As I discussed in this post the other day, I believe that an excellent way to teach critical thinking is to present students with statements that are muddled, garbled, confused, poorly written, or just plain wrong, and instruct them to identify the errors and correct the statements.
How can we train students to be critical if we just present them with an unending series of clear and correct statements?
To that end, I have been incorporating the incorrect into my teaching, and I follow up on this by using such statements on exams. The instruction is to say whether the statement is true or false, and then provide an explanation, together with a correction if the statement is false.
Saying whether the statement is true or false is not of much value in itself; it’s the explanation that I’m after. Besides giving students an opportunity to exercise their critical faculties, it’s also an opportunity for the teacher to gather information about what exactly students are thinking. This is not of much immediate use on a final exam (although it may inform changes in a future run of the course), but it is potentially more useful to address misconceptions as students progress through the course.
All of these factors make this type of “short-answer” question far superior to multiple choice questions, which give very little insight into what students think.
Here are the true/false questions on the exam in my first-year electricity and magnetism course, which sat this past Monday, together with my thoughts.
TRUE OR FALSE?
a. If you cut a bar magnet in half, one half will be an isolated North pole, and the other half will be an isolated South pole.
Comments: We had discussed this question in the course, as part of a larger discussion on the mysteries of magnetism. Unlike electric charge, which has “elementary” constituents, there seem to be no fundamental particles of magnetism, which would be called magnetic monopoles. Most people answered this correctly by saying that you would get two smaller, weaker bar magnets, each with both a North pole and a South pole.
b. In a normal household circuit, light bulbs are wired in parallel because less wire is needed, and therefore the cost is less.
Comments: This is nonsense; the amount of wire needed is not the key issue. Rather, we use parallel circuits in our homes because it is possible to control each branch of the circuit separately. For example, if you wish to switch on a light bulb, you can do so in a parallel circuit without switching off everything else in the house. A related point made by quite a number of students is that if one light bulb burns out in a series circuit, all of them shut off, whereas in a parallel circuit if one light bulb burns out the rest are unaffected.
Similarly, the voltage (potential difference) across each branch of a parallel circuit is the same, which allows each load to operate properly. For instance, placing more and more light bulbs in series makes each one dimmer; placing more and more light bulbs in parallel allows each to shine with its intended brightness.
Note that some modern strings of Christmas lights (scroll to the bottom for the full explanation) use shunts, which are a more complicated kind of circuit: a series circuit, but one in which a shunt becomes operative if one of the light bulb burns out, so that the rest remain on.
c. Equipotential surfaces are regions of space where the electric field is constant.
Comments: No. Equipotential surfaces are regions of space where the electric potential is constant, not the electric field. The electric field is the (negative of the) gradient of the potential, which means it depends on how rapidly the potential changes. Graphically, the electric field depends on how closely spaced the equipotentials are.
One of the problems with learning (and teaching) electricity and magnetism is that a good number of students confuse many of the basic concepts. Charge, voltage, current: What’s the difference? It’s all treated as “juice”. Electric field, electric force, electric potential, magnetic force, magnetic field: What’s the difference? Electric potential, electric potential energy: What’s the difference?
d. The functioning of an electrical transformer can be explained using Faraday’s law of induction.
Comments: Yes. The alternating current flowing through the primary coil creates a changing magnetic field which passes through the secondary coil, in which it induces an emf, and therefore current flows in the secondary coil.
Some students just looked at some formulas and said that the two situations had nothing to do with each other, because there were no symbols in common in the formulas.
e. Two long, straight, parallel wires, each carrying a current $I$, do not exert a force on each other, because there is no force between parallel magnetic fields.
Comments: Nonsense again. Magnetic fields do not exert forces on other magnetic fields. Magnetic fields do exert forces on moving electric charges, provided that the velocity of the charge is not parallel to the magnetic field.
Furthermore, it is not the magnetic fields that are parallel, but the wires. So it’s possible to get confused and think that there is no force because “something parallel is going on”.
Using the right-hand rule, one can determine the direction of the magnetic field at the second wire due to the first wire. Using the right-hand rule again, one can determine the direction of the force exerted by the magnetic field of the first wire on the current flowing in the second wire. By Newton’s third law of motion, the force exerted by the magnetic field of the second wire on the first wire is equal in magnitude and in the opposite direction to the force in the previous sentence.
f. Electric currents create magnetic fields, and, similarly, magnetic currents create electric fields.
Comments: Further nonsense, at least if taken superficially.
Some students said that electric currents do indeed create magnetic fields, but that there is no such thing as a magnetic current, which is fair enough, as we had never mentioned such an animal in the course.
Others, perhaps wondering what on earth I could be going on about, interpreted a magnetic current to be a moving bar magnet. They followed up by saying that if one moves a bar magnet into or out of a coil of wire, then a current flows in the coil, and so there must have been an electric field produced by the moving magnet. Good thinking!
This illustrates my point that it is not whether they say “True” or “False” that is important, but rather what they know about the situation, as revealed by their discussion, that is vital.
Some students said that the statement is false, and “corrected” the statement by saying that, “Electric currents create electric fields, and magnetic currents create magnetic fields.” No!
g. Electricity is produced at Niagara Falls by rotating loops of wire within a magnetic field.
h. Electrical power is sometimes transmitted across very long distances; the voltages used in these cases are very high so that it can reach customers faster.
Comments: Nonsense. The speed at which current flows in a circuit has nothing to do with the voltage or current. The reason that very high voltages are used for power transmission across long distances is that current is thereby minimized, which minimizes power losses. (Power is dissipated in the transmission lines as heat; the power dissipated is proportional to the square of the current, so reducing the current by a factor of 10 decreases the power loss by a factor of 100.)
Transformers are used to increase the voltage to very high levels for cross-country transmission, and then to decrease the voltage to safe operating levels for use in our homes and industries. The ease of operation of transformers with AC current is the primary reason that AC won out over DC about 100 years ago (Tesla and Westinghouse were two of the principal AC champions, while Edison was the main DC proponent; this is a very interesting chapter in history, which I’ll talk about another time.)
i. In the photoelectric effect, when the intensity of the incident light is doubled, the kinetic energy of the ejected electrons is also doubled.
Comments: No. Increasing the intensity of the incident light increases the number of photons, not the energy of each individual photon. Thus, increasing the intensity of the incident light increases the rate at which electrons are ejected from the cathode, which amounts to an increase in current in the apparatus.
To increase the kinetic energy of the ejected electrons, increase the frequency (decrease the wavelength) of the incident light/electromagnetic radiation.
j. Passing electrons through a double-slit experiment proves that light is a swarm of particles.
Comments: The statement is confused, in the first place, by using “electrons” in the first part of the sentence and “light” later in the sentence. How can an experiment on electrons prove something about light?
Setting that confusion aside, passing electrons through a double-slit experiment shows that electrons have the same mysterious, dual nature that light has. Our way of trying to understand this mystery is to use the concept of “wave-particle duality,” which stands for our lack of understanding: Sometimes electrons (and light, etc.) behave like particles, sometimes like waves.
More details are here.
(This post first appeared at my other (now deleted) blog, and was transferred to this blog on 22 January 2021.)