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.
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?