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What enlightening misunderstandings of test questions have you encountered? Of course, there are jokes about this, such as literal (graphic) “expansion” of the power of a binomial, but I am asking about real situations where the student misunderstood a test question in a way that is plausible, but which was unanticipated by the teacher.

From time to time I encounter one of the following type: The student interprets “graph $|2x – 1| \leq 3$ on the number line” to mean “graph $y = |2x – 1|$ for $y \leq 3$”.

This is very enlightening, showing me that the question is ambiguous, and needs to be more tightly phrased. (But since I am not the one who creates the test, this will take a while to happen.) You might object that the phrase “on the number line” is a pretty big hint, but I don’t agree. Such a phrase does not faze a student under time pressure. Moreover, the textbook that we are using also uses the expression “on the number plane” for the 2-dimensional case, which, to a student under time pressure, can easily be the mistaken interpretation for the other phrase. Part of the situation, of course, is that in spite of the hand full of one-dimensional graphs that are done, “graphing” is very strongly, even exclusively, associated in the minds of many students with the 2-dimensional case, the idea: “If you don’t see a wiggly line in the plane, you don’t have a graph.” This lets me know that at least once I ought to mention the caution to the students: “Look at what these examples are telling us: You don’t have to have a wiggly line in the plane to have a graph!”

So, I’m sure there are a lot of other such examples out there. What are they?

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    Totally not an answer (sorry, I couldn't resist) but there's also a well known joke where the student circles $x$ because the question was to "find $x$".2011-06-29
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    I've converted the question to community wiki, since this is asking for a big list of examples and there's no one right answer.2011-06-29
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    Joel, I knew a guy in high school who, when asked on a physics test to "name the force acting on this object", named it "Bob".2011-06-29
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    @Michael: Was it a buoyancy force? :)2011-06-29

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