Lately I’ve been wondering about what the goal of education actually is: are we solely in the business of educating, ensuring that our students learn the “correct” strategy, or are we in the business of student confidence?
During my math education class, there was a time when I and all my classmates used cut-out circles to demonstrate several geometry theorems pertaining to the circumference and the diameter of a circle. Next, we were given a fragment of a paper plate, which mimicked an antique plate fragment that was shown on the screen. We were told to trace along the edge of our paper-plate fragment onto a piece of paper and try to reconstruct the entire plate on the paper.
Since we were not told how we were to accomplish our task, I simply traced the rim of my fragment several times (with some overlap so that I drew a consistent curve) until I had drawn the entire plate’s rim. I then tried to imagine what the patterns on the antique plate would have looked like were the plate complete, since I thought the objective was to use our recently discussed geometry principles once we had completed our plates; I did not use those principles to reconstruct the plate itself.
After looking at my classmates’ reconstructed plates, it was clear that my understanding of the task had differed significantly from all others’ I saw. I was unsurprised at my different interpretation—that has happened many times in my life!—but I found it quite interesting that when I brought my interpretation to the instructor, I was not given advice as to how to apply the technique I was supposed to have learned; on the contrary, I was congratulated on finding an alternative solution.
This began an “internal debate” in my mind: is it more important for the student to learn the technique or accomplish the task in a creative way? Perhaps the answer to that question depends on the situation, but I began to re-evaluate my own teaching approach and wonder whether I had discounted my students’ perfectly rational solutions in the past for the sake of achieving specific lesson objectives.