It is not very often that a substitute teacher actually has an opportunity to teach. One of the few occasions when I was able to teach was in a week-long assignment for a middle school math teacher. After two days of work on material having to do with prime factoring, rules of divisibility, and reducing to lowest terms, the students in three separate classes took a quiz, which the teacher had prepared in advance. It included twenty-five problems; all very similar to the problems that had been included on the several worksheets on which we had been working. This particular teacher went to great lengths to insure that his students did not cheat. The students sat at round tables, four students per table. He had constructed interlocking boards that were about twenty-four inches high for the purpose of dividing the table into four equal sections. Prior to every quiz or exam, the students would retrieve the boards from behind a cabinet and would set them up. As a result it would be difficult if not impossible for a student to copy off of a classmate without being seen.
Given the time we had spent on the subject matter and the relatively straightforward nature of the material, I had high expectations, believing the students would do well. To my surprise and disappointment, the results were that better than fifty percent of the 85 students scored below 60 percent and 75 percent of the students scored below 75. Only eight of the 85 students scored above 85 percent, and only two out of the 85 students scored better than 95 percent. In other words there were 43 Fs, 21 Ds, 13 Cs, 6 Bs, and 2 As.
The next day, prompted by my surprise at the results, I spent the entire period reviewing the same material. I did not return the quiz to the students, however, and chose not to review the actual questions from the prior day’s quiz. We worked problems as a class on the whiteboard and I worked one-on-one with the students who appeared to need that level of attention. Great care was taken to avoid doing the work for them.
The following day, I had all three classes retake the quiz. In advance of the retake they were told, in broad strokes, how poorly the class had done, although no one had access to their own results. They were also assured that this was a risk-free venture as I would throw out the lowest of the two test scores. The hope was that this opportunity would motivate the students to improve their scores while alleviating performance pressure.
The new scores showed dramatic improvement by all but a handful of students. Better than ninety percent of students earned higher scores on the second quiz with several improving by two, three or more letter grades. A few students improved from failing grades to As and Bs. Roughly 80 percent of the students from the three classes scored 75 or better and a full third scored 85 or higher, 10 of whom scored above 95 percent (See Figure 1). Given the unlikelihood that the students remembered specific questions or problems, it seemed reasonable to conclude that their scores on the second quiz represented a substantially higher level of mastery.
While this may not have been the most scientific of studies, the level of improvement certainly was not a result of pure chance. The operative question is: Is it worth an extra two days to get such a dramatic improvement in subject-matter mastery. I’ll let the reader decide for themselves.