I’m really enjoying this conversation with Brett Gilland on what a high-quality, teacher-friendly, MTBoS-created curriculum might look like. I outlined some potential features of a curriculum in my last post, and Brett responded with skepticism about the value of a modular curriculum. First, Brett articulates very well what I think the goal of a curriculum should be:
First, let me reiterate that my primary focus here is on creating a curriculum that I can actually sell my colleagues on using. You know the ones. They are either total noobs trying not to drown in their first year or, more often, they have been at this for 10-20 years and have no real interest in what the crazy hippy teacher is doing down the hall.
“Sure, he seems to be having a great time, but have you seen how long his hours are? And his results aren’t that much better.”
I am not primarily focused on the unwashed masses of crazy hippy teachers that is the MTBoS. Quite frankly, you don’t need this. To be honest, you are having so much fun that the thought of a ‘canned’ curriculum might give you a stroke, even if it were the MOST EPIC MATH CURRICULUM IN THE WORLD. Which means that the question I keep coming back to- without fail- is this:
If I give this curriculum to a solidly mediocre math teacher, will it make it easier for them to be epic(ish) than to continue to be mediocre?
Brett argues that too much choice destroys
everything curriculum, because juxtaposing the overwhelming options for great curriculum on the internet with the textbook on the table over there, the mental effort required to search and find the right resource loses to the resource a teacher already has.
Brett was much more excited about the idea of a decision tree — a curriculum that offers a starting point, and multiple pathways depending on how students do. I think there’s some potential there, but my ideal curriculum is a synthesis of the two ideas, and I want to go into some more detail, because I think this is an essential feature of a truly great curriculum.
I am a much better teacher today because of the time I have spent synthesizing different curricula, finding great resources, and figuring out how to teach them well. But that process has been exhausting, and isn’t a reasonable thing to ask every teacher to do. Many curricula are soul-crushing, but they save teachers work. There are great programs out there (CME comes to mind) but textbook adoption is usually out of teachers’ hands. I’m getting ambitious here, and I want to think about what the potential of a digital, open-source curriculum could look like. So we’ve got this challenge. Most canned curricula aren’t that great, and don’t do as much as they could to develop teachers, but they’re just so much easier to use.
I think the biggest obstacle to what I would love to see is a lack of shared language about the learning process. Elizabeth puts it better than anyone, summarizing ideas from How People Learn:
STAGE 1 – a hands-on introductory task designed to uncover & organize prior knowledge. In this stage, collaborative activity provides an occasion for exploratory talk so that students can uncover and begin to organize their existing knowledge;
STAGE 2 – initial provision of a new expert model, with scaffolding & metacognitive practices woven together. The goal here is to help students bring their new ideas and knowledge into clearer focus so that they can reach the next level. Here again, collaborative activity can provide a setting in which to externalize mental processes and to negotiate understanding, although often, this can be a good place to offer some direct instruction;
STAGE 3 – what HPL refers to as “‘deliberate practice’ with metacognitive self-monitoring.” Here the idea is to use cooperative learning structures to create a place of practice in which learners can work within a clearly defined structure in which they can advance through the 3 stages of fluency (effortful -> relatively effortless -> automatic)
STAGE 4 – working through a transfer task (or tasks) to apply and extend their new knowledge in new and non-routine contexts.
This has been my mental framework for thinking about my students’ learning process recently, and I love it. This framework leans heavily on cooperative learning, but the four stages are applicable to any learning process, in any teacher’s classroom. I would want to build a curriculum on the foundation of these four stages. This is a huge obstacle, obviously — building a consensus around this common language and an understanding of how these stages fit together. But I don’t think it’s impossible for a curriculum to do.
All of a sudden, the modular curriculum looks (at least, from my perspective) much more manageable.
The introductory task is short and sweet. Let’s motivate why a new concept is worth knowing and activate some prior knowledge. Offer a discovery activity to use if a teacher wants, but it’s not the end of the world to skip it. Offer some resources for remediation if necessary.
There’s just one expert model as well. This is the part of the curriculum that’s most important for novice teachers, and also often done poorly by textbooks that lose the forest for the trees. What are the key ideas here — not just the “how do I solve problems like this” but “what is this connected to”, “how does this fit into what we already know” and “what does expertise with this concept look like”.
Deliberate practice is where things get interesting. Some groups will only need half a class period to reach fluency. Other classes might need a week. A modular curriculum presents the opportunity to move quickly to more difficult practice or return to prior levels of scaffolding. It provides several formative assessment tasks in roughly ascending difficulty that focus on different aspects of the expert model. Modular curriculum also gives the teacher a great deal more autonomy to decide, independent from “we’ve finished the last example problem in the textbook”, when to move on, and what the most appropriate next step for the class is. These are the decisions that should be difficult, where we need choice, and where a teacher’s energy should be focused. If a modular curriculum focuses on these choices, it can be high quality at the same time as it builds teachers’ expertise.
Transfer tasks are the hardest part of the puzzle for me. Is a modeling task the most appropriate? Should tasks be organized using the standards for mathematical practice? Should they synthesize multiple standards? I don’t know the answer to those questions, and I’m glad I have a variety of options to pull from to use with my students. I think a lot of the coherence in a curriculum comes from these tasks — being deliberate about the bigger ideas that a curriculum focuses on, and making those connections. I think some choice is necessary, but I also think that some choices may be much better than others, especially implemented with consistency across a curriculum.
Beyond here, I’m not too crazy about making things modular. I think it’s useful to consider multiple ways of sequencing units, but there are only so many options that make sense for a given course — I’m thinking, you could rearrange these two, or those two, but the rest should stay as it is.
I’m also really into spaced and interleaved practice, and waste way too much time writing mixed practice for homework. I would love an option to be able to synthesize these more easily, with higher quality questions. But I can let that be.
Does This Work?
This is very much a pipe dream. I’m not a curriculum writer, I just like to surf the internet and find great ways to be a bit of a better teacher tomorrow. But I do think there’s a great deal of potential here. My questions are: Is it possible, or productive, to build a curriculum off of the four-stage model of learning Elizabeth presents? Would this curriculum be overwhelming for new teachers? Would it be intriguing for experienced teachers who might not want to change? Could this curriculum, if it existed, do a better job at making better teachers?
Not knowing about American school math curricula I went to the net and found the New Jersey CC aligned one and looked at grade 7. Just a rewrite of the CCSS standards. No clues about approach etc, really boring.
I think this would be wonderful. I want to do awesome things in my classroom, but I am limited by time. I would love to have a resource to check out like this. I know there are awesome things that are out there, but it is such a struggle to find the right thing at the right time. I would love a resource that would help with that.
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The unit blueprint project was an effort to articulate the flow of courses to meet CCSS standards. They’re starting to get published, for example, you can see much of the Algebra 1 course already here. Some annoying things right now are that 1) you have to do alot of clicking to read everything (although you can download everything about the course as a pdf by clicking a download item) 2) the only linked activities are IM tasks (even though when we wrote them we included links to many external sources – but I believe/hope the external links will be included eventually) and 3) there’s no way to get it all into an editable form so it can be customized locally. So a) take a look at that because it might give you some ideas and b) it was a huuuge project… Not to discourage you, but it took many many person-hours, and once you dig into this stuff you find that even experts have sincere and profound disagreements over sequencing, the balance of the type of work students should be doing, appropriate uses of technology, etc etc. I hope you find some value in the work that’s already been done, though!
Thanks, Kate — I’ve been following the blueprint project for a while, and really like some of the structures there. I’m looking forward to seeing them get fleshed out some more, and would be pumped to see external links added as well. I think you’re right on with the weaknesses of the blueprints right now, and with the difficulty of putting all this together. Writing curriculum is more of a pipe dream and interesting thought experiment for me than anything right now, but I do enjoy looking through all these different approaches and trying to get a bit better at the curriculum prep I do.
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Great post Dylan. I agree with you, the blueprints are sets of tasks, but it is not clear on exactly how they are related and what is the mortar in between. There are no problem sets or what practicing looks like. I find many of the Illustrative Math tasks hard to build lessons around. I certainly would like to see them flushed out more and perhaps with some follow up questions.
It is exhausting to click around figure out what the authors were thinking about what is a class period looks like. Are there regular routines that I am missing? Wouldn’t it be great to have a modeling task at the beginning, middle and end of every unit? It does get overwhelming to synthesize all the resources and be the best everyday. And we haven’t even touched on the students, like notes. What is best? Especially when we are gathering resources from many places, textbooks, MTBoS, MARS Tasks, etc…Cornell notes? Summary notes? INB’s, teacher provided? We need a MTBoS course reader!
Thanks for putting your thoughts out there.
Thanks, Amy — these are complex problems. I can see a great deal of value in a common language for talking about these pieces of curriculum — but also limitations in constraining teachers to a certain approach. I’m not sure how to find a balance there.