Wanna Bet?

I adjunct teach a class in employment law. I have only three students for this class. I told all the students that attendance at the second-to-last class was mandatory. Do not miss it. And in this penultimate class, I gave my students a gorgeous present. As gift-wrapped as I could make it.

So to prepare for class tonight, I went through the final examination, which I will administer next week. I sculpted a lecture addressing each and every question on the examination. I began my lecture by announcing: “I am about to tell you, in plain and direct language, everything you need to know to get a perfect score on the final exam.” And so I did. If the students paid attention during this last lecture, they will get every question on the exam correct. I did not present the material question-for-question or directly in the order of the test; I did not say things like “the answer to question 54 is ‘C'”. Rather, I worked a discussion point with the correct answer to each question in my substantive review lecture: For example, “There is no reverse discrimination cause of action in an ADEA situation; workers over 40 are protected but workers under 40 are not.” The students took notes furiously.

This is an experiment of sorts. What do you predict will happen? After all, I gave away all the answers. Directly, frequently quoting from the test itself. And I am quite certain that I stated the correct answer to each of the 100 multiple choice questions that are on the test. The last time I gave this test, the average score was 74.8 out of 100 with a standard deviation of .978. (I was quite disappointed and questioned my own abilities as an instructor afterwards. Then I saw that at least half the questions they missed were the easy ones. So I got over it. Their bad test scores were on them, not me.) This will be the exact same test.

My thinking is that if a student did not understand the subject in the first place, the summary will do her no good. So my prediction is that I will see no significant effect whatsoever on student performance as compared to the previous administration of the test when I did not give a “gift-wrapped answers” lecture.

Anyone care to make a little wager on this — the stakes being, say, a post by the loser on the subject of the winner’s choice?

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28 thoughts on “Wanna Bet?

  1. Three students is too small a sample either to make a sensible prediction about or to draw any conclusions from. If you had more students, I’d predict that the mean goes up some but the SD goes up a lot, as the students who do take advantage of being given the answers separate themselves from the others.

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  2. I agree with Mike about the sample size, but I’d also add that 100 questions is a lot to cover in one lecture, too much for the students to absorb. So I doubt you’ll see much difference.

    Heck, in my American Government class (although unlike yours, it’s just an intro level college course), I give them all the questions (short essay) in the syllabus and cover them all in class. Exams are still rather…disappointing.* Unless one is a particularly bad professor, I think, grades are overwhelmingly dependent on the students’ abilities and own choices about investing in the process.
    _________
    *Each year I’m curious to see what the most wrong answer will be. This year’s winner was on how federal judges are selected. Apparently you have to be a police officer, then a state police officer, then a sheriff, then move up the ladder in courts and be elected a federal judge by the people.” Or maybe it’s the example of a nation-state as “a town or city in Ohio.” But those are from students who regularly chose to not come to class. It’s hard to teach them when they’re not there.

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    • I’m inclined to agree with the latter part, but not the former.
      Law is made up of rules and exceptions. If you don’t know the rules, knowing the exceptions is of limited value.
      One week might be too short a time to cultivate a meaningful understanding of basic concepts, though it might be tremendously valuable for a student whose notes are insufficient in a few isolated places.

      I’m thinking the students’ coursework through the semester is more indicative of individual interest and drive, and their scores on the finals will not deviate significantly from those averages.

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      • Hopefully this doesn’t leave you asphyxiated, but how about this answer to the question of how a bill becomes a law?

        First the bill must be voted on at a state level. [Then] it gets sent to the trial courts. Once it is there it gets sent to the congress and Senate…

        I’m telling you, though, these are from the students who skip class a lot. You’d think, “Oh, surely they learned that in high school,” but I’m pushing beyond the basics to significant details of these things, and I wonder if they catch onto that and think, “Oh, he wants those significant details, not just what I learned in high school, but I don’t know what they are, so I’ll take a wild stab and hope it’s close.”

        At least that’s my more charitable hypothesis. You can no doubt guess what my less charitable hypothesis is.

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    • Once, in medical school, I took a test that I knew going into it I would likely fail. (I had, for some reason, really struggled with the class.) Sure enough, I had no clue for many of the questions. So I simply tried to come up with amusing answers. I only remember one such answer, lo these many years later. We were asked the function of a couple of cellular proteins, to which I wrote “They make lovely book-ends.”

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  3. I don’t apologize for the long test — this is graduate school, after all. Not supposed to be easy. Agreed that 3 is too small a size for statistical significance, but that’s the difference between gambling and actuarial analysis.

    My thinking is that if a student had previously absorbed the material, a review of this sort is helpful. I was just explicit about what specific topics were under review. If the student has not yet learned the material, yeah, this would have been a sip from a fire hose and not a particularly useful thing.

    I hope I’m proven wrong, of course — it’s pleasant to see students perform well.

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    • If I came across as critiquing the long test, my writing is at fault. I didn’t mean to do that;* I was just commenting that it’s too much material to really take in during one class period (although, of course they should have learned it across the semester, and this is just refresher).
      ____________
      *Although, for my own part, I decided last year that I didn’t really need to test them on everything, I just needed to make them study for everything, then test a random sample of the questions. So of the ~70 short essay questions listed in the syllabus, I choose 8 to test them on. It makes grading faster, and as far as I can tell so far there’s no observable difference in the grade distribution. (I’m open to suggestions on the proper number of questions to choose, though. Any more mathematical folks around here have a comment on that?)

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      • James, I had a high school history final like that. First day of class, Mr Carl* gave us a list of about 25 questions and said “Here is the final, I will pick 3 questions, you get to pick one.” The questions were along the lines of Teapot Dome- describe the situation, the principle actors and the political fallout. Can you relate this to any of today’s politicians, etc.

        *He was one of only a handful of teachers that I can remember today, let alone their names. In my entire scholastic career, he was probably the best teacher I ever had.

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  4. Semi-related, I had two college professors take two interest approaches to exams:

    1.) Survey of Bio. The class was 200-300 students and met at 9AM so attendance was relatively low. I went to most but not all classes. During one of the classes I missed, the professor said, “Here is a question I will put on the exam. Those of you who are here and paying attention at this very moment will get it correct. People who are not here are very likely to get it wrong.” The question was something about the percentage of DNA that humans share with chimps and the choices were 95%, 96%, 97%, or 98%… something like that. The sort of question you either knew the exact answer to or you were guessing. Basically, kids who attended every class (or who happened to attend that class) got an extra couple points on the exam.

    2.) Intro to Philosophy. The professor was a bit of a nutball but he LOVED himself some philosophy and wanted to do more than just gloss over the heavy hitters. Despite it being a 100-level course and most people were there simply to fulfill their requirement, he wanted to push us. So, he told us on day one that the final exam was included in the syllabus. I don’t remember the exact wording, but it was something to the effect of, “Given what you have learned in class, tell me who you are and how you define a good life.” You had to cite the different philosophers and how they did or did not comport with your outlook on life. You could bring in whatever resources you wanted since if you didn’t already have a pretty good command of the material, the books weren’t going to help. On test day, he simply handed out the blue books and said, “You know what to do.” We all got to work. Well, save for one gentleman. He had been at just a handful of classes. After sitting quietly confused for about 10 minutes, he approached the professor and said, “I didn’t get a test.”
    “Yes you did. On the first day of class.”
    “I don’t understand.”
    “And it apparently took you 10 minutes to figure this out.”

    He left in a huff.

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      • If I may, I did not have a single high school teacher that offered us a syllabus. When I went to college, I spent the first week of class not doing homework because the teacher never said, “Here is your homework for tonight.” By the second or third day, I leaned over to the person next to me and said, “How did you know what to read?”
        “It’s in the syllabus, dude.”
        “What’s a syllabus?”

        Fortunately, I caught my failing early and self-corrected.

        But it makes me wonder… in elementary ed, we often talk about the assumptions we make about what students know and how this can lead to failure. There are things it is probably fair for us to assume students know and that which it is probably unfair for us to assume students know. I’m curious… does this sort of thing happen at the university level? Does anyone say, “We should spend 5 minutes making sure students know what a syllabus is”? How unique was my experience of not interacting with a syllabus before arriving at college?

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      • I’d never seen one before either; but I looked at it, read the first few lines, figured out what it was, then worked two weeks ahead of the class from then on out.
        I just assumed that if it was something they were giving me, and it had words on it, it must be important in some way.
        Later, I figured out that sticking to the syllabus isn’t required. But most do.

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      • ,

        I’d like to assume students know what a syllabus is, and that they’ll read it on their own. But with frosh? Lord, no, so I go over it. With Jr/Sr level courses, though, I just do it briefly, to highlight my expectations and how they’ll be evaluated.


        then worked two weeks ahead of the class from then on out.
        Ah, we all love students like that.

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  5. The last time I gave this test, the average score was 74.8 out of 100 with a standard deviation of .978.

    So everyone scored between 72 and 78? Or was the standard deviation 9.78?

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    • The first thing, . Your math is also exactly correct, which in your case I find completely unsurprising. (That, of course, is a compliment.) The first test had a small universe, too. So when I saw all the scores clustered together around a disappointingly low point, that made me wonder if I had somehow failed as an instructor. Until I saw the questions that came back wrong most frequently, and saw that they were all the “easy” ones (the ones operating at the recapitulation level, i.e., pick the correct definition for this bit of jargon). They did better than I expected on the “hard” ones (the ones operating at the integration level, requiring application of fact to rule and picking the correct result). Mystifying, but indicative that they skipped over a lot of the foundational stuff in their study, which to my way of thinking is an elision attributable to the student’s study habits, not the instructor, so long as the instructor did indeed cover the topic at all, which I had.

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  6. I agree with the above on sample size, but my entry into the wager would also depend on the nature of the students. If they are mid-level management professionals, accustomed to the corporate training environment where answers are more often than not hand fed for the purposes of subsequent examinations that establish ‘metrics’ but where it isn’t necessary to differentiate individual performance, I think they should do OK. They would be used to such a scenario (and may even expect it).

    Nevertheless, there will still be about a third of the group that still don’t know how to play the game despite long time experience.

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