"Recall a time when you really loved something: a movie, song, an album or a book. You wholeheartedly recommend it to someone you really like. You anticipate that reaction, you wait for it. It came back, and the person hated it. That is the exact same state I spend every working day of the last six years. I teach high school math."
--Dan Meyer, March 6, 2010, addressing a TEDx. Dan teaches high school math outside of Santa Cruz, CA. In this brief 12-minute talk, he explores the intersection of math instruction, multimedia, and inquiry-based learning. His blog can be found here.
As I think I've mentioned. I don't teach math, but I think that understanding how math is taught and how it can be taught can be instructive to all teachers. Because it is a process about process. At the risk of belaboring the obvious, a math teacher cannot fall into the trap inherent in Social Studies, Science and sometimes in English, in which we become enraptured by our content and we start shoving the kids a big pile of "stuff", often referred to as "facts." Math, as a discipline, must always be a verb and not a noun.
At their best, Science teachers know this--that's why they have labs. Hopefully, they do not tell the students too much about how a given experiment should end up. (I can remember fudging results to match the prediction--don't blame me, it started with Gregor Mendel.)
In Language Arts, this is why I argue against diagramming sentences. It tells you a lot about what things are called and how to categorize them. It's a very useful tool for linguists studying syntax, especially in comparing languages or dialects. One teacher friend who advocates diagramming tells me the students love them. But that is not an argument in their favor. One thing students really like is questions for which there are certain and "right" answers. They hate uncertainty, ambiguity and personal interpretation. But that's the way the world is built.
And most importantly, I do not know any way to draw a line between skill in diagramming and improved writing. There may be a connection, but it has not been demonstrated to me. I believe the only way to teach writing is to (a) require a lot of it; (b) give a lot of feedback; (c) require rewriting. And the writing task must itself be authentic and have an intrinsic interest to the student. Exercises in literary analysis are lovely for college students of literature, but to induce facility in writing (if not love for it), there must be motivation.
My greatest music teacher was Lew Spratlan, not because of any information or wisdom he imparted. I took Composition with him and there was one simple, hard and fast rule of the class. "Come each day with a new piece of music to demonstrate, or don't come." We learned that the most important tool for writing music was the seat of the pants--that is, learning to apply that portion of the body to a chair in order to write. And write. And write.
When I taught general music, I made sure that students were making some kind of music at least two or three times a week--not just listening, or learning terminology or other non-functional facts. (I can't tell you how much commercial music instruction material tells you all about how many children Bach had, while telling you nothing about how he put music together.)
This corresponds with Mr. Meyer's example of waiting for the container to fill. Everyone wants to know how long that will take, even if they don't care the least about how to calculate the volume of an object. A more detailed explication of this approach to math instruction is Lockhart's Lament, which I stumbled across for obvious reasons.
This is hard, it's labor-intensive, and it means you won't "cover" as much "stuff." This runs counter to the politically-driven high-stakes testing system we have in place now. But this is what we teachers must juggle today. (I just hope the politicians who advocate these multiple-choice tests have got lots of jobs waiting for our students which involve taking multiple-choice tests. Because that system will not teach anyone to think.)
"'You can know the name of that bird in all languages of the world, but when you're finished, you'll know absolutely nothing whatever about the bird. You'll only know about humans in different places, and what they call the bird. So let's look at the bird and see what it's doing--that's what counts.'" -- Richard Feynman, quoting his father in WHAT DO YOU CARE WHAT OTHER PEOPLE THINK?
"[I]f I had to live my life again, I would have made a rule to read some poetry and listen to some music at least once every week…The loss of these tastes is a loss of happiness, and may possibly be injurious to the intellect, and more probably to the moral character, by enfeebling the emotional part of our nature." --Charles Darwin