### Sunday, March 11, 2007

##
Average grades

What should an average grade be? This question actually has two very different but intertwingled meanings. Some people, when they ask it, are wondering whether the mean (or perhaps median) grade in a school/department/course should be a B or a C or whatever. Others are asking about scaling tests: is it OK for the mean (or perhaps median) grade on a test to be 90%? or how about 30%? If the answer to the first question is, say, B–, then should the 90% or 30% — or whatever — be scaled to a B–?

There is, of course, the persistent myth that C is an average grade. Maybe it used to be, and maybe there are some places where it still is, but real or imagined grade inflation has bumped the mean (or perhaps median) to a B– or B. At Harvard it’s an A–, but that’s another story. As long as people understand the system, it’s totally arbitrary whether the average (all right, I’ll stop saying mean or median, since it’s almost never clear which measure is meant) is B or C or Q — there’s no intrinsic meaning to the symbol, after all. What counts is the

Overall, 32% of our Math Department’s grades last year were A’s and another 42% were B’s, thereby making the median a fairly high B. But this leads to the second interpretation that I mentioned in my first paragraph. Some teachers grade by an old-fashioned equivalence of 80–82 for a B–, 83–86 for a B, and so forth. By so doing, they are implicitly promising that the level of difficulty of their questions is such that a minimally competent student will get about 80% on them (assuming, of course, that a B– represents minimal competence, which sounds reasonable to me). I have two difficulties with this traditional but thoroughly arbitrary scale. First, how can a teacher be so sure that the level of difficulty of the problems on every test reflects this matching of 80% with minimal competence? Second, I believe that using this scale is an indication that the students aren’t being sufficiently challenged. In the class described by the student quoted in the previous paragraph, the median grade was still a B, but it’s clear from her comment that there were plenty of challenges and high academic standards. One way to achieve these is to ask some really hard questions while rewarding good work that falls short of 80%: on some tests 75% was worthy of a B–, on others it might be 70% or occasionally even lower.

I do worry, however, when the scale is so extreme that a class median is 30% or 40%. Students may then get discouraged because they think they are being rewarded for inadequate work or because they are able to complete so few problems with successful solutions.

There is, of course, the persistent myth that C is an average grade. Maybe it used to be, and maybe there are some places where it still is, but real or imagined grade inflation has bumped the mean (or perhaps median) to a B– or B. At Harvard it’s an A–, but that’s another story. As long as people understand the system, it’s totally arbitrary whether the average (all right, I’ll stop saying mean or median, since it’s almost never clear which measure is meant) is B or C or Q — there’s no intrinsic meaning to the symbol, after all. What counts is the

*relative*average when we compare one population with another. For example, studies of the achievement gap often compare grades across racial or economic groups. Another interesting comparison is across departments. At the aforementioned Harvard, for example, grades are significantly higher in the humanities than in math and science. At Weston High School, a recent interdepartmental study showed that 38% of all History grades were A’s, but only 24% of all Foreign Language grades were A’s. Temporarily removing Foreign Language from the study, we find higher grades in History and English than in Math and Science, just as Harvard found. An article in*Wildcat Tracks,*the school newspaper, attributed most of this discrepancy to differences in the “difficulty” of each department, though one of my former students (from last year’s honors precalculus) is quoted as saying, “Math last year was the hardest class because my teacher was extremely challenging and had high standards.” I take that as a compliment, though I’m not sure that it was intended to be.Overall, 32% of our Math Department’s grades last year were A’s and another 42% were B’s, thereby making the median a fairly high B. But this leads to the second interpretation that I mentioned in my first paragraph. Some teachers grade by an old-fashioned equivalence of 80–82 for a B–, 83–86 for a B, and so forth. By so doing, they are implicitly promising that the level of difficulty of their questions is such that a minimally competent student will get about 80% on them (assuming, of course, that a B– represents minimal competence, which sounds reasonable to me). I have two difficulties with this traditional but thoroughly arbitrary scale. First, how can a teacher be so sure that the level of difficulty of the problems on every test reflects this matching of 80% with minimal competence? Second, I believe that using this scale is an indication that the students aren’t being sufficiently challenged. In the class described by the student quoted in the previous paragraph, the median grade was still a B, but it’s clear from her comment that there were plenty of challenges and high academic standards. One way to achieve these is to ask some really hard questions while rewarding good work that falls short of 80%: on some tests 75% was worthy of a B–, on others it might be 70% or occasionally even lower.

I do worry, however, when the scale is so extreme that a class median is 30% or 40%. Students may then get discouraged because they think they are being rewarded for inadequate work or because they are able to complete so few problems with successful solutions.

Labels: teaching and learning, Weston

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