Multiple Choice questions may have more value than you think

It is common for teachers in other disciplines to view multiple choice questions as the lazy teacher's way of avoiding grading.  In physics, that could hardly be farther from the truth.

Even physics teachers often think of multiple choice questions merely as a useful way of evaluating student understanding broadly and quickly -- after all, it takes a student only about 1-2 minutes per question to respond, and a teacher 1-2 hundredths of a second to grade by machine.  A multiple choice question can be even more valuable.  Some ways to use multiple choice questions creatively:

* I've detailed many times the "test correction," in which students earn back half credit on a multiple choice item they miss by explaining the answer thoroughly.

* I've also explained my typical "clicker exercise," in which teams of two students each have a chance to respond to a multiple choice item on the classroom response system.  The ensuing discussions of each questions can be more valuable than the best-designed homework question.

* Multiple choice questions can be expanded into free response-style homework question with the addition of three words: "Justify Your Answer."  Just today I decided that my class had had enough AP free response review homework.  So I took three of the tougher magnetism questions off of the recently released 2009 AP multiple choice exam, printed them out on a page, and assigned the justifications for homework.

* Even after a question has been assigned and justified, you can develop a further quiz based on the situation presented.  For example, consider a typical multiple choice question in which two railroad carts bounce of each other.  Originally, students may have had to find the amount of mechanical energy dissipated in the collision.  For some reason, that calculation frequencly causes trouble.  So, after I've demanded a thorough justification, I give a quiz -- same question, only this time the carts stick together after collision.  If the student truly understood the concept and calculation on the original problem, the new one should be no trouble.

Condider the multiple choice question below:

A car collides with a mosquito.  Which experiences more acceleration in the collision?

(A) The car, by a factor of about 10⁶

(B) The mosquito, by a factor of about 10⁶

(C) The car, by a factor of about 10¹

(D) The mosquito, by a factor of about 10¹

(E) Both experience the same acceleration.

When correcting this problem, some students will obediently go through the Fnet=ma calculation, estimate the mass of the car to be a million or so times the mass of the mosquito, and correctly answer B.  But not everyone will truly recognize the underlying principle here: This reasoning depends on Newton's Third Law, which demands that the forces experienced by each object in the collision must be the same.

So I'll ask this follow up question on a quiz:

A car collides with a mosquito. The mosquito sticks to the car after the collision.

(a) Which experiences more acceleration during the collision, the mosquito or the car?

(b) Which experiences more impulse during the collision, the mosquito or the car?

(c) Which experiences more force during the collision, the mosquito or the car?

GCJ