Friday, December 23, 2011

My other theory on grades

Assignments are either for helping the students learn, or for evaluating them. Grades are either to give them an incentive to do the work involved in learning, or to evaluate them. Two very different goals!

For evaluation purposes, grades give the maximum information is the distribution has maximum entropy, so ideally there ought to be about 1/3 A's, 1/3 B's, and 1/3 C's.

For evaluation purposes, assignments are most useful if they help distinguish students from one another, so the ideal exercise is at the right level of difficulty so as to be solvable by exactly half of the students. An exercise that is successfully done by all serves no purpose for evaluation. An exercise that almost no one can do may still serve a purpose: that of distinguishing the few students who stand out by their ability to solve a problem that the vast majority could not do. Exercises with a variety of difficulty levels help evaluate more finely. Since the primary goal of midterms and finals is to evaluate, that's how they should be designed, and the median grade for those would probably be around 50. In fact, that's more or less how things are done in France. The learning part happens in exercises that are not graded, and the sole purpose of grading is to evaluate.

In the US, my experience is that assignments are usually designed so that, with enough time, most students can do most of the assignment: their primary purpose is to help the student learn. A very different perspective!


  1. I in fact have long done what you say here. My assignments are indeed designed so that most students can do most of the assignment. On the other hand, for years my midterm and final have had an average score of about 65-67%, which is not quite your 50%, but there's only so far you can go. Also, the midterm and final scores are generally roughly uniform across a very large range.

    It's nice to see a post-hoc justification for this approach. I'll find a way to get my students to read this...

  2. A mix of the two would be to give difficult assignments but allow students to correct incorrect solutions until they have correct ones.

    That way less capable students do not leave only with the bad impression of continually failing; instead they might become aware of their relative weaknesses while gaining the positive experience of conquering a problem even if it takes them longer.

    At the same time you still have enough (in fact more) to evaluate them on, looking at the time it takes them to solve the problems, the amount of supervision they needed etc.

  3. Hi Claire,

    My approach is complementary to yours. I don't like the fact that mid-terms and finals are quite time-bounded, especially for undergrad classes where I prefer to not give take-homes: as we know, much of real-world problem-solving doesn't come with a very tight deadline. Therefore my assignments are typically (much) harder than my exams.

  4. Aravind, doesn't real-world-problem-slolving come with conference deadlines? In my world, it does :)

    Anyway, I talk about "my theory" as though that was well thought out. This would actually be more appropriately called "random musings".

  5. I tend to split evaluative purpose of grades a bit further. My homework grades are primarily meant as feedback to the students, telling them where I think they need to practice/learn more. My exam grades, on the other hand, are primarily meant as an evaluation for people reading the students' transcripts.

    (Of course, it's not quite that simple; homework grades contribute a small amount to the final course grade, and I have midterms instead of a six-hour final partly to give the students intermediate feedback.)

    My homeworks are also designed so that most of the students can actually solve most of the problems. My exams are designed so that most students can MOSTLY solve most of the problems, except the first problem on each exam which everyone should get.

    Of course homework problems are much harder than exam problems. Homework problems can be solved over several days with help from other people, and they're designed to stretch the students' brains even with those extra resources. Exam problems have to be solved alone in 15-20 minutes from a cold start, and they're designed to see how far the students' brains are already stetched.

    "...their primary purpose is to help the student learn. A very different perspective!"

    Really?? How do French students learn to solve problems, if not by solving problems?

  6. They have problem sets that are not graded.


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