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I have been doing a little bit of experimenting when it comes time to review with the class in preparation for the final exam. The last handout I have been giving my students has usually been a compilation of problems similar to the ones they have been accustomed to seeing throughout the course. Through the use of textbooks, I can save some time by not having to come up with the questions myself, but the textbooks sometimes do not use the same language that I use in class or on prior written assignments. Recently, I have been considering the option of either:

A) a list of twenty-five possible questions, out of which eight to ten will be on the final exam, or
B) the exact eight to ten questions that will be on the final exam, with the particulars blacked out (particulars being numbers, equations, functions, etc.).

Benefits of A:

  • allows students to strengthen all core skills required to say that they have a satisfactory understanding of all course material
  • if all twenty-five questions are completed to perfection, the student should have no problem reiterating the solution come exam day (barring test anxiety, time management problems, and other factors)
  • hedging bets (we all know this problem when we studied stats): what is the minimum number of questions I should be completely clear on how to do if I want to have a good chance of scoring at least an $80\%$, etc.

Benefits of B:

  • allows students to focus solely on the exact type of question they should expect
  • gives students the opportunity to predict how much time should be spent for each question, and, by extension, how much time can be spent studying for each topic

To current students: if you were given the option, which would you prefer? Can you think of other ways that each option can benefit you?

To teachers: which option have you personally used with your students before? If neither, do you see yourself employing either of these methods when it comes to exam preparation for your students?

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  • $\begingroup$ How about a list of 15 questions, out of which 8 to 10 will appear on the exam? Just wondering why you think A or B are the only options? $\endgroup$ – Namaste Oct 18 at 21:49
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    $\begingroup$ @Namaste I imagine that your comment suggests that 25 question is too many -- when I wrote 25, I suppose that number was arbitrarily chosen, but I do have this idea that there has to be a sufficient number of potential questions given the number of questions there actually are going to be on the exam. Of course, none of these numbers are yet set in stone (though there must be a minimum number of questions that will be on the exam). In your experience, do you feel 8 to 10 out of 15 would be more beneficial compared to 8 to 10 out of 25? $\endgroup$ – Andrew Chin Oct 18 at 22:04
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    $\begingroup$ And I am definitely not suggesting that my two options are the only two options. I have gone through a number of different types of exams (e.g. "here are $x$ questions, do all of them" or "here are $x$ questions, do $y$ of them" or "do two from section A, three from section B"). But, as it pertains to the two options that I have described, is there one that, in people's opinion, works better? $\endgroup$ – Andrew Chin Oct 18 at 22:07
  • $\begingroup$ I believe that at least some of the recent "specs grading" trends look something akin to B, though there are other differences in the goals of exams. This is an interesting question. $\endgroup$ – kcrisman Oct 18 at 22:15
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    $\begingroup$ "B" seems a bad option, but it depends on your goals. "A" seems to be testing (1) diligence and (2) the ability to regurgitate answers that have been figured out by someone, perhaps someone else; and (3) failing (1) or (2), the ability to apply course concepts in solving problems for which they have been (perhaps) adequately prepared to do on a timed test. While "A" has significant shortcomings, I've used it before in a limited way (~1/3 of the test was from the set of problems) because I've witnessed its effect on good students. They worked hard, even if helping each other, to understand. $\endgroup$ – user1527 Oct 21 at 1:23
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I prefer A. It essentially says these 25 questions represent the whole course. Knowing them, you know it all. The 8 selected will be broad, but by nescessity (time constraint) won't cover whole course. So if you only give B, yuu're basically leaving too much of the course as untested. (In that people won't prepare to know anything other than what is on the test.) I mean even on professional certifications, there is a lot of material which can't all be covered in the exam. If you gave only the 8 questions, you'd be allowing people to blow off too many topics int heir prep.

In comments, there was discussion of making number 15 versus 25, but I would lean more in the opposite direction, so you cover more possible material. About one per lesson.

FYI: In my mind I'm thinking of a diffyQ or integral calc course, wher each topic is a new technique. If you've mastered a question from each lesson, of "medium" level difficulty, you've mastered the course. Of course, you could have lessons that cover a couple subtopics. Or could imagine questions that synthesize lessons. But I think one per lesson/lecture/text-section is a reasonable amount for a review.

I would be fine with the obscuring specifics in addition, or better yet, giving specifics, but telling them that the format of the question will be repeated with different specifics. (Thus they can use the question as a drill problem still...but have some need to be able to do more than regurgitate come the final...at least minor differences.)

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