When I first started teaching, I leaned pretty hard on constructivist pedagogy. I would take a unit, look at the number of days I allotted for the unit, then divide that unit into little understandings. Each day, my goal was to give students some clever questions that would help them figure out the understanding I had in mind. They’d practice some, and we’d move on.
I’m skeptical this was particularly effective pedagogy. Any given day, some students had already figured out my understanding, some figured it out through my lesson, and others came up short. The numbers of students in each boat varied widely day by day — many students fell behind, and a bunch more were bored. Not very inspiring, and I have decent evidence that it didn’t lead to very durable learning for my lower-skilled students.
Cognitive Load Theory provides an interesting, albeit controversial, explanation of why that might not be the best pedagogy. My students were, generally, novices, and the mental effort (working memory space) they expended trying to figure out something new impeded that something new from actually entering their long term memory. Here is a great summary of some research around working memory, arguing that there are vast differences between novices and experts in terms of their ability to rapidly encode new learning. There’s some great debate as to what that actually looks like, and I especially like Jason Dyer’s takedown of applying that principle too broadly, but I think there’s something to be said for the fact that novices struggle with minimally guided instruction.
Bryan Penfound wrote a great post recently referencing a study by Slava Kalyuga and Anne-Marie Singh that throws a wrench at Cognitive Load Theory. I’m oversimplifying here, but one element of Bryan’s argument is that Cognitive Load Theory assumes the goal of any instructional activity is to move a piece of learning into long term memory. That’s an important goal, but it’s also just one subset of the learning process. In particular, the goal of an instructional activity could be “motivation to learn, activation of prior knowledge, engagement with the task, searching for deep patterns (as opposed to surface characteristics), or making students aware of gaps in knowledge”. Maybe Cognitive Load Theory is not particularly relevant to thinking about what students are doing during this part of the learning process. Next, students need to move some learning into long term memory (Bryan uses the more technical language, “acquisition of domain-specific procedures and concepts”). Finally, he notes that Kalyuga & Singh suggest a set of high-level goals around knowledge that is likely to transfer to new tasks.
This really fascinates me, and I think it connects really well to another favorite blog post of mine this year from Elizabeth, referencing How People Learn. I’d like to try to bring together three sources here — Bryan’s writing on cognitive load theory, research on the differences between novices and experts, and Elizabeth’s description of the learning cycle.
The Learning Cycle
Stage 1: An introductory activity. Elizabeth argues that introductory tasks should “uncover & organize prior knowledge”. Bryan points out another purpose I like a lot — “making students aware of gaps in knowledge”. I would argue a primary purpose of an introductory activity centers on the idea of intellectual need — it creates a purpose for the learning that’s about to occur, and helps to point learners toward the place in their cognitive architecture that the learning will move into. Here, I’m treating students as novices — they may have the right level of background knowledge to incorporate new ideas through discovery, but the primary purpose of this activity is not to develop new schema, but to prepare for future learning.
Stage 2: Initial provision of an expert model. This can take lots of forms — it could be discussion-based, teacher-led explicit instruction, or carefully scaffolded group work. But what’s important here is that the introductory activity leads to an opportunity for the whole class to stop and consolidate their understanding. Michael pointed recently to a moment where he felt like instruction during the learning process was ineffective, and that resonated with me — I think there’s a necessity here for whole-group consolidation of knowledge, without the distractions of trying to figure out something new. I think that, in most cases, this involves delivering less information than we might think. It doesn’t necessarily mean working examples for every iteration of a concept; instead, it means making clear key concepts, connections, and mathematical structure for students to use in future learning. Again, I’m treating students as novices — students with significant expertise are likely not to need the explicit instruction — but the point here is to level the field and make clear the essential elements of a concept.
Stage 3: Deliberate practice with metacognitive self-monitoring. Students do math. They have their expert model; now we are looking at constant cycles of practice, with different representations and contexts, and formative assessment, to figure out where to focus future practice. Over time key elements of the expert model will need to be made explicit again, at times for the whole class and at other times through group work. I wrote recently about a framework for thinking about what these moments are.
Stage 4: Transfer tasks. Either students have gained significant expertise or they haven’t. This doesn’t happen on day two; it takes a lot of time to move learning into long term memory. But at some point, let’s find out how well students have internalized key concepts, provide the opportunity to deepen learning through transfer, and set the groundwork for further instruction if necessary.
There is a specific place in the learning cycle where I am making an explicit effort not to tax students’ working memory, and that is when I first provision an expert model. Some students may be able to incorporate new learning without that explicit instruction, but others will not. More importantly for me, relying less on an introductory activity to magically lead students to a new understanding opens enormously the variety of possibilities for that part of a lesson. Then, students practice — spaced, interleaved practice, through plenty of different pedagogical strategies, but still practice, to encode learning in long-term memory. Ideally, students start to gain expertise in the topic, move relevant schemas into long-term memory with enough sophistication to apply broadly to a variety of problems, and then move into transfer tasks applying that learning in new ways.
I still have lots of questions about this, particularly about the speed and structure of transitioning from novice to expert understanding. People love to throw around the 10,000 hour rule but I think that’s pessimistic garbage. How much does that number vary topic by topic? What is the grain size of expertise? What is the role of productive struggle at different moments in the learning cycle? What strategies are most effective for increasing metacognitive activity?
All that said, this framework gives me a great base to work off of in order to learn from my teaching. It lowers the stakes of introductory tasks — their goal is to set up future learning, and if they are unsuccessful, we can move on and rely more on the provision of an expert model. In these parts of a lesson, I’m focusing on intellectual need, and also on a concise activity that does not distract from larger goals. When I provision an expert model, my focus is on the minimum instruction I can provide to get students to a basic level of competency in their deliberate practice. The goal is not to cover every possible iteration of a concept, but to focus on key ideas that are broadly applicable, and to do so in a clear way. When students engage in deliberate practice, I am looking for ways to move their thinking forward that are transferable to future topics and productive in building flexible understanding, while also looking for areas that are worth addressing explicitly relative to gaps in their understanding.
No easy answers here, but hopefully some guidelines for thinking about my teaching that are (more) based in research (than they were yesterday).