*Barry Garelick, who wrote various letters under the name Huck Finn and which were 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 seven:*

All my classes were getting ready to take their first quiz later in the week. My second period class was the second-year Algebra 1 class. We were working on systems of linear equations covering the various ways of solving two equations with two unknowns.

I was preparing for my second period class by looking over the upcoming quiz and identifying the questions that most students would likely get wrong. As I reached the disturbing conclusion that this would be almost all the questions, Sally, the District person who talked to the math teachers about Common Core the day before school began, stuck her head in the door and asked if I had done any of the activities she had talked about that day. These were discovery-oriented projects that lead students to explore certain topics (specifically: probability, repeating decimals, and solving systems of equations) while allowing teachers to do formative assessments. Which means evaluating students by observing them “communicate and defend their thinking”.

What I wanted to say: “I’ve got other things to worry about than doing something that’s only going to tell me what I already know: that the majority of students shouldn’t have been placed in an algebra class in the first place. I’ve got quizzes coming up in all three of my classes that many students are likely to fail. And as far as providing students the forum to communicate and defend their thinking I prefer they communicate using math language that they are actually taught.”

What I did say: “Not yet.”

I explained that I didn’t know if I’d be able to do any of the activities except the systems of equations for my second year algebra 1 class. “We’re not covering probability, and the activity on repeating decimals is a problem.”

“Why is that a problem?” she asked.

“I have students who can’t divide.”

She nodded in a way that vaguely suggested sympathy. “Yes, that would be a problem,” she said and then vaguely brightened. “Why don’t you give it a try? Maybe have them use calculators or something.”

“Yeah, I might be able to do something like that,” I said with vague optimism, and she left. A few minutes later, my second period students started filing in.

The second period class was a mix of maturities; all had made it through the first half of Algebra 1 the previous year. Only a third of the class had sufficient mastery and maturity to handle the second half. There were about six students on the JV football team and all but one was struggling. Lately one of the boys, named Gray, was making an extra effort. With the upcoming quiz and football game, he was suddenly more cooperative. This was the first quiz and thus would constitute his provisional grade for the class. An average grade of D or below would mean he couldn’t play in the game—until it came back up to at least a C. His grandparents were coming from out of town to see him play, he told me.

My first meeting with Gray had been an auspicious one. I accidentally kicked his backpack as I circulated around the room. “Hey! Watch where you’re going!” he said.

“You need to learn some politeness, young man,” I said.

“Well you kicked my backpack.”

“It was an accident and I’m sorry; and you need to learn some manners.”

He wore the chip on his shoulder for a few more classes but I made a point of working with him to gain his trust. We were now working on word problems and he was struggling with wind and current problems. I asked the class if anyone could help set up the equations for the following problem: “An airplane flying against the wind can travel 3000 miles in 6 hours. Flying with the wind, it travels the same distance in 5 hours. Find the speed of the airplane in still air and the speed of the wind.”

“Who can set up the equations for this problem” I asked. Gray raised his hand. “I’ve got this,” he said. “When it’s going against the wind its 6r - w = 3000 and with the wind it’s 5r + w = 3000.”

I wrote the equations on the board and asked the class: “Do we agree with how we represent the wind speed?”

Gray suddenly shouted: “Dude! It’s right. You subtract the wind speed in the first case, and add it for the second equation. I know it’s right!”

“Dude! You’re wrong,” I said.

It isn’t my habit to be so blunt but it was the first time I had been called “Dude” and wanted to take advantage of it. I worked the problem at the board showing how (r+w) and (r-w) are the speeds of the plane and went over the distributive property. But working with Gray later, I saw that his understanding was hit or miss.

Quiz day came the next time we met. The strugglers in the class continued to struggle. Gray made a valiant effort but was not grasping key concepts. At one point he raised his hand and asked me, “How do you do this problem?” It was a boat and current problem.

“How do you represent the speed when it’s going with the current?” I asked. He wrote “r + c”.

“OK,” I said. “So now, how do you represent distance?” He made the same mistake and did not distribute the multiplication of time across “r + c”. I did the unthinkable. I wrote down one of the equations.

My justification was weak but it boiled down to this: based on the other work I saw on the quiz, I could tell he was not going to get a passing score. I did the same for others who were in similar danger. I’m fairly certain I’m not the only teacher in history to do this.

The next day was my off day. As was my custom, I came in to prepare for the next days’ lessons. Gray came in before the first period.

“What’d I get on the quiz?” he asked.

“You got a 45 percent.” He looked sullen.

“Is there anything you can do? I mean I know you can’t raise my score; I’m not asking for that. But I have to play in the game on Friday.”

“I’ll tell you what,” I said. “I won’t enter the grades until the weekend. So you’ll be OK for this week.” He looked at me as if I had found a cure for cancer.

“Dude!” he said.

“But you know as well as I do that this is temporary, don’t you?”

“Dude!” he said and left.

The other football dudes who failed the quiz were in a similar state of temporary eternal gratitude.

## 1 comment:

The one time I had to do grading, I ended up fudging a lot too. I was grading engineering lab reports and part of the grading was supposed to be on the writing. But, a number of the students were not native English speakers and had quite poor English skills. Asking them to suddenly learn English seemed ridiculous, so I ended up fudging that part of their grade. I couldn't see grading them down 10% on every assignment just because they were international students.

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