During my finite mathematics exam today, I had a little bit of time to ponder and I came up with two ideas worth exploring. Most likely, I shouldn’t implement them this semester, but I haven’t ruled it out. For posterity and potential discussion, I offer the following.

**Filling the Empty Bucket**

As a first approximation to the process of learning course content, imagine an empty box. This does not represent the knowledge of most of our students. Everyone has a few items in their box: some old postcards, two dead AA batteries, a dirty single sock, a couple of credit card applications, etc. The goal throughout the course is to fill that box. On occasion, a student might lose some things in their box after partying with Jack from next door and his cousin Daniels. However, with any reasonable effort, a student can keep the flow going into the box rather than going out. At the end of the course, their grade might simply be the percentage of the box that gets filled.

From a grading point of view, this suggests that my usual way of posting grades has a significant flaw. At any time, a student can see what their grade is, computed as a percentage of the possible points *so far*. Ah, there is the rub. A student might do well on the first quiz, regress a bit on the second, look at their grade and see 78%. Not great, but not too shabby considering they only need a C to graduate and they didn’t expect to be so close to a B-. Somehow, I’ve already lost. What if, instead of telling them how they’re doing relative to the available points, I gave them their grade in terms of the whole box? If my philosophical position is that their knowledge at the end of the course rather than their intermediate knowledge should determine their grade, then I should be telling them things like, “You have now mastered 21% of the material.”

There is an obvious problem with the original box metaphor: boxes are generally of constant size. It can’t all be about knowledge, though. I want their box to grow. This is not about content standards, but about them learning to think: the application of knowledge in logical and creative ways. How should I reflect that in the gradebook? Or is a one semester course insufficient to judge such growth? These aren’t new questions. David Cox explains things quite well here. I don’t have any new answer yet…but I’m still thinking.

**The Exam Enigma**

I mentioned in my last post how frustrated I am by the students adherence to the typical college way of studying. I had considered changing the names of exams to something less obvious; perhaps it might fool them. But who I am kidding. If I put it on the schedule, the students will figure it out. Maybe the whole problem is that I separate things in the first place. What if instead of treating these three exams as tests of retention, I simply clumped them in with the assessable standards portion of the grade? Right now, if a student does poorly on the standards, but studies hard and pulls off a good score on the exam, they get two grades: one says they don’t know what they’re doing, the other says they do. That makes no sense to me. I suggest (to myself) that I don’t differentiate quizzes and exams in the gradebook. The 75 minute exam should count no more than a daily quiz, except that the student will see more standards than usual on the test. This remands retention to the final exam.

Does it give the student an incentive to study throughout the term? Maybe it has the opposite effect. Maybe students will think nothing of the 75 minute exam and save up their study power for the final exam. It would be suicide, of course. *They* certainly won’t be able to cram the material in such a short time. Moreover, under this system, the final exam would be 20% and the standards + exams longer quizzes testing standards would be 70%. Some would still put all of their eggs in the final exam basket (another basket metaphor?), but that person won’t be helped by any system of assessment I try.

**A Final Thought (read “Vent”)**

I was told today that one of my students was complaining about homework not being assessed. This student is having trouble because he or she isn’t doing any of the homework, nor asking about homework problems, nor writing me emails, nor attending office hours, etc. The student freely admits all of this, but, for not requiring homework, blames me. What is going on when people want to be treated like little children? Nothing is stopping the student from doing the homework problems but himself or herself. “But if I do the homework, how will I know if I got it right?” Aside from asking me, they could just look up the answers in the back of the book. I put up videos on youtube of me working the review problems. I put up links to videos of people explaining each standard. I beg for students to communicate with me outside of class. But it is my fault this student is struggling and because I don’t require him or her to do the homework? Well, sign up one more for the nanny state. Perhaps a class discussion is in order; let the kids doing the work hear from the kids not doing the work and see what they say to them.

I had a co-worker who taught something like your “fill the box” method. On the first day of Algebra class he gave out a 30 question packet that was essentially the final exam. Students would know 5% or less. Then they’d go over it. Every Friday he gave the same test (different numbers) and watched them improove. At the end of the semester, they almost all got A’s. He thought his method was tremendously successful. Our state gives an end-of-course assessment. His students were on par with the rest of our school and most of the state, so I’m not sure how wonderful it was. But very interesting. I’m not at that school anymore so I don’t know how he’s doing now.

Comment by Mike Mathews — November 3, 2010 @ 10:07 am |