Monday, March 31, 2008

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.


Anonymous said...

Oh dear. I tutor calculus, and I recently had a student who'd managed to make it all the way up to calculus with no understanding of what a weighted average is.

kai said...

Though, it seems to me if the student in question couldn't figure out the scoring, she had reason to worry about her performance…

Zeno said...

I'm afraid you're right, Kai. The student in question has now demonstrated that her inability to understand weighted averages extends to the concept of doing decimal arithmetic with signed numbers.

Megan said...

I was a TA in a class (not math) where there were a million points possible. Quizzes were 20000 points each. Exams were 250,000 points, with individual questions worth 1000 to 10000 points. The problem with this method is that it's possible to lose track of the zeros... I gave a students 50,000 points on a 5,000 point question, which was only noticed when we were tallying pages, and the page didn't have that many points on it.

But, all points were equal!

(I think this instructor didn't like people whining about "I'm only half a point from an A!" so thought this would be a great way to avoid the issue. Instead, it was "I'm only 5000 points from an A..." was the new mantra. I didn't see how this was an improvement, but what did I know, I was just a TA.)

Rhoadan said...

As I found out recently in a class on accounting, sometimes the problem isn't the concept of weighted averages; it's the implementation. I was having to calculate interest payments for an annuity, and kept weighting things from the wrong part of the year. I eventually got it right. *sigh*