Monday, May 21, 2007


The agony of algebra

This semester I did something I had never done before: I refused to return an exam.

The circumstances were admittedly unusual. My introductory algebra class had lurched from one disaster to another. The latest was the exam for the last chapter in the syllabus. The standard syllabus for introductory algebra finishes up with the quadratic formula, providing the attentive student with the means to solve any quadratic equation. It's a nice pay-off. My students in previous semesters have customarily done well on the test for the last chapter, even though a few of them always insist on using the quadratic formula even when it would be simpler and neater to use factoring, or perhaps completion of the square.

No matter. The quadratic formula is a nice, neat package and students tend to grasp its utility fairly quickly. What's more, I downplay memorization in most of my classes and permit students to use a handwritten notecard during exams. There's really no excuse for running into serious trouble on the last chapter test of the semester.

This semester my students ran into serious trouble. The average score on the exam was 58%. An F plus, I suppose. And the clock had run out. It was the last day of classes and we were supposed to be reviewing for the final exam. My students morosely awaited the results of the chapter test, but I declined to pass them back. Instead, I handed each student a blank copy of the exam that most of them had failed. Each copy came with a cover sheet. The cover sheet gave these specific instructions:
  • Work out each problem carefully on scratch paper, showing all your steps.
  • After you have checked your solutions and are confident that your work is correct, carefully write out a detailed solution on the exam.
  • This take-home exam is due by noon on Monday, in my office. You can slip it under the door if I am not there. Late papers will not be accepted. Hand in the exam only. No scratch paper.
  • There are no restrictions on the resources you use to complete this exam. Use your notes, your text, and consult with others. The writing on the exam, however, must be your own.
  • The score you receive on this exam will be entered into my gradebook as a new exam, equal in weight to the others. It is therefore a good idea to take advantage of this opportunity to score 100. (This new exam is in addition to, rather than a replacement for, the previous exam.)
  • I will answer questions you may bring me during my office hours, but I will not solve the exam problems for you.
  • In addition to giving you a chance to raise your score, this test rerun will be good practice for the final exam, which will contain several problems similar to those on this chapter test.

A week went by and some (not all!) of the students returned their take-home exams to my office. I promptly graded them. After a full week of taking a second crack at an exam they had already tried once before, with no restrictions on seeking assistance, what were the results? Brace yourself.

From high to low, the take-home exam scores were 97, 96, 96, 96, 95, 95, 89, 70, 69, and 69. The 90s aren't too surprising, are they? The last three, however, especially the two 60s, are just gob-smackingly awful. And three students didn't bother to turn the exam in at all. You can do the math: five of my thirteen students did not pass an exam (originally intended as an in-class test) that they had been allowed to take home for an entire week.

I can confidently state that the teacher and students are united in their eagerness to see an end to this semester. Then the healing can begin. And half my students can sign up to retake the class.

Please, not from me!


John Armstrong said...

Makes me wish I could roll up the exam paper and tap the students on the nose with it.


PlatoisDerrida, said...


I've seen similar, if not more perplexing, behavior in the humanities classes I teach. This semester I gave a pop-quiz which half the class promptly failed. So, I told them that they would be taking the same quiz the next class, and reminded them what the questions would be. At the next class meeting, only one more student passed the quiz.

Perhaps "F's" are like tattoos--a mark of defiance and rebelliousness against "the man" and his unreasonable expectations that they read and then study the assigned material?

Brian said...

Back when I was teaching calculus as a TA, I came up with a policy to encourage students to pay more attention to the homework problems I assigned: one problem would get used on the next quiz. No reworking the format of the problem, no replacing names of variables, no changes at all.

After one homework assignment, I was puzzled why people hadn't done so well on one particular problem. So, we discussed it in class and I worked out for them how to solve it. (I no longer remember anything about the problem other than I didn't consider it one of the more difficult ones.)

I thought the attention I lavished on the problem A) would've made them understand its solution, and B) given them a hint I thought it important and they might be seeing it again.

Of course, I put it on the quiz and their performance on that problem was equally dismal. We went over it yet again in class, they diligently wrote down every word I said and copied every scribble from the board, staring at me blankly when not writing.

You can probably guess the next development. I put the same problem, verbatin, on the next test. And, of course, you can guess the outcome.