact under three layers of wrong physics, plus a few layers of bad pedagogy. The analogy between impulse and heat is flawed; see item Even if the analogy were overhauled so as to make it correct, it would violate the pedagogical principle that learning proceeds from the known to the unknown.
If you learn those words by rote, they may turn out to be correct, if you later learn a correct definition for the words. However, the ideas that Teaching Introductory Physics attaches to these words are not correct.
It is questionable both from a pedagogical and from a practical point of view to emphasize what something is not. As discussed in item 39 , the key question is not asked, let alone answered. However, the quoted statement is clearly talking about paths in state-space. That changes everything, because momentum is a function of state That allows us to carry out the following calculation: impulse.
My Acquaintance with Arnold Arons
Teaching introductory physics
Teaching Introductory Physics by Arnold B. Arons (1996, Paperback)