Wednesday, February 4, 2015

Conversations on the Rifle Range 24: The Quadratic Formula Redux and an Unintended Act of Defiance

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 24:

On a late-start Monday in early May, the math department had a meeting. Sally, the person from the District, had called it for the purpose of discussing what to do about “below grade” students next year (those getting a D or failing). In particular, she wanted to explore how Common Core deals with such students. It must have been an important meeting because even the principal was there.

Despite its importance, I have trouble recalling what was said. I remember Sally admitting that the standards for Algebra 1 under Common Core do not cover everything that the current Algebra 1 course does. “Common Core takes a deeper dive into math than the mile-wide inch-deep approach we used to use,” Sally said. Common Core was going to be so much better than the "procedural" approach we use now. "Procedures don't stick with kids; they forget them. They need to learn critical thinking and problem solving."

Jim, one of the math teachers to whom I turned for advice now and then—a very nice man who had been teaching there a while—mentioned that some of the “below grade” students were missing key knowledge from day one. “Some of them don’t know the basic math facts, or how to do basic operations.”

“That’s because they haven’t been taught how to think,” Sally pronounced.

“No, that’s not it at all, Sally” Jim said.

I had recently learned that Sally had been a math teacher at the school. From what I heard, she was pretty good at it. Her husband had passed away a few years ago, and she took a leave of absence for a year. When she returned, she took her present position at the District.

She did not reply to Jim, though it was evident she knew what he was saying. To me, a newcomer, it appeared that their past shared experiences created a loyalty between them that allowed Jim to accept what her circumstances and the swing in the educational pendulum had turned her into. This loyalty extended to a lot of teachers who may also have been affected by the pendulum’s swing. In fact, there was a lot of love for her among the teachers.

The principal—also a newcomer to the school—added his two cents about Common Core at the end. “Common Core is requiring us to rethink how we teach,” he began.

It doesn’t really, but that’s the prevailing narrative in education that blends in with a host of others.

“What’s really important is collaboration,” he said. “If you look at workplaces nowadays, it’s all about collaboration. You have to know how to work as a team. Now I’m not saying that we abandon individual learning. But we also have to foster how to work together.”

I disagreed but said nothing. In the adult world, people bring their individual expertise and knowledge to the team, based on my experience. In the student world, they are novices. It’s either the blind leading the blind, or the one smart kid who gets stuck with all the work.

The meeting ended shortly after that and I took that opportunity to scour the metal supply cabinets in the room for pencils and whiteboard markers that weren’t dried out. The principal, oblivious to me, was talking with Mrs. Perrin, the math department chair, about a "great math teacher" he saw at another school. “She’ll fit right in here,” he said. I could imagine that his view of what was “great” likely included student-centered, group activities, inquiry-based math and facilitating rather than teaching. The fact that he sought to have this conversation out in the open with me in full sight was an indicator that I wasn’t exactly being groomed for any kind of position there.

I tried to put all that out of my mind, given I had a full day of teaching ahead, plus a meeting at the end of the day on a student’s “504 plan”. A "504" is an accommodation plan, usually given in lieu of students receiving special ed services. It lists accommodations for the student that teachers can make, like having a peer give the student notes, or having the student take tests in a quiet room.

The student, Calvin, was in my algebra class—currently averaging a D. He had been homeschooled for the first part of eighth grade, and was re-enrolled in the school and placed in algebra. At the meeting, his teachers were there, his counselor (a young woman named Theresa), his mother, and a tutor from the learning center in which he was enrolled. He had been diagnosed with ADHD and the mother explained that Calvin has test anxiety and doesn’t perform well on tests but that he was very capable. Most teachers told a different story and all agreed that though he was very cooperative and good natured, he had a difficult time focusing and absorbing what was being taught. When the discussion turned to math, they asked for my input. I said the same—his difficulty was not confined to just tests. He had been struggling all semester.

Theresa explained that next year all schools will be teaching math via Common Core. “So no more ‘here's the assignment from the book, and there'll be a test on the material next week’. It will be more about understanding". She added cheerily that this could be helpful because Calvin wouldn’t be burdened with memorization of procedures. He will be required to explain how he got an answer, and could get credit for explanations even if the computations are wrong.

At this point, Calvin, perhaps wanting to prove to Theresa that memorization was not a burden to him (and not picking up on the Common Core party line she was spouting) interrupted. “I actually memorized the quadratic formula,” he said and then recited it perfectly.

“Excellent! Well done, Calvin!”, I said. I turned to the others. “We’re having a quiz this Friday on quadratic equations.” Theresa didn’t appear impressed.

“Of course, under Common Core, he might not be required to memorize the quadratic formula, but would have to explain how and why it works,” she said.

How a student could be deemed to understand the quadratic formula without knowing it was puzzling. I suppose they could memorize “The quadratic formula is obtained by solving the general quadratic equation by completing the square”. Such rote understanding might pass for explaining how and why it works in the world of Common Core. But I’ll take as demonstration students who can complete the square or who can reproduce the derivation of the quadratic formula for the extra credit points on the upcoming quiz. Or Calvin’s memorization of the quadratic formula.

I knew my approach would likely not pass muster with Theresa or Sally or the principal. I also knew that I was proud of Calvin.


Anonymous said...

"How a student could be deemed to understand the quadratic formula without knowing it was puzzling."

I wish someone would pin down one of these Theresas and make them answer this question without vagueness and hand-waving. What *exactly* does this mean?

SteveH said...

So how much do these people really believe what they are saying? It seems so ironic that they spout this rote educational line.

Anonymous said...

Did this strike anyone else as weaselspeak:

“If you look at workplaces nowadays, it’s all about collaboration. You have to know how to work as a team. Now I’m not saying that we abandon individual learning. But we also have to foster how to work together.”

Was he talking just about the students working as a team, or the teachers too? And perhaps working as a team means 'shut up and tell the same lies everybody else does.'

Mnemosyne's Notebook said...

I wonder if the layers of irony involved in memorizing and repeating the statements “So no more ‘here's the assignment from the book, and there'll be a test on the material next week’. It will be more about understanding" ever occurs to the sorts of folks who say things like that. What "understanding" preceded that memorization? How would they compare and contrast "understanding" with "passive, rote acceptance."

One can appreciate the value of the quadratic formula (and the value of memorizing it) because it leads to the solutions of quadratic equations. What is the value of memorizing the babble above? Continued employment in public education. So it gets memorized, without any skepticism.