Friday, August 8, 2014

"The Points Don't Matter"

[TL;DR:  Tthere is not much difference in the average grade for a course if you redistribute the weights for exams, homework, and the like after the fact.]

When students see a new course syllabus for the first time, the first thing many look for is the breakdown of grading for the course.  "What do I have to do to get the grade I want?"  At least I always did.  Every semester, every class.  Not ashamed to admit it, either.  That university curricula are so grade-centric instead of outcome-centric (and have been for decades) is a rant for another page, and has been addressed thoroughly, here, here, and here among probably a dozen other places.

But does the course grade breakdown really matter that much?  That is, do the weights we assign to each category of work truly have a large impact on final course grades?  To find out, I pulled up the grades for an introductory course I taught a couple years ago and recomputed their final grades using five different weight combinations.  There were about 30 students in the course, and in terms of structure it was rather mundane: lecture, homework, quiz, exam.  It was earlier in my teaching career; forgive me!

Here are the breakdowns I tested, using all the assignments we did that semester:


Homework Quiz Exam 1 Exam 2 Final
Option 1 25% 15% 20% 20% 20%
Option 2 40% 10% 10% 10% 30%
Option 3 20% 10% 20% 20% 30%
Option 4 20% 10% 15% 15% 40%
Option 5 30% 20% 15% 15% 20%

Depending on the instructor, I think any one of these breakdowns would be pretty standard for a lower-division science course that doesn't have much of a team-based or lab component.  But standard as they might be, each of these five would potentially have huge impacts on student perception of the course and the instructor (especially option 4. Brutal!).  And I'd say it's highly likely that study and work habits would be different too, depending on what the actual scale was.  I know of no way to test how different those habits would be if students had been presented a different distribution up front -- we can only look at how grades would be different after the fact.  If you know a better way, please hit the comment box below.

So yes, I'm making a key assumption here:  to make this comparison I have to assume that perceptions and study habits and such would not be different as students complete any given activity, regardless of which of the five breakdowns would be used.  Again, I know this is a stretch.  For each option, here is the distribution of the students' final grades:



Highest 75th %-ile Median 25th %-ile Lowest
Option 1 99 87 80 70 53
Option 2 99 87 81 67 54
Option 3 98 88 81 70 52
Option 4 99 88 81 68 51
Option 5 99 86 80 70 53



From a class-average point of view, every option gives a nearly identical distribution!  The greatest variability occurs, expectedly, at the bottom of the distributions which includes students who were badly deficient in one of the categories (rarely attended class so had quiz grades < 50%; missed or didn't turn in key homework or team assignments; poor test takers; etc.).  I also checked the number of students who achieved 90%, 80%, etc., as those would be my rough cutoffs for letter grades.  No surprise: for this course the number in each category changed by no more than one student (out of ~30) regardless of which category distribution was used.

Because it's much more recent, I won't show the results from another course, although they are very similar.  To me, it's clear that as long as the distribution chosen is a reasonable one, the actual percentages simply don't matter that much to final grades.  We'll almost always curve a point or two, here or there, to accommodate bad exam questions and grading mistakes and uncertainty and whatnot, and so even the variability in the lower half of these distributions is just in the noise to me.


Have I tried to use this information to the advantage of my students?  Yes.  Given that test anxiety is real and observable, I've lowered the stakes on my in-class exams (toward something like option 5 above) so that those assessments count a little less, and the untimed and out-of-class work counts a little more.  Because of the tendency to think of out-of-class work as "grades I earn" and exams as "grades you give me," students hopefully will take more ownership of their learning when the percentages shift in their favor.

Even though, ultimately, the points don't matter.  Much.  :-)

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