A year or so ago, our school’s upper level math teachers met to define curriculum requirements for algebra two.

I’d been dreading this day for several weeks, since we agreed on the date. I teach far fewer Algebra 2 topics than the other teachers. Prioritizing depth over breadth has not made me terribly popular with the upper math teachers–who of course would dispute my characterization of their teaching. There were three of them, plus two math department leaders who’d take their side. I’d be all alone playing opposition.

Only two possible outcomes for this meeting. I could, well, lie. Sign off on an agreed curriculum without any intention of adhering to my commitment. Or I could refuse to lie and just and fight the very idea of standardization The good news, I thought, was that the outcome would be my choice.

Then the choice was taken away from me.

Steve came into my room beforehand. Steve is the member of the upper math group I’m most friendly with, which means we are, well, warily amicable. Very different characters, are we. If you’re familiar with Myers-Briggs, Steve is all J and I’m as P as P can be. But over the years we realized that while our approaches and philosophies are polar opposites, we are both idiosyncratic and original in our curriculum, more alike than we’d imagined. He was interested by my approach to quadratics and his approach to transformations is on my list of innovations to try.

So Steve tiptoed into my room ahead of time and told me he wanted the meeting to be productive. I went from 0 to 95 in a nanosecond, ready to snap his head off, refusing to be held responsible for our departmental tensions, but he called for peace. He said it again. He wanted this meeting to be productive.

I looked, as they say, askance. He asked me if I would be willing to settle for good, not perfect. I said absolutely. He asked me to trust him. I shrugged, and promised to follow his lead.

For reasons I won’t go into, no one expected Steve to run the meeting. But in the first five minutes, Steve spoke up. He said he wanted the meeting to be productive. He didn’t want the perfect to be the enemy of the good.

We all wanted what was best for our students, he said. We all thought we knew what was best for our students. But we had very different methods of working. If we tried to agree on a curriculum, we’d fail. Eventually, someone in power, probably at the district, would notice, and then that someone might make the decision for us.

So rather than try to force us all to commit to teaching the same thing, why not agree on the topics we all agreed were essential, “need to know”? Could we put together a list of these topics that we’d all commit to teach? If it’s not on the list, it’s not a required element of the curriculum. If it was on the list, all teachers would cover the topic. We’d build some simple, easily generated common assessments for these essential topics. As we covered these topics–and timing was under our control–we’d give the students the assessment and collect the data. We could review the data, discuss results, do all the professional collaboration the suits wanted.

If we agreed to this list, we would all know what’s expected. All of us had to agree before a topic went on the “need to know” list. No teacher could complain if an optional topic wasn’t covered.

I remember clearly putting on my glasses (which I normally don’t wear) so that I could see Steve’s face. Was he serious? He saw my face, and nodded.

Well. OK, then.

Steve’s terms gave me veto power over the “need to know” list.

Wing and Benny were dubious. What if they wanted to teach more?

As requested, I backed Steve’s play. “We could make it a sort of teacher federalism. The “Need to know” list is like the central government. But outside these agreed-upon tenets, each individual teacher state gets complete autonomy. We can teach topics that aren’t on the list.”

“Exactly,” Steve added. “The only thing is, we can’t expect other teachers to cover things that aren’t on the list.”

In other words, Steve was clearly signaling, no more bitching about what Ed doesn’t cover.

We agreed to try building the list, see if the results were acceptable. In under an hour, we all realized that this approach would work. We had 60-80% undisputed agreement. At the same time, Wing and Benny had realized the implications of the unanimous agreement requirement. A dozen or more items (under topics) the other three teachers initially labeled eessential) were dropped from the “need to know” list at my steadfast refusal to include them. Steve backed me, as promised.

While all three raised their eyebrows at some of the topics downgraded to the “nice to have” list, they all listened carefully to my arguments. It wasn’t just “Ed no like.” As the day went on, I was able to articulate my standard–first to myself, then to them:

- we all agreed that students had to come out of Algebra 2 with an indisputably strong understanding of lines.
- We routinely have pre-calc students who need to review linear equations. In fact, I told them, this realization was what led me to dial back algebra 2 coverage.
- Non-honors students were at least a year away from taking precalc, which was where they would next need the debated skills. If some of our students weren’t remembering lines after three years of intense study, how would they easily remember the finer points of rational expressions or circle equations, introduced in a couple weeks?
- This called for limiting new topics to a handful. One or two in depth, a few more introduced.
- Our ability to introduce new topics in Algebra 2 was gated by the weak linear knowledge our students began with. If we could convince geometry teachers to dramatically boost linear equations coverage, then we could reduce the time spent on linear equations in algebra 2.

Once I was able to define this criteria, the others realized they agreed with every point. Geometry priorities were a essential discusison point, but outside the scope of this meeting and a much longer term goal. That left all debate about point 4–how much new stuff? How much depth?

This reasoning convinced them I wasn’t a lightweight, and they all knew that my low failure rate was extremely popular with the administrators. So they bought in to my criteria, and were able to debate point 4 issues amicably, without loaded sarcasm.

I knew I needed to give on topics. At the same time I was shooting down topics, I was frantically running through the curriculum mentally, coming up with topics that made sense to add to my own curriculum, making concessions accordingly.

The other teachers looked at the bright side: I’d be the only one changing my curriculum. Every addition I agreed to had to be carefully incorporated into my already crowded Algebra 2 schedule. I did have some suggested additions (a more thorough job on functions, say), but none of mine made the cut. The other teachers’ courses were entirely unaffected by our “need to know” list.

At the end of the day, we were all somewhat astonished. We had a list. We all agreed that the list was tight, that nothing on the “like to know” or “nice to have” list was unreasonably downgraded. I want to keep this reasonably non-specific, because the issues apply to any subject, but for the curious: rational expressions were the most debated topic, and the area where I made the most concessions. They covered addition and subtraction, multiplication and division, graphing. We settled on introduction, graphing of parent reciprocal function and transformations, multiplication and division. Factoring was another area of dispute: binomial, of course, but I pushed back on factoring by groups and sum/difference of cubes. We agreed that exponential functions, logarithms and inverses must be covered in some depth, enough so the strongest kids will have a memory.

“What about grades?” Benny asked. “I don’t want to grade kids just on the need to know list.”

“But that’s not fair,” I objected. “Would you flunk kids who learned everything on the need to know list?”

“Absolutely,” Wing nodded.

I was about to argue, when Steve said “Look, we will never agree on grading.”

“Crap. You’re right.” I dropped the subject.

In a justly ordered world, songs would be sung about “That Day”, as we usually call it. Simply agreeing to a federalist approach represented an achievement of moon walk proportions. Then we actually built a list and lived by it, continually referring to it without the desire to revisit the epic treaty. Stupendous.

I didn’t write about the agreement then because I worried the agreement would be ignored, or that other senior math folk would demand we revisit. Instead, our construction of the “Need to Know” list shifted the power base in the math department in interesting ways. Our point man on these discussions did indeed express displeasure with the Need to Know list. It’s too limited. He wants more material on it. He expected us to comply.

Wing, Benny, and Steve could have easily blamed me for the limits. “Oh, that’s Ed’s doing. We all want more on the list.” Instead, upper math folk presented an instantly united front and pushed back on incursion. No. This works for us. We don’t want to break the agreement. We like the new productivity of our meetings. Team cohesion is better. Wing and Ben still think I’m a weak tea excuse for a math teacher, but they understand what we’ve achieved. With this unity, we are less vulnerable.

In short, we’ve formed our own power base. As I’m sure you can guess, Steve is the defacto leader of our group, but he gained that status not by fiat, but by figuring out an approach to handle me that the others could live with. No small achievement, that.

Will it last? Who knows? Does anything? It’s nice to watch it work for the moment. I’ll take that as a win.

We’ve used that agreement to build out other “need to know” lists for pre-calc and trigonometry. They aren’t as certain yet, but Algebra 2 was the big one. Worth the work it took to update my curriculum.

Our teacher version of federalism has allowed us to forge ahead on professional practices, lapping the lower level crew several times. In fact, on several department initiatives, the upper math department has made more progress than any other subject group, something that was duly noted when hot shot visitors dropped in on our department meeting. The other groups are trying to reach One Perfect Curriculum.

I’m not good at describing group dynamics unless it’s in conversational narrative. But I wanted to describe the agreement for a couple reasons.

First, some subject departments operate in happy lockstep. But many, even most, high school math departments across the country would recognize the tensions I describe here. . I recommend teacher federalism as an approach. Yes, our agreement may be as short-lived as some “universal curriculum” agreements. But the agreement and the topics list are much easier to agree to, and considerably more flexible. I’ve seen and heard of countless initiatives to create a uniform curriculum that foundered after months of work that was utterly wasted. Our group has had a year of unity. Even if it falls apart next year, that year of unity was purchased with a day’s work. That’s a great trade.

But in a broader reform sense, consider that none of the four teachers in this story use books to teach algebra 2. Not only don’t they agree on curriculum, but they don’t use the same book. Some, like me, build from scratch. Others use several books as needed. Our epic agreement doesn’t fundamentally change anyone’s teaching or grading. We simply agreed to operate as a team with a given set of baselines. Noitce the words “Common Core” as the federal government (or state, your pick) defines it never made an appearance. It was simply not a factor in our consideration.

Does this give some small hint how utterly out of touch education policy is? How absurd it is to talk about “researching teacher practice”, much less changing it? I hope so.

June 30th, 2017 at 9:09 pm

As a non-american I cannot perfectly understand the implications of the math teachers’ coalition because of the particularities of the curriculum (pre-requisites and mandatory/optional courses). But you mention that this pact has been accepted for a whole year and I got a question. Have it interacted with other courses’ groups, e.g. as making a request to other teacher to include something you perceived that the students were lacking or to inform a following course teacher what they should expect that was already covered by the algebra 2 class?

July 3rd, 2017 at 7:41 pm

Sorry, I missed this comment earlier. The people affected by the downstream implications were all in the meeting. That is, the upper math department includes all the teachers who teach the topics beyond algebra 2: trignometry, precalc, calculus, stats, etc.

June 30th, 2017 at 9:14 pm

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July 1st, 2017 at 3:43 pm

Does this give some small hint how utterly out of touch education policy is? How absurd it is to talk about “researching teacher practice”, much less changing it? I hope so.Maybe I’m stupid this morning, but I’m not getting the hint. What is it? (or What are they?)

July 1st, 2017 at 7:38 pm

Huh, I thought it was obvious. How can you even begin to discuss things like curriculum, or even textbook selection?

July 1st, 2017 at 8:04 pm

Maybe it was those two pieces of leftover pizza but I’m still not getting it.

Why can’t you (who is you?) “even begin to discuss things like curriculum, or even textbook selection?”

If it’s outsiders, education researchers, why can’t they observe what teachers do, ask them questions, and see how students do? Of course, they’d have to be honest and have well-functioning b.s. detectors.

It seems like the five of you discussed and came to a not awful decision on curriculum, in particular “this is what every student should know (and, no, this is not a wish list, we really mean it).”

Are you saying that there is a difference between inside knowledge and outside knowledge, that outsiders will never be able to really know what teachers are doing and what students are learning?

July 1st, 2017 at 8:07 pm

Yes, but also what is the point of making big, expensive mandates that are premised on the false belief that all teachers are doing the same thing?

July 1st, 2017 at 8:53 pm

Okay. I always assumed that people who favored mandates were saying that “this is what all teachers SHOULD be doing, and if the different things they do no don’t include this, they should be required to change.” Very much a “we know best.”

And certainly mandates are hardly new in the business. State legislatures periodically pass laws requiring x, y, or z to be taught. A few decades ago, “standard-based education” was the big thing. The state education department promulgated “standards” saying what should be taught in each grade and major course: “Students will understand that … , Students will be able to …”

The Massachusetts Department had a big booklet that was revised every few years and is now on the web.

July 2nd, 2017 at 3:35 am

Right. So how are four teachers clearly teaching a bunch of different things, finally agreeing on a bare minimum, doing what you just described?

July 2nd, 2017 at 9:56 pm

They’re not. Not if the standard is minimum AND maximum. (The reductio ad absurdum being what I was once told about France: the Ministry of Education had a nationwide calendar, setting out what should be taught every day of the school year (I don’t know if that is true now or was ever true).)

And certainly not if the standard-setters don’t have major input from the people actually teaching and give them the power to decide what winds up in the standards.

But sort of if the standards just provide a minimum and allow teachers freedom to add what they want–or not add anything if they don’t want. Of course, the standards have to be realistic. They can’t be wish lists. My impression is that many state standards, and the Common Core, are over-inclusive. ” If students have a good teacher who knows how to challenge them, they can and will learn this.” Yeah, right.

It makes me think of Trofim Lysenko. He was Stalin’s number one guy for agriculture. His people would tell farmers what to plant, when, where, and how. “If you follow our instructions, you will have a bountiful harvest.” But mostly they didn’t. Stalin thought Lysenko was a scientist who knew what he was talking about. Unfortunately, often tragically, he did not.

July 3rd, 2017 at 6:37 am

But read people like Petrilli and Riley and it’s clear they see it as much more limited.

July 3rd, 2017 at 6:11 pm

What you describe here is exactly what goes on in my school. For each year, we have a document describing the “must cover”s, and everything else is optional. This leads to a great deal of sloppiness in terms of coverage, but exactly as you describe — it also leads to a great deal of happiness and collaboration in the department. We all get along quite well, and I think this is a main part of it.

What so many reform-niks don’t get is how much control teachers get over our situation. There are ways to temporarily make our lives unpleasant if we don’t play ball, but few sustainable ways to really force the matter.

As you said: this is a huge limitation of the standards reform movement.

It’s not clear to me that, in the long-run, something like Common Core won’t have ANY impact on what teachers teach. I think it will, actually, because many teachers keep an eye on their textbooks while teaching, and many of the exams require different sorts of coverage.

That said, the history of these sorts of reforms suggests that teachers will twist and finagle the new standards until they resemble something very familiar. Nobody should be surprised that the standards of mathematical practice have made very little difference in what goes on in curriculum or teaching. Nobody should be surprised that departments like your’s make decisions without a keen eye on the standards.

The two ingredients for a national reform movement: (1) an imagined crisis; (2) ignorance of the past. Without these in place, it’s hard to muster much excitement for the whole project.

July 10th, 2017 at 8:50 am

[…] An interesting glance at a high school’s math curriculum debate, and the compromise that was […]