Last year, the principal of the school where I taught wanted me and the other math teacher to attend six all day professional development sessions over the course of the school year. According to the flyer advertising the PD the sessions encouraged “collaboration” amongst the math teachers in the county where I taught. It was to be facilitated by someone who believes that students who are faltering but need just a little more time to get it are lacking some key bit of information. Her solution is “just in time” learning in which the problem dictates what the student needs to know in order to solve it. I don’t think much of “just in time” learning and have written about it elsewhere so will spare you any rants about it.

I was distressed about having to attend the PD. My distress was not only because of missing six days of teaching. It was the idea of sitting around with other teachers sharing dubious ideas, including but not limited to the virtues of working in groups, “just in time” learning, differentiated instruction and other ineffective practices that pass as superior to the traditional methods that are derided as “having failed thousands of students”.

So when I learned the PD had been cancelled because I and the other math teacher, James, at my school were the only two people who had signed up for it, I was delighted.

My delight was rather short-lived, however. The moderator was one who didn’t give up easily. She met with our principal and came up with the alternative of having a two hour meeting with the two of us at our school in the early part of the day before our classes started. To her this was a win-win since she got to deliver her PD and we wouldn’t have to miss any class time.

We tried it out one time. I happen to know a bit about her background because I took a look at her blog. She’s a fan of Phil Daro, who is largely responsible for the Common Core math mess, and getting California to adopt the standards. He talks a lot about how in traditionally taught math, students are taught “answer getting” but not understanding in math. It was evident that she bought in heavily to the idea of “answer getting” vs “understanding” during our confab with her.

She began our two-hour collaboration by talking about how the state tests that are aligned with Common Core in California are not about “answer getting” anymore—rather students must explain their answers. The tests now evaluate whether students are able to see problems in more than one way. Which raises the question of why a student is deemed to lack “deeper understanding” if they get the answer in one way, but cannot show additional ways. She said the tests aim at certain “targets” which are more the Common Core Standards of Mathematical Practice (SMP) than they are of Common Core’s content standards. The SMPs are generic competencies like “persevere in solving problems”, “find structure and repeated reasoning in problems”: things that would come about anyway from practice of content, rather than trying to develop “habits of mind” outside of the context of content.

Given that the focus of the test is on vague and largely immeasurable competencies, she went on to say that on the state test, students can get full credit on problems where they have to provide explanations even if they get the numerical answer wrong–provided the reasoning and process are correct. (Full confession: I give partial credit to my students if they set up a problem correctly, but I do take off points for numerical mistakes.)

But now she was warming up to what she really wanted to talk about. She said that explaining answers is tough for students and for this reason there is a need for “discourse” in the classroom and “rich tasks”.

I was doing a good job of keeping my mouth shut, but at this point I could contain myself no longer and asked “Could you define what a ‘rich task’ is?”

She answered as follows: “It’s a problem that has multiple entry points and has various levels of cognitive demands. Every student can be successful on at least part of it.”

This, of course, says nothing very eloquently. I had had some experience with rich problems so I knew exactly the type of problem to which she was referring; problems like “A rectangle with an area of 20 has what dimensions?” or something similar.

The one-sided conversation she was having continued for a few more minutes. Apparently she loved math while in school but was doing what she described as “following the rules and getting an answer”. (And she had given us forewarning that “answer getting” is not a desired outcome.) Later when she taught math, she found she couldn’t explain to students all the time what were the underlying reasons. I found this interesting given that I do understand a lot of the underlying reasons, and I had the same traditional math background she described—and she was a math major like me.

At this point James could take it no longer. He said that meeting for two hours for five sessions was superfluous if it was just the two of us. “I teach three different math classes plus doing IT for the school and don’t have time to delve into alternative approaches other than to follow the script and curriculum as laid out in the book.”

She took this as another “entry point”—the two of us must have seemed to her like a rich problem. “Books are just tools,” she proclaimed. “They may be strong in one area but weak in another. Traditional textbooks tend to be lacking in opportunities for conceptual understanding and are old school in their approach.”

She sensed that both of us were more than willing to let her dig her own grave here. She quickly added, “Though there’s nothing wrong with old school.”

I saw no need to tell her I use a 1962 textbook by Dolciani for my algebra class.

She asked if we relied on our textbook for a “script”, meaning scope and sequence. She turned to me and asked “Do you read just one textbook?”

“I read lots of textbooks,” I said. She looked surprised.

“He’s also written books,” James said.

“Oh, how nice!” she said and feigned an interest by asking me what they were about. I gave a “rich” answer. “Math education,” I said.

“Wonderful!” she said.

I then tried to summarize our feelings by saying that the collaboration idea seemed superfluous. Neither of us teaches in a vacuum. I read lots of textbooks and talk to lots of teachers. James had a lot more experience than I do (he’s been teaching for 22 years) so he has acquired knowledge as well. I didn’t think that this 2-hour collaboration every month was going to add much more. In addition I said I was getting mixed messages.

“On the one hand I’m told by the administration that I’m doing great, and I hear from parents that I’m doing great,” I said. “But then I’m told that I MUST attend this PD. Is there something about my teaching that’s lacking? What is this about?”

She assured us that there’s nothing lacking in our teaching and that she’s sure we are both fantastic teachers.

I said “What is it then? Is this about test scores? Is that it? They think this will raise test scores?”

She had no answer for this except something that I can’t remember.

She saw the handwriting on the wall and said “No use beating a dead horse” and said she would talk to the administration about it. I felt a bit sorry for her, but not that much.

Later on in the day I met with the principal on another matter. Normally she is quite cheery but she didn’t look happy to see me, so I knew she was disappointed.

But the next day she was cheerful again, life went on as normal and another of life’s disappointments had passed.

Good job ! Not only did you succeed in getting rid of the sessions, but you did not learn anything bad. I cringed just reading about this attempt to re-program you and force you to adopt something that does not make sense. Hold the course!

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You escaped with the skin of your teeth 🙂

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“It’s a problem that has multiple entry points and has various levels of cognitive demands. Every student can be successful on at least part of it.”

This reminds me so much of what my son’s early grade school teachers said about differentiated instruction – or rather, differentiated learning. “Success” without mastery – “answer getting”. The onus was on the kids and the parents. The assumption is that their process will do the job and if there is failure, then it doesn’t belong to them. Meanwhile, more and more parents take up the slack at home and set higher expectations. The teachers point to those kids as proof of their process.

“answer getting”

Haven’t they every studied homework problem sets in any good textbook? There are so many variations that “answer getting” really means something. Students can’t possibly learn them all by rote. However, they can learn by rote the words that make teachers think they know more than what they do.

Life goes on and parents and tutors cover for them, and we still have no study that separates out the results of those kids who received outside help. Big data doesn’t help if you don’t collect the right data. You will see some kids do well and then come to the wrong conclusion.

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