Out in Left Field proudly presents the tenth in a series of letters by an aspiring math teacher formerly known as "John Dewey." All personal and place names, with the exception of Miss Katharine's, have been changed to protect privacy.
I Say Goodbye and Head Out for the Territories
Tina's moods were an up-down affair. On one day she could be very pleasant; but the next day she would be super-critical and negative. I tried working around her moods, but it was difficult. I knew her moods were due to her father passing away. And in all fairness, her advice to me—though annoying—was generally pretty good.
“When you ask a question, you have to give them time to answer it,” she would tell me. “Otherwise, they know you’ll just tell them the answer, and you’ll never get a response from them.” This is valuable advice—wait time is critical. And in the pre-algebra classes I taught, we used a direct instruction technique which entailed asking questions—and waiting for answers. Critics of the direct instruction method will tell you that it is all about kids sitting in rows, facing front, while the teacher lectures and provides instruction by rote. Well, first of all, our students were seated in groups of four, though I would have preferred rows. Secondly, I tried to engage the students by asking questions—not just “lecturing”. Third, with the exception of the Pythagorean Theorem, there was nothing rote about how we taught.
In the discovery based algebra class, students were expected to work in groups and come up with an answer, much of the time without the benefit of prior instruction. The method they were to have discovered would often be revealed in the next section. No one ever seemed to catch on to this. Tina’s admonishment to me in that class was similar: “You’re telling them the answers; let them figure it out themselves.”
I tried to follow this advice while they were learning to solve systems of equations with two variables. They had learned about eliminating variables; that is, given two equations like x + y = 6 and 5x – 2y = 8, you can multiply the first equation by 2 to obtain 2x + 2y = 12. Adding the two equations result in the 2y’s dropping out. But suddenly the book presented these two equations: 4x - 3y = 1 and 3x – 4y = -1. The students were stumped. Even the brightest student, Jorge, didn’t know what to do. He asked for help. Tina was out of the room. That was the other thing. While she criticized me a lot, she also gave me time alone with the class.
I wanted to stay true to what Tina wanted, so I did the following, knowing that Jorge was quite bright and would catch on to the hint I was about to give him. “Remember when you were learning how to add fractions, what you did when you added 1/3 and ¼?”
“Yeah, what about it?”
“What did you do?”
“Found a common denominator,” he said, clearly not getting where I was going.
“Which was what?”
“How did you do that?
”Multiplied 3 by 4.”
“OK,” I said. “Look at your equation. You have a 3y up here and a 4y in the second equation.”
“OH!” he said “You multiply the top one by 3 and the bottom one by 4.”
Now I imagine Tina might have criticized that, but I felt I wasn’t giving it away and was using proper scaffolding techniques. I tried the same technique with other students, and they eventually saw where I was going.
I guess when push comes to shove, although I dislike the CPM program, I’ve seen worse. It covers what needs to be covered. This doesn’t let CPM off the hook. It could be done a lot more efficiently with a lot more practice problems. Going back to first principles like generic rectangles and guess and check leaves a lot to be desired and takes credit for the hard work teachers do in the pre-algebra courses.
I also think that Tina gave more direct instruction in that class than she was willing to admit. There were plenty of times when kids weren’t getting it that she would stop everything and offer instruction at the front board. All in all, I think Tina is a good teacher and relies more on direct instruction than she might think. She often advised me on things that sounded an awful lot like things I would say.
I was ready for that. I was always ready for student questions. “Oh, you know I have terrible allergies and they’re mowing the lawns today.” They were in fact. “Whenever that happens, my eyes just itch and burn.” She seemed satisfied with the answer, but I don’t know if she believed me.
Although sometimes I couldn’t wait for student teaching to be done, I miss working with Tina and I think of my students often, with great fondness. I tried to teach them as if what I was teaching mattered. I have an idea of who it mattered to and who it didn’t. For most, though, I simply couldn’t tell.
Well, I guess I better wrap this up. I appreciate Miss Katharine letting me tell my story. I really don’t know what’s going to happen to me; teaching jobs are pretty hard to find. But thank you all for listening. I’ve said just about everything I had to say. For now, anyway.