Multiple Mark Questions – Agile Learning

I’ve recently become a fan of the “mark all that apply” type of question my classroom response system facilitates. I call these “multiple mark” questions in my book. Here’s one I used in the linear algebra course I’m teaching this fall.

This question is adapted from one of the questions written by Project MathQuest out of Carroll College. Their version of the question wasn’t a multiple mark question. Instead, it included a fifth option, “More than one of the above are possible.” While that option makes the question more interesting and more challenging for the student, it also yields inconclusive data about student learning since students submitting that response may have different ideas about which of the four options are possible. That’s not all bad, of course. Given my interview with Kelly Cline, one of the PIs for Project MathQuest, I can imagine Kelly leveraging that ambiguity into a productive classwide discussion of the question.

However, I decided to turn this question into a multiple mark question by adding the instruction, “Mark all that are possible.” As you can see from the results, 20 of the 20 students present that day indicated that option 3 was possible, 19 of the students indicated options 1 and 2 were possible, and 14 of the students felt that option 4 was possible. This was very useful feedback for me, since I could quickly tell that the class was in agreement on options 1 through 3, but option 4 deserved some further discussion.

I’ll admit, however, that I got a little tripped up on my own question logic here. As it turns out, all four options are possible, which was not my intent when I included this question in my lesson plan. Option 2 is only possible if the third plane intersects the two overlapping planes and option 4 is only possible if the three planes are parallel because they are in fact the same plane. The way I’ve worded the question, these wrinkles aren’t addressed, making all four options possible. As a result, the question doesn’t do a great job at uncovering student understanding of these wrinkles.

Here’s the question I should have asked instead:

Suppose you have a system of 3 linear equations in 3 variables. Which of the following conditions would guarantee that the system has an infinite number of solutions? Mark all that apply.

All three equations represent the same plane.

Two of the equations represent the same plane.

The three equations represent planes that intersect along a line.

The three equations present parallel planes.

With this question, only options 1 and 3 are correct. With option 2, it could be that the third plane is parallel to but distinct from the two overlapping planes, yielding no solutions instead of infinitely many solutions. With option 4, it could be that the three planes are not the same plane, again yielding no solutions instead of infinitely many solutions. This wording of the question puts the special cases in their proper places.

Have you used multiple mark questions? Do you find them more difficult to write? How do your students respond to them?

Biggio Center says:

October 20, 2009 at 12:42 pm

Derek – there is a technology limitation factor here. While multiple-mark has many pedagogical benefits, what if your clicker system cannot handle it? Any suggestions on how to deal with this?

derekbruff says:

October 20, 2009 at 12:56 pm

Good question. I should point out that my multiple mark question is a bit of a hack. The system I use, TurningPoint, has a “priority ranking” feature used, for instance, to have student rank the top three causes of something in order. You can set up the scoring system for these slides so that the student’s first choice receives 3 points, their second choice receives 2 points, and their third choice receives 1 point (like the Borda count in elections).

That’s the intended use of this type of slide, but I find it more useful to assign 1 point to all the students’ answers, which effectively creates a multiple mark question. So my system doesn’t directly support multiple mark, but I can change the settings to create such a question.

If that’s not an option, I guess the traditional approach is to add answer choices like “A and B” or “A and C” or “B and C.” If you have only three answer choices, then that’s manageable, but with four answer choices, you’re looking at 11 possible configurations (other than single answers and the “none of the above” case). You would then probably have to guess which of the 11 possible multiple-answer responses are likely to be popular with students.

You could also break this into multiple, shorter questions. Have the students think about the multiple mark question, write down their answers in their notebooks, then respond to a series of questions of the form “Is A a correct answer to the question at hand? Yes or No.” This isn’t quite as slick as the multiple mark question, but is generates essentially the same data and would (I think) foster essentially the same class conversation since you’d still have to address each of the possible answers individually.

Joss Ives says:

October 20, 2009 at 6:52 pm

I often use the “how many of the following apply/are correct” and give 4 statements or reasons and then make the answers 0-4. I use iclicker so don’t have the multiple mark option. I like these types of questions for generating classroom discussion, and there’s usually a really large spread in the answers. I usually have some ambiguous choices in there to make sure that there’s some sort of a spread. This always leads to good discussions about in which types of cases the ambiguous ones would apply or not. All that being said, being able to see the specific responses for each statement would be nice, but I think I would find clicking through y/n on each of the statements to be a bit tedious. I will try it sometime and see how I like it.

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