Crushed by the weight

Innumeracy strikes again

My student was deeply concerned. Deeply and unduly. She was worried about her quiz scores in our prealgebra class and beside herself with concern over the points she had lost. I hastened to set her mind at ease. I failed signally.

Many of my colleagues and I like to give frequent short quizzes to keep our students alert and to underscore the topics we mean to emphasize. Most of us, however, choose to give rather little weight to quizzes in computing the semester grades. After all, they're used more as learning tools rather than proficiency assessment tools. I like to give quizzes at the beginning of the period, after which I immediately solve the problems on the board. Since the students were just struggling with the selfsame problems, it's often a teachable moment. If the students pay attention, they'll be ready to acquit themselves well on the exams. Quizzes ought to count, but not too much. These days I've been weighting quizzes at 15% of the course grade. (The bulk of the weight is allotted to the chapter tests and final exam.)

My students, unfortunately, tend to have difficulty with the concept of weighted averages, and those who most need to understand it are the least able to puzzle it out. My prealgebra student is a case in point. She sees the points assigned to the quizzes and tests and cannot help but consider them equivalent. Since I grade quizzes on a 20-point scale, she figures that five quizzes must be as important as a 100-point chapter test. In reality, if I were to try to grade quizzes on a scale that takes into account the relative weights of quizzes and exams, the quizzes would be only about three points each. Of course, that would make grading them quite difficult.

Perhaps I should make the exams each worth 600 points instead. Some of my colleagues have decided to do something like that, simply making all points equivalent. They accumulate them throughout the term and assign grades to students on the percentage of points earned. Such a system, however, is not to my taste; if you decide to give more quizzes, they automatically count for more. By prescribing their weight in advance, I can control their impact on students' grades.

The downside, of course, is clear. The students don't understand the grading system because weighted averages are too complicated for them. Rats. Nevertheless, I'll take another run at explaining the weighting system after we've done the prealgebra unit on percentages. I'm a math teacher. Hope springs eternal.