Saturday, January 29, 2011

Grading system

In French high schools, grading is in the range [0,20], and typically follows a Gaussian distribution centered at 10 or 11 and with standard deviation about 2.
The correspondence with US letter grades is roughly as follows in my opinion:
A+ 16 and above
A- 14 and above
B 12 and above
C 10 and above
Fail below 8 (makeup exam between 8 and 10).

In US high schools, it seems that grading is roughly as follows:
A 93 and above
B 85 and above
C 78 and above
Fail below 70 (D between 70 and 77, whatever D means)
Weird because most of the information is in the neighborhood of 100.
It makes more sense to think of the complementary measure, i.e. the distance to 100:
A 7 and below
B 15 and below
C 22 and below
Fail above 30 (D between 23 and 30).

This mean that in France, exams are design so that the typical student will be able to answer slightly more than half of the questions, while in the US exams are designed so that the typical student will be able to answer most of the questions.
No wonder my students at Brown say that my exams are particularly challenging!

From an information-theoretic point of view, the French system yields the most information.


  1. If these grading systems only use integers, then it looks like the US system yields the most information since there are more distinct numerical values in common usage than the French.

  2. Perhaps, if graders really understand the difference between, say, a 53 and a 54. I have my doubts on that...

  3. As a final grade I think it doesn't make too much of a difference how the distribution sits, if it is common knowledge. However, does this also mean that typically homework and exams in France are designed so students just get 50% of things correct on average?

    (I see courses like this sometimes and to me it seems tantamount to giving students hard problems they can only solve if they are bright, very dedicated or lucky, rather than teaching everyone one skill at a time in a way that instills confidence.)

  4. Final exams, definitely: their goal is not to teach but to evaluate.

    Homeworks, it depends, but a problem often consists of a sequence of three or four progressively more difficult questions, the last of which can be quite challenging.

    I admit that instilling confidence is not on the radar of the French educational system.

  5. That sounds fair enough. My comment was also motivated by the fact that I just finished grading (part of) 230 first-year calculus exams here in Lausanne, and it's quite a different experience having to meticulously give everyone partial credit compared to back in N America where often half of the students can easily be seen to get any given question totally correct. But, lazy graders are not a reason to make final exams easier.


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