Tag Archives: curriculum sequence

Teacher Federalism

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:

  1. we all agreed that students had to come out of Algebra 2 with an indisputably strong understanding of lines.
  2. 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.
  3. 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?
  4. This called for limiting new topics to a handful. One or two in depth, a few more introduced.
  5. 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.

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Content Knowledge and Reading Comprehension: Bold Talk and Backpedaling

Empty buckets seldom burst into flames. –Robert Pondiscio, Literacy is Knowledge.

People who push curriculum as a solution are generally pushing content knowledge, and they’re pushing content knowledge as a means of improving reading comprehension. Most of these people are in some way associated with Core Knowledge, the primary organization pushing this approach. They aren’t pushing it for money. This is a cause.

Pondiscio’s piece goes to the same well as E. D. Hirsch, who founded the Core Knowledge Foundation to promote the cause of content knowledge in curriculum, Lisa Hansel, the CK Foundation’s current Pondiscio, and Daniel Willingham, who sits on the board of Core Knowledge.

Pondiscio even borrows the same baseball analogy that Hirsh has used for a decade or so, to illustrate the degree to which content knowledge affects reading comprehension. Many Americans are unfazed by “A-Rod hit into a 6-4-3 double play to end the game”, but might be confused by “I’ll see how the wicket is behaving and then decide who are the bowlers I’ll use in the last few overs.”

We can understand content if we have the background knowledge, Hirsh et. al. assure us, but will “struggle to make sense” of reading if we’re unfamiliar because, as Pondiscio asserts, “Prior knowledge is indispensable”.

Let’s take a look at what some people do when they read without requisite content knowledge. (you can see other examples from my early childhood here).

Let’s pick another sporting event—say, the Kentucky Derby, since I don’t pay much attention to it. I googled, saw a headline at Forbes: “Final Kentucky Derby Futures Wagering Pool Opens Today”.

I don’t watch horseracing, I don’t bet, I know about futures because they were a plot point in “Trading Places”, but until that google I had no idea that people could bet on who won the Derby now, in advance. And now I do.

I was not confused. I didn’t struggle, despite my lack of prior knowledge. I constructed knowledge.

But Pondiscio says that any text on horse-racing is a collapsing tower of wooden blocks, “with each block a vocabulary word or a piece of background knowledge”, to anyone unfamiliar with horseracing. I have too few blocks of knowledge.

Robert Pondiscio would no doubt point out that sure, I could figure out what that Kentucky Derby headline meant, because I knew what the Kentucky Derby was. True. I’ve known what the Kentucky Derby was ever since I was 9 or so. I didn’t get the information from my parents, or my privileged life (I grew up decidedly without privilege). I read through all the Highlight articles at the doctor’s office and picked up a Sports Illustrated out of desperation (the internet is a glorious place; I just found the article) and then did exactly what Pondiscio suggests is impossible—read, understood, and learned when before I knew nothing.

I first knew “derby” as a hat, probably from an Enid Blyton story. But I had recently learned from “The Love Bug” that a derby was also a race. What did racing have to do with hats? But now I learned that horse races could be derbies. Since horses were way older than cars, the car races must have gotten the “derby” idea from horses. Maybe jockies got hats when they won horse races. (I learned many years later, but before today, that I was wrong.) I not only built on my existing knowledge base, I learned that the Kentucky Derby was a yearly horse race almost a century old and the results this year were upsetting. No one expected this horse to win, which probably was why people were upset, because just like the bad guy had a bet with the Chinese guy in “The Love Bug”, people made bets on who won. The article also gave me the impression that horses from Venezuela don’t always win, and that lots of horse races had names.

Pondiscio gives another example of a passage requiring background knowledge: the Dutch in New Amsterdam. Oddly enough, I distinctly remember reading just that sort of passage many years ago back in the fifth or sixth grade, about New Amsterdam first being owned by the Dutch, then control going to the English. I knew about Holland from Hans Brinker, which I’d found in someone’s bookshelf, somewhere, when I was six or seven. So New York was first founded by the Dutch–maybe that’s why they called the dad Mynheer in Legend of Sleepy Hollow just like they did in Hans Brinker, because according to the cartoon I’d seen on Wonderful World of Disney, Sleepy Hollow took place in New York .And then the English took it over, so hey, York must be a place in England. So when done, I knew not only that the Dutch had once been in the New World, but that other countries traded colonies, and that while we all spoke English now, New York had once been Dutch.

I didn’t carefully build content knowledge. I just got used to making sense of chaos, grabbing onto whatever familiar roadmarks I saw, learning by a combination of inference and knowledge acquisition, through haphazard self-direction grabbing what limited information I could get from potboiler fiction, magazines, and limited libraries, after gobbling up all the information I could find in schoolbooks and “age-appropriate” reading material. And I learned everything without prior knowledge other than what I’d acquired through previous reading, TV and movies as came my way. I certainly didn’t ask my parents; by age six I acknowledged their expertise in a limited number of topics: cooking, sports, music, and airplanes. In most important topics, I considered them far less reliable than books, but did deem their opinions on current events useful. Yes. I was obnoxious.

My experiences are not unique. Not today, and certainly not in the past. For much of history, people couldn’t rely on information-rich environments and supportive parents to acquire information, so they turned to books. Using vocabulary and decoding. Adding to their existing knowledge base. Determinedly making sense of alien information, or filing it away under “to be confirmed later”.

But of course, say the content knowledge people pushing curriculum. And here comes the backpedal.

E. D. Hirsch on acquiring knowledge:

Almost all the word meanings that we know are acquired indirectly by intuitively guessing new meanings as we get the overall gist of what we’re hearing or reading.

That describes almost exactly what I did for much of my childhood. But this is the same Hirsch who says “Reading ability is very topic dependent. How well students perform on a reading test is highly dependent on their knowledge of the topics of the test passages.” Nonsense. I scored at the 99th percentile of every reading test available, and I often didn’t know anything about the topic of the test passage until I read it—and then I’d usually gleaned quite a bit.

Pondiscio slips in a backpedal in the same piece that he’s pushing content.

Reading more helps, yes, but not because we are “practicing” reading or improving our comprehension skills; rather, reading more is simply the most reliable means to acquire new knowledge and vocabulary.

This is the same Pondiscio who said a couple years ago:

What is needed is high-quality preschool that drenches low-income learners in the language-rich, knowledge-rich environment that their more fortunate peers live in every hour of every day from the moment they come home from the delivery room.

Well, which is it? Do they think we learn by reading, or that we only learn by reading if we were fortunate enough to have parents who provided a knowledge-rich environment?

Take a look at the Core Knowledge promotional literature, and it’s all bold talk: not that more content knowledge aids comprehension, but that content knowledge is essential to comprehension.

I’ve likewise tweeted about this with Dan Willingham:

Me: Of course, taken to its logical conclusion, this would mean that reading doesn’t enable knowledge acquisition.

Willingham: if you have *most* of the requisite knowledge you can and will fill in the rest. reading gets harder and harder. . . ..as your knowledge drops, and the likelihood that you’ll quit goes up.

Me: The higher the cog ability, the higher ability to infer, fill in blanks.

Willingham: sooo. . . hi i.q. might be better at inference. everyone infers, everyone is better w/ knowledge than w/out it. yes?

So Willingham acknowledges that IQ matters, but that as knowledge and IQ level drops, engagement is harder to maintain because inference is harder to achieve. No argument there, but contrast that with his bold talk here in this video, Teaching content is teaching reading, with the blanket statements “Comprehension requires prior knowledge”, and attempts to prove that “If you can read, you can learn anything” are truisms that ignore content knowledge. No equivocation, no caveats about IQ and inference.

So the pattern: Big claims, pooh-poohing of reading as a skill that in and of itself transfers knowledge. If challenged, they backpedal, admitting that reading enables content acquisition and pointing to statements of their own acknowledging the role reading plays in acquiring knowledge.

And then they go back to declaring content knowledge essential—not useful, not a means of aiding engagement, not important for the lower half of the ability spectrum. No. Essential. Can’t teach reading without it. All kids “deserve” the same content-rich curriculum that “children of privilege” get not from schools, but from their parents and that knowledge-drenched environment.

And of course, they aren’t wrong about the value of content knowledge. I acknowledge and agree with the surface logic of their argument: kids will probably read more readily, with more comprehension, if they have more background knowledge about the text. But as Daniel Willingham concedes, engagement is essential as well—arguably more so than content knowledge. And if you notice, the “reader’s workshop” that Pondiscio argues is “insufficient” for reading success focuses heavily on engagement:

A lesson might be “good readers stay involved in a story by predicting” or “good readers make a picture in their mind while they read.” ..Then the children are sent off to practice the skill independently or in small groups, choosing from various “high-interest” books at their individual, “just-right” reading level. [Schools often have posters saying] “Good readers visualize the story in their minds.” “Good readers ask questions.” “Good readers predict what will happen next.”

But Pondiscio doesn’t credit these attempts to create engagement, or even mention engagement’s link to reading comprehension. Yet surely, these teachers are simply trying to teach kids the value of engagement. I’m not convinced Pondiscio should be declaring content knowledge the more important.

Because while Core Knowledge and the content folks have lots of enthusiasm, they don’t really have lots of research on their product, as Core Knowledge representatives (q6) acknowledge. And what research I’ve found never offers any data on how black or Hispanic kids do.

Dan Willingham sure seemed to be citing research lately, in an article asking if we are underestimating our youngest learners, citing a recent study says that we can teach young children knowledge-rich topics like natural selection. He asks “whether we do students a disservice if we are too quick to dismiss content as ‘developmentally inappropriate,'” because look at what amazing things kids can learn with a good curriculum and confidence in their abilities!

Of course, a brief perusal of the study reveals that the student populations were over 70% white, with blacks and Hispanics less than 10% total. Raise your hand if you’re stunned that Willingham doesn’t mention this tiny little factoid. I wasn’t.

Notice in that study that a good number of kids didn’t learn what they were taught in the first place, and then a number of them forgot it quickly. Which raises a question I ask frequently on this blog: what if kids don’t remember what they’re taught? What if the information doesn’t make it to semantic memory (bottom third of essay). What evidence do the curriculum folks have that the kids will remember “content” if they are taught it in a particular sequence? (Note: this essay was too long to bring up Grant Wiggins’s takedown of E. D. Hirsch, but I strongly recommend it and hope to return to it again.)

Like reformers, curriculum folk are free to push the bold talk, because few people want to raise the obvious point: if content knowledge is essential, instead of helpful, to reading comprehension, then no one could ever have learned anything.

But contra Pondiscio, empty buckets do burst into flames. People do learn without “essential” content knowledge. Even people from less than privileged backgrounds.

Here’s the hard part, the part too many flinch from: Smart people can learn this way. All anyone has ever needed to acquire knowledge is the desire and the intellect. For much of history educated people had to be smart and interested.

In recent years, we’ve done a great job at extending the reach of education into the less smart and less interested. But the Great Unspoken Truth of all education policy and reform, be it progressive, critical pedagogy, “reform” or curricular, is that we don’t know how to educate the not-smart and not-interested.