Tuesday, February 15, 2011

The Quintessential Question

Recently, I was examining a grade sheet for a class whose grades are calculated by adding up all of the points earned and dividing by the points possible. I admit that's not too exciting. However, my mind needed some form of distraction and started playing around with the numbers on the sheet. Then, I began to notice some anomalies.

Consider the following situation, which I put into a graph:



There are two students, Bob (the black line) and Joe (the red line) whose understanding of the content material does not match their grades.

Allow me to explain this (unrealistic and overly simplistic) situation. There are two students, Joe and Bob. Their understanding of a certain idea will be mapped by five various assignments (worksheets, tests, etc.) and will be averaged together at the end for their final grade on this concept. Each assignment is worth one hundred points, and no one assignment will be weighted above the others in the final averaging.

Now, Bob's (black line) understanding of the subject is superior to Joe's (red line). However, on the day of the first assignment, his girlfriend breaks up with him, his grandmother dies, and he falls on ice and breaks his arm. He's somewhat distracted, and he lets it get to him--in fact, he only earns 60 of the 100 possible points. Joe, however, is having a good day and is able to guess his way through this assignment (it's all multiple choice) and aces the paper. In addition, he brought in a box of Kleenex, so he was able to tack on 10 more points to his "grade."

Here's where the problem comes in. Bob actually understands the subject matter, and is able to receive all of the 100 points possible on the four following assessments of his knowledge. He is consistently able to demonstrate that he knows what he is talking about.

Joe's luck, however, does not continue to hold out. On the next assignment, he only earns 95 of the potential points, then 90, then 85, and so on, losing 5 points from his score each time. If these assessments are truly gauging the knowledge these students have, then shouldn't we conclude that Joe does not fully understand the material--and shouldn't we also conclude that Bob's grade should be higher than Joe's?

However, at the end of the series of assessment of knowledge, Bob's and Joe's grades are equal--a 92%, 460 points earned out of 500 points possible. Although I may be becoming a parrot, this is the primary flaw with using averages to determine a grade: averages include the history of a student's understanding instead of the student's current understanding.

This seems to be the question every edublogger asks: Which is more important, the history or the present?

To me, it's clear that the answer is the present. What about you? 

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