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29 August 2009

Mailbag: Should you guess on multiple choice problems?

From Joey Konieczny, from Georgia:

Another question I had was about how you grade your multiple choice questions. The AP exam takes off 1/4 points for every wrong answer, correct? Do you do the same? Do you encourage your students to not answer your exam questions if they are not confident in their answer?

Yes, the AP multiple choice exam is graded exactly like the SAT: with 5 choices per item, students get 1 raw point per correct answer, and lose ¼ raw point per incorrect answer as a correction for guessing. And yes, I do the same on my in-class tests, because they are given as authentic AP practice exams.

However, I encourage my students to answer EVERY SINGLE multiple choice item, regardless of how confident they may be. Why? Look at the mathematics, to begin with.

Imagine a 100 question multiple choice test answered completely randomly, with absolutely no hint as to the correct answer. A person who leaves everything blank gets zero raw score. The person who answers every question will, on average, get 20 right for 20 raw points; but this person will get 80 wrong, for -20 raw points, leading to an overall raw score of: zero. Exactly the same as if the test were blank.

My point here is that, contrary to the myth that some idiot test-prep corporations propagate, there’s no harm in random guessing. On average, random guessing scores exactly the same as leaving blank. Of course, there’s really no point to truly random guessing: if someone runs out of time with ten questions left, I do not advise randomly filling in bubbles.

However, this analysis shows that there is, in fact, benefit to guessing that is in any way not random. Now, some will give the advice that if you can’t surely eliminate a couple of answers, then you shouldn’t guess. I disagree. My students – and, since you’re reading this blog, yours too – develop pretty good instincts about physics problems by the end of our year-long course. Even if they can’t bet their life on the wrongness of an answer choice, my students are certainly more than 20% likely to pick out the correct answer on virtually every multiple choice problem I’ve ever assigned. So they should always guess! In the best-case scenario, these non-random guesses add a few raw points to the overall raw score. And in the worst case – THIS IS THE CRUX OF MY ARGUMENT – these random guesses do no harm.

My rule is, if you read a question, mark an answer.

Now, it’s actually a rather tough process to convince students to guess, because they’ve heard for so long about guessing penalties. The most convincing argument to encourage students to guess on multiple choice questions came from my former student, Bret Holbrook, who truly understood the methods to my madness. He reminded his classmates that I make students do a correction for every multiple choice question that isn’t right, whether or not an incorrect answer was marked. So, he reasoned, he might as well guess. That gave him at least a 20% chance of avoiding the hard work inherent in the correction that he’d have to do anyway if he left the question blank.

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