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Grading Students based on “Central Tendency”
I was watching one of your videos on the Stenhouse site this morning and you said that teachers should use central tendency instead of averaging to determine a student's grade because it increases accuracy and is more truthful. I want to be sure that I am clear on what you meant. I understand that there are three central tendencies in math: mean, median, and mode. Mean is the average, median is in the middle, and mode is the one that occurs the most often. When you say "central tendency," are you referring to median?
Thanks for the question. I’m thinking about both median and mode. Basically, central tendency is the most consistent level of performance over time, not all performances over time. Throwing out the outliers, as Olympic judges do, is one approach. It turns out grading on a trend has a higher correlation with outside-the-classroom testing (see, for example, Robert Marzano’s book, Classroom Assessment and Grading that Work). So if we want our grades to represent what we claim they report, we will avoid averaging and instead grade on the pattern of performance over time.
Remember, too, that “average” was invented to get rid of sample error in statistics – that’s it. We can only average scores, data, etc., if we keep the experimental design the same. Because tests have different topics and formats and can include many other distorting factors, we end up changing the experimental design and thus do not get an accurate report of what students know and can do against standards. The best we can do is make sure we have clear and consistent evidence of students’ understanding and learning over time, not single-sitting, snapshot tests that distort the accuracy of the grade report.