The Problem with Averaging Grades

It is common practice for teachers to calculate grades for their students by "averaging." That is, teachers add up the points students have been assigned for their work, and divide by the number of points possible. Mathematically, that's what "averaging" is--computing the mean for a data set.

For example, imagine that a student received the following marks on assignments throughout the term:

92, 84, 87, 60, 88, 89

Calculating the mean (average) would entail adding up these numbers:

92 + 84 + 87 + 60 + 88 + 89 = 500

And then divide the sum by 6 (because there are six items in the list):

500 ÷ 6 ≈ 83.3

Which means the student's grade would be an average of 83% when written as a percentage.

If you are a mathematician, you will be nodding by now and saying, "Ummm...yep. Your point is...?"

But here's the thing--I think that kind of "averaging" may not accurately reflect a student's learning. Think of the assignments above. Even if you buy into the idea that a collection of points on assignments is an accurate way to measure a student's learning (I'm beginning to really doubt this, by the way), I'm not sure that the 83.3% really captures the true learning. That one "60" brought the average down--probably a whole step on the grading scale, if not more. Does that one score diminish the rest of the learning from the term?

Maybe it's clearer if we discuss really low scores. What if the "60" was a "32" instead? Now the situation would result in an average of 78.6%. Does that seem right? When all the other scores for the term were centered in the upper 80s?

Or how about a zero? What if the "60" were changed to a "0"? (Maybe the student didn't turn in this assignment at all?) Suddenly our student's average has plummeted to 73.3%!

Now, here's the thing--if you would throw out the low score (whether it's a 60, or a 32, or a 0), this student's average would be an 88%.

Thinking over the whole term's scores, what seems to be the truest measure of what our student has learned? 88%? 73%?

And let's really think about what that percentage represents. In the situation resulting in the 73%...does that mean our student has learned 73% of the material taught this term? If our student had turned in that missing assignment--the one we scored as "0"--would that mean our student has actually learned 88% of the material instead?

I think there are four real problems with the Bucket-O-Points method of averaging grades:

1. Averaging grades this way can turn our students into grade-grubbers, fighting for and quibbling over every point. Rather than focusing on whether or not they are learning, they are focused on what they are earning. And don't get me started on extra credit...in my experience, it's not the kids who could really use the extra points who come looking for it...it's the kid with a 98% who really wants the straight "A." (I have other concerns with extra credit as well...not really the point of this post...maybe another time.)
2. Averaging grades this way can turn evaluation something punitive: on the teacher's end, we "punish" students for not turning in work or for doing incomplete work. In my mind, this doesn't really show what students have learned. The meaning of the grade is distorted, and becomes a measure of compliance, rather than a summary of learning.
3. Averaging grades this way can make teachers seek to assess what is easily quantifiable (factual knowledge, right-or-wrong answers) over what is most valued (holistic understanding, depth of thinking.) I'm not suggesting that student shouldn't "know"things. But I hope we are more interested in how students put the things they know together: how they apply, analyze, synthesize, and evaluate ideas.
4. Averaging grades this way seeks to reduce the richness of a student's learning to a single symbol. I think this is a culture-wide problem, not just one in schools. We love to quantify and rank and compare and an average grade allows teachers to do this more easily. The problem I see in this is that this kind of reductionism has to leave things out. A portfolio of artifacts is--of course!--going to be a more authentic means of demonstrating a student's learning than a single symbol. But we have so much cultural inertia behind the quantifying...

I think that we educators need to give our assessment practices a serious, honest look. Does "averaging" really give an accurate picture of students' learning? And if not, how shall we proceed?

Students, parents, and fellow educators, I'd love to hear your feedback and reactions to these ideas!

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A bit of a postscript on this topic...

To be fair, I'm still struggling with this in my own teaching practice. Back in 2007 as a middle school teacher, I began using standards-based grading practices in my science and computers & media classes. Now that I've moved into higher education, I've swapped back into a sort of Bucket-O-Points method. I'm really wrestling with this right now--I continually strive to reduce the gap between my philosophy of education and my actual classroom practice, and I see this as a big problem right now.