Monday, January 5, 2015

Conversations on the Rifle Range 20: More Complaints, Factoring, and Grand Master John

Barry Garelick, who wrote various letters  published here under the name Huck Finn, is at work writing what will become "Conversations on the Rifle Range". This will be a documentation of his experiences teaching math as a long-term substitute. OILF proudly presents episode number 20:



When I was hired for the long-term sub assignment, the principal told me it would likely last the whole semester. In order not to unduly alarm the parents, he had announced I would be there for just the third quarter. But the day came when I told my classes that Mrs. Halloran would not be coming back and I would be their teacher for the remainder of the semester.

All my classes cheered wildly. But as much as I wanted to believe I was entirely worthy of such adulation, I suspected they were reacting to the news that the super-strict Mrs. Halloran would not be returning.

My doubt was tied in large part to the email I had received from Brian’s mother , which suggested that Brian’s poor performance in algebra this semester was due to me. In even larger part, my doubt was tied to other news I received from one of the school counselors, a young woman named Robin. She had met with me the day before I made my announcement. She started on a complimentary note: “I can't imagine walking in mid-year like you’ve done and trying to figure this all out,” and then got down to business. Two students had complained to her about my algebra 1 class. Who they were she could not disclose. The essence of the complaint was that I didn’t teach like Mrs. Halloran.

“They said she taught things one topic at a time, but you do several,” she said. This made no sense to me at first, until I remembered that in my lesson on word problems, I presented both mixture, and rate and speed problems. Ironically, Mrs. Halloran’s lesson plans called for one more, but I felt that would be too much.

“I asked them if they had talked to you about this,” Robin said. “They said they didn’t want to hurt your feelings.” As touching as this may have been to Robin, I was not impressed. I strongly suspected that 1) Brian was one of the students and 2) they feared retribution rather than hurting my feelings.

Robin closed the meeting as she had opened it. “I can't imagine walking in mid-year and trying to figure this all out.” I felt like saying “Try doing it with only two weeks’ worth of lesson plans.” I thanked her instead and left.

My algebra classes were now on the chapter on factoring. With this chapter, I had started teaching differently. I made up my own problem worksheets for homework. I didn’t like Holt’s presentation of problems, in which they tend to give complex problems at the outset instead of ramping up slowly and building expertise and confidence. My worksheets drew from Dolciani’s algebra textbooks as well as my old textbook from 50 years ago. The reaction from the students was noticeable. When I turned them loose to do their homework, I heard remarks such as “These are easy!” After a few minutes when they got to the harder problems and students started asking for help, the progress continued to be good.

Coming up was factoring of trinomials (for example, factoring x2+ 5x + 6 into the binomials (x+2)(x+3) ). I decided I would first have them practice multiplying binomials again, but this time using the shortcut method known as FOIL (for First terms, Outer terms, Inner terms and Last terms). I had already taught them how to multiply binomials (and polynomials in general) by using the distributive property. That is, (x+3)(x+2) is equivalent to x(x+2) + 3(x+2).

I had not taught them FOIL for two reasons: 1) I wanted them to get used to using the distributive property; 2) In case the “math must be taught with understanding” police came by, I would be on the right side of the law. (Some teachers believe that teaching FOIL harms students, as if it magically wipes away any understanding.) There was actually a third reason for my waiting: I wanted to save the FOIL method in preparation for learning how to factor trinomials. When using the FOIL method, students learn to do the middle term step in their heads, which helps in factoring trinomials.



Students caught on to the FOIL method immediately and some students asked why I hadn’t taught it earlier. “You’ll see,” I said, hoping that would explain things. It did for the most part.

I had students work some problems at the board, but it was a bit slow-going. To speed things up, I picked John, a Chinese boy whose parents started him at Kumon when he was four years old. He was the most adept at algebra in the class. John and Brian were now at the board, and I said my next thought aloud: “This is looking like a competition to me,” I said to see what would happen.

The class responded immediately. “Yeah, Brian against John!” they shouted, and then “I get to play the winner!” The game organized itself rapidly. (Unfortunately no “student-centered classroom police” were there to see the students making their own rules. ) Two people would be up at the board. They would face the class while I wrote the problem twice, so each contestant had the problem in front of them. Someone stood between them so they couldn't see the other's work.

John won the first round hands down and continued to beat his challengers. In the meantime, they were getting faster and faster at multiplying binomials using FOIL and computing the middle term in their heads. Pamela, a girl who often smart-mouthed me in class (and who I suspected was one of the students who complained about my teaching) then came up. “Looks like we have an Asian thing going on here,” she said.

I didn’t know what to say but she went on. “I’m Japanese, you know.” I didn’t know. She lost to John.

“Maybe you ought to go against John,” she said.

“I can’t,” I said. “I’ll lose!” John was also unwilling. "I can't compete against the teacher."

The class responded to the dialogue: “Mr. G! Mr. G! Mr. G!”

“Give it your best,” I said to John as we stood on our marks.

“You too,” he said.

We were given the signal to start; he beat me by a millisecond. I shook his hand and proclaimed him “Grand Master John” which became his name for the remainder of the semester.

I then started the class on a worksheet of 43 problems. “Why’d you give us so many?” they asked. “We’ll never finish!” I was worried about that myself, but they finished with time to spare. “I knew I should have given you more,” I said.

They assured me that I had done just fine.

2 comments:

RTSD Academics said...

Love this. Katharine could you email me when you have a second?

Katharine Beals said...

Thanks! I don't have your address; you can email me at katharine dot p dot beals at gmail dot com.