Out in Left Field proudly presents the third in a series of letters by an aspiring math teacher formerly known as "John Dewey." All personal and place names have been changed to protect privacy.
I student taught for 15 weeks at Aragones Junior High. The school is located in an agricultural region known primarily for its strawberry fields. It is in a residential neighborhood surrounded by hilly farmland. Some of the farms have cows on them, but most grow strawberries. The make-up of the school is about 96% Hispanic students, many of whose parents work in the fields I would be passing on a daily basis. During my time there, the students sometimes appeared to me as adults, sometimes as kids, and other times as people caught in between.
The first weeks of my program I would be observing the three classes I would be teaching; by the fourth week I would begin to teach some classes. On my first day Tina, my supervising teacher, asked me to circulate among the students during the algebra class and answer questions or offer help as needed. The algebra class was a discovery-based class that used the CPM textbook (College Preparatory Math). The problems the students were working on in their groups of four were “guess and check” problems. The book spends more than half of the semester on these types of problems and even provides instruction in how to set up tables of values to maximize the efficiency of an inefficient process. Tina even gave instruction and pointers on how to do this during the class. She’s a good teacher and explains things well, which bolsters a point I’ve made in my previous incarnation as John Dewey: It’s possible to do something horrendous tremendously well.
A moment of full disclosure: I went to school at a time when math was taught in a traditional manner in K-12. Despite my average intelligence and despite claims from various quarters that such method was more destructive than typhoid fever except for very bright people, I managed to learn enough to allow me to major in the subject. The algebra book I used started almost immediately with how to express words as algebraic expressions, and to use that skill to set up and solve equations. The book briefly discussed the “guess and check” technique which at that time was called “trial and error”. It illustrated how a problem could be solved using trial and error, and then how the same problem could be done quickly and efficiently with algebra which then remained the focus of my algebra course.
A boy named Rudy asked me for some help with a problem. Rudy was fairly bright and his group mates seemed to rely on him to get through the problems. The problem was as follows: “In making a batch of soup, the number of cans of tomato paste was five more than twice the number of cans of noodles. A total of 44 cans were emptied into the soup. How many cans of each ingredient did the team use?”
I was mindful of the not-very-optimistic warning I got from the local university which placed me at the school: “You are a visitor/guest in the classroom. If there are any differences of opinion with the teacher, things have to be done as she wants them since it is her classroom.” Thus, I strived to adhere to the guess and check nature of the assignment. I knew from watching a pre-algebra class earlier that students learned how to translate English expressions into algebraic ones. I figured that these students knew how to do that at the very least. But while CPM touts itself as connecting knowledge, connecting to what they learned in pre-algebra was apparently not on the agenda.
“OK,” I said. “If you have twice the number of cans of noodles, how can we write that?”
They stared blankly at me
“How do we write ‘twice’?” I asked. “What number do we use?”
Rudy brightened and said “Two”.
“Yes, two; so if I have four cans of noodles what’s twice that amount?” Rudy thought a bit while the others in the group looked at him.
“Right! So if I call a can of noodles ‘x’, what’s twice that amount?”
Rudy thought again. “2x?”
Now we were getting somewhere. “OK, so if the number of cans of tomato paste is 5 more than twice the number of cans of noodles, how do we say that?”
Rudy thought for a moment. I expected to hear “2x + 5” but instead, he said: “Paste.”
I asked the others. They all said “Paste.” The others now started to giggle. What I didn’t know was that the students had been setting up guess and check problems with headings like “cans of noodles”, and “tomato paste = twice the number of cans of noodles + 5”. Rudy was stuck on “paste” as an answer and the more he said it, the more I tried to get them to use letters rather than words. The futile conversation with Rudy was making them all laugh. They tried not to, but that only made it worse. They all spoke English well, but for all practical purposes we were speaking different languages. For lack of experience and anything better to say I told them, “If you want to joke around, you’re wasting your time and mine,” and moved to the next group.
Tina told me later that the class wasn't ready yet to translate into expressions using “x”. “You don’t know what ‘guess and check’ is about yet,” she said. The motif of old school teacher meets the modern method then became the basis for her retelling the story to others in the teacher’s lounge. “Guess and check isn’t easy to teach,” she said consolingly. "The book eventually does connect guess and check with equations, and then the light bulbs come on when they put it all together."
I was about to say it might be a lot easier just to teach them algebra. But I thought it probably would be best to keep my mouth shut, so that’s what I did.