*Out in Left Field proudly presents the twelth 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.*

Dedicated readers of my letters may recall my reaction to the Common Core’s “Standards for Mathematical Practice” (SMPs). I continue to see these SMPs posted in various math classrooms where I sub, though I try to ignore them as much as I can as I continue to drift down the ideological divide, otherwise known as math teaching.

The SMPs came to my attention again recently while subbing at a middle school. For me the day started as sub assignments usually do: by reading the teacher’s directions to the sub. That day, the teacher wanted me to administer a “district assessment” for each of her classes and then have them start on their homework.

I glanced at the assessments and saw some mention of “Common Core” on the front of the answer sheet. Neither the answer sheets nor the instructions that I had to read aloud gave the reason for these tests, other than that the students would be evaluated as to how they solved and analyzed problems. I expected that students would ask me if their tests figured into their grades, so I called the front office before first period class and asked.

“I’m not sure,” said the person in the front office. Pause. “Well, let me think.” Pause. “No. I’m pretty sure they don’t figure into their grade.”

The test had four problems which students had to answer by showing their work directly on the exam and “explaining their answers.” Before my first period class started the test, one boy raised his hand. “Our teacher always tells us to ‘Attend to precision,’” he said, pointing to that particular SMP which was posted on the wall behind me. “Could you say it please?” The class looked at me expectantly.

"Attend to precision.”

"Thank you," he said.

“You know, I don’t even know what that means.”

“It’s one of the things she has on the wall,” the student said.

“Yes, I know. But it’s just so vague. Here’s what it means to me. It means use the right math vocabulary, and show your work. So for this test, if you just write a number down for your answer, it won’t be enough. You have to write what you did so someone else can follow it.” This seemed to satisfy the class, which is to say that probably not one person focused on what I said.

The questions had to do with discounts and percentages, which they seemed comfortable with. One question asked them to say whether an item was marked down 25% four times in a row, explain whether or not the final price after the four discounts would be $0, and provide the reason for their answer. From what I could see when I glanced at the tests while collecting them, most students didn’t get the answer right, but they had no problem putting down an explanation.

The situation was quite different with the eighth grade algebra classes, however. Their test only had two questions. One involved an L shaped figure with dimensions like x+15 on one side; i.e., no simple numbers were used. The question asked for the students to write an expression for the area of the figure. This involved splitting the figure into two rectangles, figuring out what various missing dimensions were, and then writing the area as the sum of the area of two rectangles—something that would amount to an algebraic expression.

After a few minutes of quiet, there was suddenly a flurry of indignant questions: "Do they want us to calculate the actual area? Like a number?” “What does 'expression' mean? Is that like an equation?" I was struck by the difference between the seventh graders who simply wrote down their process, and the eighth graders who were confused by what was required of them. One student put it into perspective for me. "What do they mean 'explain your reasoning'? I just do it." I took this to mean that all year they’ve learned how to express ideas algebraically, with showing their work being sufficient explanation. Given that that's what they thought they were doing to begin with, requiring them to “explain their reasoning” made no sense.

Of course, the students would not know that there are people who view those who can't "explain their reasoning" (however correctly they solve a complex problem) to be doing "rote work" and lacking "understanding." But it seems to me that if we really want students to do such explaining, then we should tell them how. Simply telling students to "explain your reasoning and attend to precision" is not likely to accomplish much. Knowing how to explain something precisely doesn't come automatically with understanding. And students are not likely to pick it up by themselves working in groups and the like.

As it was, I had a class full of eighth graders at a near-riot level. I stood in front of the class and said, "OK, I'm going to show you something." They were still talking. "Please listen," I said and then added "Actually, please don't listen because I'm probably going to get fired and/or shot for doing this." The class immediately got quiet.

I drew a square on the board and labeled two of the sides with an "x". I said "This is a square with sides of x units. How do we express the area?" The class said "X squared".

“Can you explain why?”

Someone said “Area is length times width.”

"That's all I'm going to tell you,” I said and erased the figure.

I'm still waiting for someone to knock on my front door and put the handcuffs on me.

## 3 comments:

That is how far "explaining your work" should go, and no further unless the student wants/needs to go further.

I think you have an excellent example to the students (and I enjoyed this post).--Lynne Diligent

Thank you for writing this. I have been concerned for some time now about whether or not the old-school "work" will be good enough for the new "you-must-show-understanding" common core standards. Think I'll be talking with my kids' principal...

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