Demotivation
In fourth grade, our class was learning about long division. I remember figuring out a shortcut (though I don’t remember what it is now) that allowed me to do the same operation, but with marginally less writing, perhaps a 20% savings. I think that basically my “improvement” amounted to me recording some intermediate quantity in memory instead of writing it down in the appropriate position on the paper, as the teacher had instructed. It’s worth noting though, that I was still doing most of the math on paper, using basically the same procedure that the teacher was. I just made a modification to it that made it more efficient and less tedious for me. I showed my work, and got all the correct answers using my modified procedure.
Perhaps unsurprisingly, given the common modes of teaching employed in elementary school math classes, my teacher was not impressed by my modified procedure. I can’t remember whether or not I approached the teacher directly about my method before turning in my work, or if I confronted the teacher after my work had been graded. What I do remember is that when I tried to explain how my “improved” procedure worked, the teacher basically just told me it was wrong. Despite getting the correct answers on my homework (and showing my work), I received only minimal credit. I was told that in order to get credit for my work, I must follow exactly the same procedure that the teacher had shown. As far as I could tell, the teacher didn’t even understand what I was doing, despite my attempts to explain why and how it worked.
I still find it very frustrating to think about that scenario, and not just for myself, but because it is indicative of a larger problem in the American academic system, wherein intelligent, motivated students are discouraged from finding creative solutions to problems and from seeking intuitive means of understanding course material. Instead, in many cases, much more emphasis is placed on following directions than on developing an understanding of important concepts. Students who approach course material from perspectives different from the teacher are commonly shut down without consideration, and are often threatened with failure if they challenge teachers’ preconceived notions of how things actually work, or whether or not there is a “right” way to solve a problem.
I had other similarly discouraging math experiences in elementary school as well—the fourth grade scenario mentioned above is a good example, but it was by no means a unique incident. I was extremely frustrated and discouraged by that particular teacher’s dismission of my work as incorrect in spite of the fact that my procedure (1) arrived at the right answer (2) clearly demonstrated that understood what I was doing and (3) took less time to do the so-called “right” way. One result of that frustration was that I disengaged from that lesson, and developed a long-standing distaste for long division. The cumulative effect of the many similar experiences that I had from second grade well into high school was that by the time I graduated, I thought that I hated math.
Throughout my undergraduate program, I didn’t take a single course dedicated entirely to math—it wasn’t required and I had no interest in subjecting myself to more frustration and discouragement. When I decided to go to grad school however, it quickly became clear that I needed to catch up. I signed up for a precalculus course offered below the undergraduate credit level, and though I was determined to do well in that course, I entered it feeling very apprehensive about its utility or my ability to enjoy it at all. Luckily, my teacher for that course, whose name was TJ, was a far cry from fourth grade. He was a young graduate student, not that unlike myself, who believed that understanding the concepts was much more important than following directions. He put a lot of effort into explaining things in ways that enforced an understanding of the logical interrelations among procedures and concepts, and he emphasized the relationships among various techniques and mathematical theories in ways that highlighted the power and richness of mathematics. I loved that course. TJ really changed the way I thought about math.
Though I took several other useful math courses in graduate school, none of them quite stood up to that precalculus for its illustration of why math is interesting and valuable. I also unfortunately discovered that many of the problems that I had dealt with in elementary school were alive and well in college as well, especially when I tried taking calculus II, which I dropped out of in disgust after realizing the entire semester was dedicated to memorizing formulas and procedures for solving integrals, with basically no discussion of the meaning of integrals whatsoever.
I was lucky enough to have a second chance at math, but I recognize that second chances do not always present themselves, and I wish very much to contribute as little as possible to the reasons why they are necessary. Although I have thought at length about what could have been done differently to change my own demotivating experiences, most of the potentially effective changes were well outside my capability to effect at the ages I was when the experiences occurred (about 6 to 14). I do think, however, that a much more important question which naturally follows from that analysis is: how I can make sure that the actions I take now, as an educator and simply as a actor in the human social drama, do not create similar problems for the students and other people who look to me now for guidance and understanding. In this way, I try to make the best of my own demotivating experiences, by taking away from them lessons about how not to demotivate others.