It’s time for me to start justifying the “What I Learned” part of the title of this blog. I’ve written an article with a similar title, namely “Thoughts on Teaching: What I Learned about Why My Students Didn’t Learn More“, centered on a list of 10 specific things I learned. Below is number 1. I’ll post the other nine in the near future.
It’s important to note that in some sense I knew most of these things very early, certainly after my first month of student teaching; but I didn’t know any of them deeply enough to apply them effectively. By the time I started this essay, 18 months later, I could apply all of them (pant, pant). In addition to the education courses I took and my experience in the classroom, I learned a great deal from outside reading, especially the superb books by Polya (1957), Holt (1982), and Lockhart (2009), the latter with its scathing and eloquent critique of math-education practice.
Naturally, these ideas don’t apply equally to students of all ages; in general, the younger the students, the more relevant they are.
And without further ado, here’s the first thing I learned.
1. To a great extent, students really are responsible for their own learning. To be crystal clear, I mean that students are in control more than anyone else is—certainly more than their teacher—of how much and what they learn. This may be the single most important thing I learned. This idea can be paraphrased in many ways, for example, a statement that’s often attributed to Einstein: “I never teach my pupils; I only attempt to provide the conditions in which they can learn” , and Holt’s (1982) statement:
“I doubt very much if it is possible to teach anyone to understand anything, that is, to see how various parts relate to other parts, to have a model of the structure in one’s mind. We can give other people names, and lists, but we cannot give them mental structures; they must build their own.”
But I’ve tended to feel that, if the students aren’t learning, it’s “my fault”, and one day last fall, I said something to a far more experienced instructor that made that clear to her. She told me in no uncertain terms that it was a mistake to have that attitude, but I still didn’t get it. Last spring, I taught high-school math as a maternity-leave replacement. Near the end of my time there, a class (Honors Algebra II) went especially poorly one day, and I thought of five or six reasons why. All or nearly all were things I’d done or failed to do. The next day, before that class, I talked to Mrs. W., the teacher next door, about my frustration that students weren’t “getting” what I was teaching, and that very few were taking advantage of my repeated offers of help outside class. To my amazement, she told me that Mrs. P. (the teacher I was filling in for) typically had 10 or 15 students in her room getting help before school! Hearing this, I suddenly realized that my teaching was by no means the only reason my students were having trouble. I might have one student come in before school and one after school, and often not even that. But clearly they weren’t coming in outside of class because they weren’t motivated; wasn’t this in itself a problem with my teaching? It’s hard to tell, but—being as honest as possible—I’d say it was mostly because of factors that I couldn’t control, for example, the temporary nature of my position. (I told my class what Mrs. W. had said and again urged them to get help from me outside of class; I didn’t see any increase in help seekers, but I felt considerably better about my teaching after that.)
Thus, the question above “Did I teach the average student as much as Mrs. P. would have?” is seriously misleading. A better question is “Did the average student learn as much as they would have with Mrs. P.?” The answer is almost certainly no, but there were mitigating circumstances.
Holt, John (1982). How Children Fail, revised ed. Addison-Wesley.
Lockhart, Paul (2009). A Mathematician’s Lament. New York: Bellevue Literary Press. Part I of the book (the “Lament” proper) retrieved May 4, 2012, from the World Wide Web: http://www.maa.org/devlin/lockhartslament.pdf
Polya, George (1957). How to Solve It, 2nd ed. Princeton University Press.