Having described in my previous post the most important deficiencies of problem-based tests (as I see them), I am now going to list what I perceive as the most important merits of Multiple Choice Tests (MCTs), and illustrate why I regard them as a better choice, especially for introductory, foundation type courses. Here too, in order to keep the discussion concrete I shall focus on physics tests.
Imagine the following scene:
Venue: Universita’ degli Studi di Genova, Italy, 1982. Packed in a small room, in the sweltering July heat, a bunch of first-year physics students, most of them teenagers, having written a physics exam whose outcome was nothing short of a disaster (about fifty sat for it and maybe five were admitted to the oral portion — quite a normal occurrence in those days), listen mortified, as the professor sternly berates them, his teaching assistant nodding along, bowing his head toward him, almost in adoration. I am one of those students, looking at my own paper — 25% is my score.
“The thing that bothers me the most”, pontificates the professor, “is your helplessness. As soon as I assign a problem that is more difficult than those given as homework, you all collapse !”.
From the back of the room, comes a question. A student asks: “Excuse me, Professor, what is the point of assigning on a test a problem that is more difficult than those given as homework ?”.
I cringe. How can anyone ask a question at such a dramatic juncture, never mind one so insolent in its naivete… “Do, you, Sir, believe that everyone is entitled to a physics degree ?”, is the reply. “Has no one ever explained to you that a physicist should display extraordinary abilities, and that if you lack them, maybe this is not your calling ? That maybe the humanities are better suited for you ? Think about it, Sir ! Think about this fact, all of you !”.
Oh, well… that student asked for that answer… right ?
Um, no. His question was bang on. The Professor was arbitrarily, unreasonably failing so many students largely because he wanted to be at the beach, rather than at school administering oral exams. I am appalled at the thought of how many potentially good physicists were back then turned away by lazy, pompous, arrogant fools like that professor.
What are exams and tests for, anyway ?
It may be in order to remind ourselves what the aim of testing students is. As I wrote in my response to one of the comments to my previous post, I regard testing as a necessary evil. Its purpose is that of providing society with an official assessment of the proficiency and mastery of a given subject on the part of a student. Simple as that. That is what society (e.g., high schools, colleges, government, private and public sector employers, fellow researchers) expects of someone like me.
I am charged with expressing such an assessment in the form of a numeric/letter grade, based upon which important decisions affecting the future of each students will be made. I thus see a test as a measurement, one that should be as much as possible unbiased, objective and reproducible.
I am not asked to evaluate someone’s IQ, deductive reasoning, creativity, communicative skills, quickness, intuition, nor any other “extraordinary ability” — I am not qualified for that anyway (not sure who would be) .
I try and design my tests and exams so that any student who
1) has memorized basic definitions (e.g., physical units) 
2) has assimilated fundamental concepts, by reinforcing them through methodical study and practice
3) can apply them to solve simple problems
will do well. I do not see what else an instructor should measure by testing, especially in courses like freshman physics, which, to most students, are only propaedeutic — very few students will actually major in physics.
Those students who can go beyond that, who possess superior analytical skills, I am talking deep thinkers with uncommon creativity or talent for science, will have plenty of opportunities to showcase their extraordinary abilities later on, through research rather than course work.
Why MCTs ? Here’s why:
This is what a well-designed MCT will enable me, the instructor, to do:
1) By means of targeted questions, focusing on just one specific concept, directly assess a student’s knowledge of the basics. Student will not ignore units, or dimensions, if a question or two about them can appear on a test.
2) By carefully drafting the different possible answers, give a chance to students who may not remember the full procedure, or who under pressure may be prone to making algebraic mistakes, to utilize orders-of-magnitude considerations, as well as simple physical understanding to arrive to the correct answer by exclusion .
3) Promote a concrete, goal-oriented, individual approach to problem-solving in science, emphasizing the ability to arrive at the correct answer (possibly in an unconventional way), rather than strict adherence to a given procedure or formalism.
4) Evaluate students in a relatively straightforward and objective way, without having my judgment affected by my (dis)like of their writing skills, methodology, reasoning, and without having to make difficult judgment calls when it comes to taking points off due to “imperfections” in the solution.
What are the main objections to MCTs ?
Perhaps commenters will point out the most serious drawbacks of MCTs. These are some of the most commonly heard:
A student will receive no partial credit. This is actually a plus, in my opinion. There is no objective, consistent way of assigning partial credit without making a judgment call. Ensuring fairness to all students (including those who enrol in a different section of the same course, with another instructor) is impossible. Plus, giving partial credit provides wrong incentives to students, as I tried and explain in my previous post. Rather than lack of partial credit, students should focus on the fact that all they have to do is pick the right box.
True, a student will receive no credit if, by mistake, (s)he checks the wrong box after working out the correct answer. However, I think that that is sufficiently infrequent an occurrence not to regard this as a major problem, and it is also compensated by more frequent lucky guesses.
Students can pick the right answer by luck. This is a weak one. Sure, one answer can be picked by luck, maybe even two or three, but the likelihood of selecting by luck enough right answers to earn a passing grade is pretty small.
Sometimes two answers will only differ by a small amount, and one will miss a point for calculator round-off error. MCTs can be well or poorly designed, like any other test. Including two answers that “only differ by a small amount” is bad testing procedure.
 I might be asked to comment upon some of that on a letter of recommendation, where I may, at best, offer an opinion, which one may regard as more or less reliable. However, a test score should be considered akin to the outcome of a measurement, which in principle others should be able to reproduce (within the obvious limitations coming from the fact that measurements on humans are far more complex than those on the objects with which physics deals).
 I do not care how smart you are. Just like you cannot speak a foreign language without memorizing the verbs, you cannot do physics if you do not memorize some basic notions like units, or definitions like work, kinetic or potential energy, electric field, flux, circulation etc., as well as experimental laws like Coulomb’s. Anyone who says the contrary is either a con man or does not know what (s)he’s talking about. Not that I have strong feelings about this — not at all.
 This is one of my favorite questions when I teach introductory electricity and magnetism:
Two point charges of equal sign, worth in magnitude Q and 9Q, are located at a distance L from one another. Assuming that they are held at fixed positions, where should a third point charge q be placed, between the two charges, along the line that connects them, in order for it to be in equilibrium ?
1. It depends on the sign of q
2. Right in the middle, at a distance L/2 from either
3. There is no equilibrium position anywhere between the two charges
4. At a distance L/4 from the charge Q
5. At a distance L/3 from the charge 9Q
A student who has learned the basics can pick the right answer without doing a single calculation.