Thursday, December 4, 2008

on to exams...

Mr Burchell Mr Burchell, what can I do to bring up my grade?

Last day of classes this semester.

My students are in desperation mode as the exams draw near and they start to care about their grades. I have enjoyed playing a different role in exams these past few years. As a teacher, I am on the side of accuracy and validity, and that role comes with its own responsibility and stress. The student objective in the situation is to somehow or other obtain a grade which favorably misrepresents their skill level. This desire for an A transcript with C work leads to many of the crises that dominate my interactions with students lately. They are not genuinely worried about seeing an unfair exam, but the idea of a fair exam has them all a little jumpy.

In a few of my classes today, the topic of negative marking was brought up by students. Part of their exam will be multiple choice, so they are concerned about negative marking. Anyway, negative marking was a hot topic because I quickly told them that it is a great idea, which made about three more of them look up with terrified eyes at the teacher who might take away their not-so-secret weapon on multiple choice tests: blind luck. I find that topics involving grades are fertile ground for effective discussions about math. Students care about their grades more than they care about most of the other topics we discuss, which is ironic, because if they paid attention to the other topics... but that's only my humble teacher opinion.

Negative marking represents another one of those badly misunderstood tools of education that bring out the irrationality of students.

I once wrote a monograph on the subject... a mere trifle, really. The subject of negative marking, that is, not the irrationality of students. And it's not really a monograph, but a handout. I am still researching the irrationality of students.


  1. I had never heard of negative marking before. Wow! Thanks for the great idea, Nate. I dread super long essay exams and short answer finals are usually overwritten anyway and in the interest of not spending forty billion hours grading finals, I've been toying with the idea of including some multiple choice next semester. Negative marking makes it all seem a little game-showy. Are you SURE you want door number one? More fun, right?

  2. This is the system used on SATs. Great monograph. You summed it up nicely and covered all the angles. That being said, I'm very glad that many of my teachers did not use this system. It inflated my grades a bit.

    Also, nice Homes reference in the last paragraph of your blog entry.
    -Dave Bliss

  3. I enjoyed your monograph, even though my eyes were starting to cross by the time I got to the end... probability never was my strong suit, as you probably (nearly 100%) remember... that and the phases of the moon...

  4. What happens if a student is a bad guesser ans gets all the questions wrong.
    The student actually gets a negative score. Perhaps grades lower than F will need to created for this case.


  5. Well, the student could indeed be a bad guesser and get 0 of the guesses correct, in fact probability suggests that it will happen (but rarely). The important thing is that with negative marking the error has an average of zero and is due to chance, while without negative marking the error is predictably positive and is due to a flawed measurement. In other words we know something systematic about the error which is not due to random chance.

  6. ...Negative marking does not get much use except for those scientific tests that are carefully designed to measure your ability, because for statistical reasons it takes care of a few biases afforded by the multiple choice format... For the everyday tests, only the most cold-hearted teacher would begrudge a student a 20% that was the result of lucky guessing.

  7. So, that's why I didn't do so hot on my SATs... just kidding!