~ Lessons for Other People ~

§ Launch

For just about three years I wrote math lessons that I wasn’t sure I’d ever teach. It’s a strange exercise, writing lessons for other people. The big experience we think of as INSTRUCTION reduces, at the tactical level, to a series of conversations among a particular group of human beings in various states of mathematical maturity. Trying to facilitate those conversations without immediate access to the relevant humans is hard.[citation needed] It made me uncomfortable, in the best and worst ways, personally and professionally. It also provided me an interesting view of the curricular landscape. After a humiliating number of failed attempts to catalog my time in deep and frustrating contemplation of what curriculum is and how it actually functions, here are some things that I currently think. I think.

§ Creep and Retreat

There’s a phenomenon in consumer economics known as feature creep: the tendency for products to accumulate new features beyond the point of usefulness, desirability, and sometimes sanity. Your remote control is probably an instructive example. I count 61 buttons on mine, excluding those with multiple degrees-of-freedom or combinations involving the SHIFT key. I’m not certain how many I actually use, but considerably fewer than that. For sure.

I own this monstrosity because there’s often a significant gap between what we actually want or need a product to do and what we require of a product in order for it to entice us in the marketplace. If you ask professional DVD remote engineer to design a DVD remote, there’s a good chance you’ll end up with something nuts. A professional DVD remote engineer must satisfy not only your actual consumer needs, but also your perceived consumer needs — needs that are sometimes created right there on the spot for the sole purpose of being immediately satisfied.1 And so you end up with a contraption that lets you watch your movies backwards at three-quarter speed with Esperanto subtitles rotated 90° clockwise. Because the professional DVD remote engineer knows, from experience, that given the choice between that contraption and one that only lets you watch your movies backwards at three-quarter speed with Esperanto subtitles in unrotated text,2 you’ll pick the first one nine times out of ten. Especially if they’re right next to each other on store shelves. Which, of course, they are.

If, on the other hand, you ask an average user to design his or her own personal DVD remote, you’ll likely end up with buttons that (exhaustively) play, pause, stop, rewind, fast-forward, skip chapters, and eject. You’ll end up with (only) those buttons because they cover 99% of use cases for a normal human being who wants to watch a DVD on planet Earth.

The things we want to use and the things we want to buy are often very different. Of course what we want to buy wins out — almost by definition — and so we’re stuck with products that are easy to desire but hard to wield. Like a hoarder who’s convinced that someone, someday, will desperately require that terrarium full of bottle caps, we end up buried under the ghosts of hypothetical need.3

Curricular materials are consumer products. They suffer from the same gap and are subject to the same pressure. Except the curriculum situation is even worse, because the pressure can operate in opposing directions. For some consumers, features creep in the ordinary way: they see materials with more scaffolding, more steps, more structure, and think they’re getting a bargain. The apparent bang/buck ratio gets high enough that the bucks seem justified. As a result, you get lessons or activities that feel increasingly stifling, claustrophobic, overdetermined. Hands are tipped too early. The author or teacher is doing work that might be better left to the student.

But for a certain subset of consumers, many of those same features scan as bugs. When these folks evaluate materials, their internal voices whisper things like Be less helpful. They want activities that students can shape to their own thinking. They want lesson structures to emerge organically rather than come fully formed, hard-coded by the creator. They want to offer a simple prompt and watch the class notice and wonder its way to discovery. They want…less. But then teachers end up working in a potentially uncomfortable space with very little in the way of lumbar support. The specter of amorphous time looms large. Planning for ill-defined possibilities gets hard quickly. Let’s call this phenomenon feature retreat.

The important point is this: in either case features are being pushed in the wrong direction, or at least too far in one of those directions. Assuming there’s some optimal level of structure/scaffolding/buttressing, creep and retreat both urge users toward products they’ll find problematic in the wild, and authors find themselves struggling to toe an impossibly thin line between adequate support and adequate flexibility. All while trying to make “adequate” seem marketable.

Here’s the fundamental — and potentially unresolvable — problem of curriculum design: it might be impossible to right-size the feature list for math lessons on anything approaching a universal scale. The best that authors can hope for is to provide a structure that’s easily adaptable by an individual teacher as she feels around for her own personal feature list in real time. In today’s technological climate, this problem has some interesting consequences for both teachers and authors.

§ The Cult of Customization

I said “the best” back there as if it were well defined, but even in such a narrow sense that’s pretty obviously dumb. Sell sheets for curricular materials are longer than one sentence precisely because they claim to solve a bunch of pedagodical problems simultaneously. If a product aspires to serious consideration, it has to do more than rescue individual teachers from having to create all their own stuff4 — regardless of how much opportunity there is for arbitrary customization or how easy that opportunity is to realize. The rise of customization has increased the tension between creators and consumers of curriculum in a way that threatens the very notion of “curriculum” in the first place. Maybe that’s a good thing, maybe not. It’s complicated.

For intance, one thing you’re ostensibly paying for when you invest in curriculum is some kind of unifying vision. That vision could be methodological (the Discovering Mathematics series), schematic (the Connected Mathematics Project), philosophical (College Preparatory Mathematics)5 — all kinds of adjectives — but it’s part of what makes a curriculum more than a collection of items.6 An intentional, high-level view of some region of the mathematical landscape is what gives us hope and/or confidence that our students can come to appreciate the same vantage. It might actually be the thing you’re paying for.

So at this point I’m in the common and somewhat awkward position of having said two reasonable and mutually exclusive things: (1) It’s desirable for teachers to have some level of practical influence over their materials, and (2) It’s important for those materials to faithfully represent the principles that form their foundation. Teachers aren’t going to be particularly satisfied without (1); authors aren’t going to be particularly effective without (2). Like I said, complicated.

It comes down to control. Creators have a lot of it — for obvious reasons — and until relatively recently they had a lot more. The move toward open resources, along with the technologies and networks that have led to their proliferation, means that teachers can increasingly exercise control in curation and adaptation.

For many teachers, curriculum now functions more like a playlist than an album: assemble some greatest hits, arrange them in a pleasing order, and hit play. No junk. No filler. In a world where the studio album is dead and the raw material for compilation is so abundant, this seems like a self-evidently reasonable strategy.

Of course abundance is a major part of the problem with this emergent freedom. A quick7 Google search for “math lessons” turns up 96 million results — almost four times the number of songs in the iTunes store. That’s an awful lot of noise to scan for your particular signal. And, even if you manage to find it, the process of compilation is a very subtle art. It’s incredibly hard to organize something lucid and meaningful from a collection of disparate minds and voices. To do it right is probably not any easier or less time-consuming than starting from scratch, which most teachers would agree is a deal-breaker.

Curriculum developers function as a pressure valve for teachers who already have too many other things to worry about. They not only create the discrete units of consumption (which enterprise, based on the numbers cited above, teachers are plenty willing to reclaim a sizable chunk of), but also handle the crucial and unsexy job of assembling them into a coherent whole. To put a finer point on it: given the considerable8 non-curricular demands teachers face, they just aren’t equipped to perform what would amount to a second full-time job. At least not as well as someone — more likely a team of someones — doing it as a first full-time job.

Instead, or additionally, teachers can roughly accept an extant curriculum but adapt it at the level of the individual lesson or task. That’s not really theoretical; it’s simply what teachers do every single day. Few teachers, in few cases, decide that some piece of curricular magic is unimprovable for a particular classroom situation. It’s just that now the tools for making, organizing, and sharing those edits are the best they’ve ever been and continue to improve rapidly.9

But there’s only so much changing of individual pieces you can do before you start to affect things on a macro level. You quickly run into a Ship of Theseus problem, at which point what curriculum are you really using? Or — if you’re a developer — what are you even selling?

In any case, the idea of authorial vision is fundamentally at odds with consumer adaptation. So here we are in this situation where authors can’t (a) write materials with optimal support, or (b) offer too much opportunity for customization without sacrificing the unifying thread that makes for a coherent user/student experience. It’s fun to speculate about what’s going to give, but it’s seeming more and more that something has to.

§ The Barthes Ultimatum

One obvious solution to the difficulties surrounding authorship is simply to kill off the author.10 Or at least the idea of an author as not only the originator of content, but as its perpetual source of authority.11 A good piece of content is strong enough to stand on its own, thank you very much, and the details of who created it or why or how are largely incidental to its inherent goodness. Essentially, content is a sola scriptura kind of deal.

Ignoring for a moment that pieces of content do not a curriculum make, having lessons run around on their own in the wild comes with its own set of issues. Take, for instance, perpetual #MTBoS darling “Barbie Bungee.”12 In a recent study wherein I thought for a minute about the most blogged-over lessons in history, it’s definitely in the top five. If you’re interested, you can easily find a whole bunch of community implementations to help you prepare. But here again the paradox of choice rears its head. Which one is right for you? And an often more pressing concern: where should you turn for support?

Smaller, shall we say boutique, lessons are less overwhelming. Like maybe Matt Vaudrey’s lovable “Mullet Ratio.” Having a more or less canonical version is really nice, and part of its lovability — at least for me — is knowing that it’s Matt’s. But if you’re looking for someone or something to turn to in a moment of pedagogical need, you’re pretty much stuck hoping Matt is free. Or doing a bunch more Googling.

It would be great if we could find a way to combine centralized support with community contribution for open curricular resources.

§ MatHub

I’m about to make a suggestion that’s wrong in specific and important ways, but probably right in general. We need GitHub for math curriculum.

To say that the community repository model has done wonders for open source software is a massive understatement. To what extent that success translates to curriculum I’m obviously unsure, but I have randomly-ordered reasons to suspect it’s appreciable:

  1. Centralized support with decentralized control. Materials have a canonical home and form, but it’s trivially easy to create and adapt local forks. You can make your own stuff without starting from scratch, or assemble your own stuff without having to build a framework.
  2. Modifications are automatically integrated. Changes at the local level aren’t just tacked or collected in a secondary place. And they don’t need to be tracked or disseminated.13 The moment modifications are made, they’re fully integrated into a new product and are immediately available across users.
  3. Ease of rolling back failed experiments. You’re never locked into something that sucks, so experimentation is essentially zero-risk. If version B turns out to be terrible, rolling back to version A takes about five seconds.
  4. Simple system for managing differentiation. We’re talking about a steroidal version control system here, so it’s not surprising that the managing multiple versions is a big win. Create a parallel branch for students who need modified assessment materials, or one with some minor modifications for 3rd-period. Importantly, you get to decide what level of granularity makes sense.
  5. Both downstream and upstream improvements. If you like something that’s changed in the main repository, just pull it into your fork (or, if you don’t, don’t) instantly. But if you make some local changes that might benefit the overall project, you can also submit them upstream for inclusion in the canonical version. With the current setup (even among OER), that’s approximately 100% impossible.
  6. Discussion and decision points persist. Since everything is always a work in progress, there’s no incentive or expectation for contributors to hide their rough-draft efforts. Discussions, disagreements, and justifications about important (or un-) decisions are just part of the package: always there, transparently awaiting your inspection whenever you wonder, “What the hell were they thinking?”
  7. Low barriers to entry. Anyone can participate in creation or curation of materials, or at least be well informed about what’s going on, without any kind of privileged status in the curricular universe.
  8. At worst, it’s at least as good as the status quo. The system makes all these great things possible, but it doesn’t make them mandatory. Not only are modifications locally low-risk, the apparatus is itself globally low-risk. You can just accept an extant curriculum as-is (in which case you’re in roughly the same position you’ve always been in), or you can ride the bleeding edge. Or you can settle somewhere in between.

Most crucially (so I’ll break it out of the bulleted list), collaboration is built into the DNA. I said “you” a lot in that list, but only because English lacks a distinct plural second-person pronoun. “You” could be your algebra team, or your math department, or your district curriculum folks, or…you. The whole point of community curriculum repositories would be for a group of education professionals using their collective expertise to take ownership of curriculum in a sustainable way.

There are certainly many important obstacles to a system like this. Somebody still needs to create quality, coherent, base curricula to start from (and decide which kinds). Those people need particular expertise and availability beyond that of the average classroom teacher. They need incentives. Repositories need to be actively and expertly maintained. Key personnel still need to fill key rolls, lest we end up with another worksheet boneyard or ironically named BetterLesson. Burnout in this arena is real, so maybe let’s not heap that on top of people in a profession with a five-year half-life as it is. And none of this will solve the problem of companies trying to make a dollar on the backs of hardworking open-source creators and maintainers.

The implementation details are, shall we say, unresolved.

But here are some things that aren’t obstacles: the technological infrastructure for massively distributed, real-time collaborative systems; resources and platforms for building rich content; or a large and connected community of thoughtful professionals. With those things in place (and always improving), I have a hard time imagining barriers that are insurmountable — to whatever future. I’m so curious about what that’s going to look like.

  1. ‘Murrica.

  2. Like a naivulo.

  3. And typically at least one dead cat.

  4. Although that’s a pretty important selling point for everyone involved in this transaction.

  5. Which seems to have undergone a 3M-like abbreviation rebranding, but still.

  6. Because we always intended our lesson library to be supplemental, the vision at Mathalicious took a less holistic form. It was14 certainly philosophical (i.e., a supremely important reason for studying mathematics is that it equips you to better engage in meaningful thought and discourse about the world), but mostly it was a narrative vision at the level of the individual lesson. We were at least as much a storytelling company as a curriculum company; we just happened to be telling stories made possible — or at least more deeply satisfying — by a hefty dose of 6 - 12 math.

  7. ≈340 ms

  8. To put it rather lightly.

  9. Even when curriculum companies try to make things infuriatingly difficult.

  10. Sometimes violence does indeed solve problems.

  11. Relevant here is D.F. Wallace on B.A. Garner and authority vs. Authority.

  12. The major style guides are silent on whether lesson titles should be quoted or italicized. They seem to me closer to poems or short stories than novels.

  13. Slope_Intercept_Form_Lusto_version4(FINAL)(FINAL FINAL)(ACTUALLY FINAL).docx

  14. I’m going to talk about Mathalicious in the past tense even though it is — at the time of writing — still a very present-tense sort of thing, only because I’m probably no longer qualified to speak to its current philosophical state.