Today, I filled in for an algebra teacher's first period class. Following the lesson he'd left to a "t," I walked the students through a problem on solving for absolute values. This, of course, after a quick flip through the chapter while thinking to myself, "Oh, crap, what's an absolute value?!" It's been a long time since high school algebra. (For the record: an absolute value is pretty much exactly what it sounds like. It's basically the distance of an integer from zero on the number line. So the absolute value of 2 is 2. The absolute value of -2 is also 2. Etc.)
I wrote an answer to one particular problem, and was met with a raised hand and an inquiring, "How is the answer negative five, and not seven?"
I looked at her, then at the book. "Hmm."
Then I smiled at her. "The book says so?"
This elicited a grin from her in return. I added, sheepishly, "It's been over 20 years since I took algebra." The kids understood.
Later, in an email to my colleague, I wrote, "You might want to review a few points with them tomorrow..."
When lunch rolled around, I had an officer meeting with four choir girls who are my officers and Teacher Interns. We didn't have a lot to discuss today, so we quickly just started to chat. They're darling kids--bright, enthusiastic, awesome in so many ways. I found myself telling them about my adventures in algebra this morning, and they laughed with me.
"Look," joked one of them. "I know that the Pythagorean Theorem works. I don't care how it works, and I don't see why I have to prove it!"
This got me talking about the four semester of music theory I took in college, and how so much of it has been forgotten because I simply never use it. I suppose if I were a composer, I'd use more, but as a teacher, so much of the higher-level theory I learned really isn't useful.
"For example, I know what a secondary dominant chord is, but it isn't important to teaching choir." Sure, some of our songs may use that type of harmony, but that doesn't necessarily mean my kids need to know about it, and most of them certainly don't have the capacity to truly understand it.
These girls, however, all play piano.
"What is a secondary dominant?" asked one. She was echoed by the others. So I launched into the quickest explanation I could make, using solfege.
"Okay, when you play a simple song in C Major, you will play the I chord, the IV chord, and the V chord." I explained which ones those are in terms of fingerings and note names. They all got that. "Now, say that the piece of music throws a D Major chord in--that has an F-sharp. C Major does not have an F-sharp. How do we label that chord in a song that's in C Major?"
I started showing them the chords on the piano.
"Well, turns out the D Major chord is the V chord of G Major, which is the V chord of C Major. It's the five-of-five chord. As the fifth note of a scale is the 'dominant,' this is a secondary dominant chord."
A chorus of "Ohhh," arose, so I guess they got it. What I love is that they're curious, that they humor their music nerd of a choir director when she gets on her music theory tangents.
Teaching is fun. :)