Tuesday, November 18, 2014

Conversations on the Rifle Range16: Parallelograms, the Mercy of the Court, and Kit Kat Bars

Barry Garelick, who wrote various letters under the name Huck Finn, published here, 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 16:

A “prep period” –a period in which teachers have no class—is one of education’s most sacred and cherished traditions. Mine was first period and involved making copies and putting finishing touches on lesson plans, as well as pacing nervously in anticipation of the day ahead. The stage fright dissipated when class began but would return if I didn’t pace things right and had slack time left over at the end of class. The resulting restlessness of students spelled disaster and invited clock-watching, students getting out of seats, general disruption, and lining up at the door (though I put an end to that practice quickly).

My fourth period pre-algebra class was the one class I dreaded most, though in the end it turned out to be my favorite. It was the most crowded, and also had six students who were “English Learners”. A Spanish-speaking aide was in class to help them. Mrs. Halloran had explained to me that because they were “low” in ability, they weren’t part of the regular class, and were relegated to the back of the class where they worked on an online course on computer tablets. They were given a special “pass/no grade” credit for the class. With the aide working with six students, the conversations at the back of the room served as a stimulus for other students, many of whom had self-control problems to begin with, to start talking. When the din got to a certain volume I had to raise my voice to quiet them. If that failed, Allysandra, a rebellious Mexican girl would yell “SHUT UP” at the top of her voice. This would generally do the trick.

Then there was Trevor, a disruptive boy, not well-liked by the other teachers. He got into fights and was even suspended for a week for one of them. He had a gift for arguing convincingly even when wrong. I first noticed this when he put some make-up work in the wrong place. When I told him where the correct bin was, he said “Chill.” My reaction was so swift it caught both me and the class by surprise: “Don’t you EVER tell me to chill!” I said. The class became a tomb.

“No, I didn’t mean it like that,” he said. “I meant ‘chill’ in the same way you say ‘cool’ or ‘OK’. That’s how I meant it.” He was convincing so I backed off and the class din resumed after about a minute. When I related this tale the next day to a teacher, she told me “Oh, that’s Trevor! He always has some excuse about how he didn’t mean this or that. He’s good at that.”

I mentioned to her that he was on the school’s mock trial team. This team competed with other schools in a mock trial, judged by a real court judge. “Given his gift for arguing and being on the mock trial team, I would guess he’ll end up being a lawyer,” I said.

“I hate to think who his clients will be,” she said.

I put that thought aside and tried to reach out to him. He would sometimes read a book quietly if he either 1) finished his homework early or 2) was avoiding doing the homework. Rather than try to find out which it was, I would ask him about the book he was reading and he would tell me. I sensed a more cooperative side to him, but wasn’t sure whether it was because I was showing an interest in him, or because of the impending championship mock trial coming up that was helping him focus his energies. Since I had members of the mock trial team in all of my three pre-algebra classes, I decided to tap into these students’ argumentative gifts during the unit on geometry.

I was finishing up a chapter on parallelograms. I decided to put a figure up on the screen in each of my pre-algebra classes and asked if anyone could tell me if two particular line segments in the figure were congruent and why. Some parallel lines were marked as such. The two line segments of interest were marked as being perpendicular to one of the two parallel lines and were, in fact, opposite sides of a parallelogram and therefore congruent.

I offered a Kit Kat bar to any student who could answer the question. Students immediately rose to the challenge. In all classes, some student would inevitably say “Can’t you just measure the two segments?” to which I would reply “Inadmissible evidence! The court will not allow rulers or any type of measurement devices in this trial. Demonstrations must be made using definitions and theorems only.”

As expected, the members of the mock trial team rose to the challenge. Some tried to get around my restriction of no measurement devices by saying “They look equal” but I easily put that to rest. “Not adequate. Visual comparisons are not allowed.”

In fourth period, upon hearing the “Inadmissible evidence” warning, Trevor rose to the challenge. He stood up and said “I got this! I got this!” and then proceeded to make spirited, breathless demonstrations that didn’t quite make the case.

I gave him some hints. “Do you think these two line segments are parallel?” I asked.

“Yes, definitely,” he said.


“Because they’re both at right angles, at right angles!” Trevor said as if pleading to a jury that his client did not deserve the death sentence. “What about the right angles?” I asked.

“It proves it,” he said.

“Proves what?” I asked.

“Proves that the lines are congruent.”


“Because they’re right angles, they’re right angles!”

I paused as if giving the matter great thought and the class quieted.

“Do you mean to say if two lines are perpendicular to the same line they are parallel?”


“So why are they congruent?”

Someone shouted “Because it’s a parallelogram!”

In the best spirit of courtroom drama, Trevor protested: “Unfair! I was going to say that!”

“There will be silence in the courtroom,” I ordered to no avail. “Counsel will be seated, please,” I said and continued: “The court will show mercy and recognize that counsel’s observations and arguments have merit and has provided indications that he knows that opposite sides of a parallelogram are…what?”

“Congruent!” Trevor shouted.

“One Kit Kat bar is awarded.” The class applauded, though the person who identified the figure as a parallelogram wanted one also.

“Come up and claim your Kit Kats,” I said and presented the awards. To Trevor’s credit and my satisfaction, after he took his Kit Kat, he shook my hand.

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