Coaching Letter #198

On understanding before opining

Hello, I hope this finds you well. I’m tired and busy and excited about lots of things and looking forward to others and happy about the way lots of projects are going and super worried about a couple. So all is normal.

This Coaching Letter is about Building Thinking Classrooms (BTC), but it’s also about other things as well, particularly the theory and research underlying instructional approaches.  But if you’re not au courant with BTC, or you just don’t care,  then you should skip this one. Or, if you want to learn more about the approach before reading on, you can look at the overview on the BTC website, or listen to this Cult of Pedagogy podcast.

There have been a couple of Twitter threads and/or blog posts taking issue with the approach to teaching mathematics described by Peter Liljedahl in BTC (2020). Apparently, not all of these thought leaders have actually read the book, so I didn’t read what they wrote, either. I hope that’s OK; I don’t want anyone to think that I’m being intellectually dishonest or even disrespectful by just dismissing what they have written without reading it. It did save me a lot of time. And you know, I’m as clairvoyant as the next person. Presumably, they’re not going to read what I write, either, so we can just go round in circles for a bit. But for the benefit of anyone still out there who needs to actually engage with someone’s thinking before they judge it, here’s what I have to offer…

If I were to guess (which is what happens when you don’t actually read what someone has written, which is obviously a disadvantage, but I’m committed now…) I would say that critics of BTC are probably relying on the research that students benefit from a guided approach to teaching, with that guidance coming from, for example, teacher explanation, use of worked examples, and corrective feedback from the teacher in response to formative assessment—as opposed to approaches through which students are asked to figure more out for themselves.  There is an interesting article by Kirschner et al. (2006) whose title says it all, really: “Why minimal guidance during instruction does not work: An analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching.”  The article, and others like it, draws on several aspects of human cognition to explain why minimally-guided instruction MGI does not work; more explicitly, productive struggle is simply not efficient, which causes it to be ineffective. Here are the big ideas that tend to come up most often, in my experience:

1. Working memory. A very famous article by George Miller (1956) must be cited about a thousand times more often than it is actually read, because it is a slog. The big idea here is that however you take in information, the number of chunks of information that you can hold in your head at any given moment is 7, plus or minus two, and you’ve probably heard that before. But the article also describes how “the span of absolute judgment and the span of immediate memory impose severe limitations on the amount of information that we are able to receive, process, and remember.” Miller called this an “informational bottleneck.”  I don’t know if you’ve had that feeling, but I know it well: building master schedules before computers did it for you, explaining complicated ideas that feel just out of reach because you’re not totally familiar with them.

2. Cognitive load theory. This term was coined by John Sweller (1988) in an article that actually accomplishes several things. One is that, because of the limitations of working memory, schema acquisition and development of problem-solving abilities likely interfere with each other. In other words, according to his definition of schema (which is slightly different from, for example Anderson et al., 1977), learning new information and working on a difficult thinking task both make such heavy demands on our cognitive resources that we can’t do both at once.  For example, I try to track down original research for any given topic that I’m writing about, because  it’s important to me to feel confident that I have a decent intellectual grounding in a subject before I speak or write about it (imagine that!).  Because that means I am frequently trying to read articles in fields in which I have only a general background, such as information theory or behavioral economics or developmental evaluation, my comprehension of any given paragraph is constrained by the fact that there are several terms being used that I don’t have stored in long-term memory, and I am unable to use that information to solve problems until I have developed schemas for the concepts in question. But I don’t have the cognitive capacity to do both (acquire new information and execute difficult thinking processes) simultaneously. Cognitively speaking, we can’t walk and chew gum at the same time. Multi-tasking is not a thing.

3. Expert-novice distinction. The way that novices learn is different from the way experts learn. Specifically, in a school context, students are novices. They don’t have the schema to problem-solve, because problem-solving requires subject-specific knowledge, and acquiring information in order to build their schemata should be the top priority, and the most efficient way of accomplishing that is through direct instruction. For those of you who have been in our coaching workshops, this is analogous to the Hattie & Timperley (2007) research that suggests that novices need different feedback from experts, because novices don’t yet know enough to be able to self-regulate, and what they need from feedback is information that helps them build an understanding of what competent performance looks like. MGI is inefficient and ineffective if it assumes that students are going to engage in problem-based learning as though they are miniature experts, when actually developmentally appropriate instruction for them is different in kind and not just in degree.

I’m not going to argue that this collection of research is misleading or irrelevant when it comes to BTC, because it totally applies to all instructional settings. I’m not even going to quibble with it, although other researchers have—I’m going to accept it without cavil for the purposes of this discussion. My argument is that, for the purposes of discussing the viability of BTC, the problem with relying on the research on cognitive psychology  and MGI to suggest that BTC can’t possibly be an effective teaching method is that BTC is not really MGI in the first place. Here is my thinking about that:

1. Students are never totally without guidance. Chapter 9 of BTC explains in some detail that the role of the teacher is to ensure that students are working on a problem that is within their zone of proximal development (Vygotsky, 1978). This can be done in a few ways, including techniques such as thin-slicing, which manages content in a way that students are presented with incrementally more difficult tasks, typically varying only one component at a time so that the difference between the slightly easier and the slightly more difficult task are easy for students to notice and figure out how to approach. But most importantly, the teacher is keeping students engaged in the task, and therefore the learning process, by providing hints and extensions based on what students need: either more support because they are beginning to find the task frustrating, or more challenge because the task is too easy. In other words…

2. The teacher is constantly responding to feedback from students—there is, in other words, a very powerful feedback loop. Students make their thinking visible, and just as importantly, make their thinking audible while they are working on a problem. A great deal of professional development time is spent in education persuading teachers to be more responsive to students, by eliciting thinking not just of the students whom teachers believe will give a complete, correct, or convincing answer to a question, but of all students. We teach them techniques such as cold calling and using popsicle sticks and mini whiteboards. And in BTC we have a lovely, simple way of knowing what all students are thinking because the teaching method requires them to display it constantly. It is an elegant method and has application beyond mathematics, including for adult learning.

3. There is plenty of explanation, it just doesn’t happen at the beginning of the lesson. One of the greatest flaws of MGI—indeed, the essential flaw of MGI—is that it often requires students to construct meaning with inadequate background knowledge to do so effectively or efficiently, or at all. I highly recommend the book Seven Myths About Education by Daisy Christodoulou (2014). The counterargument to that has been that students need clear explication, and worked examples, and corrective feedback. And I agree with that. And what BTC does is upend that a bit, and put the explanation and concept extension deeper into the class period. So I would say that the greatest mistake of people who think that they don’t like BTC is that they see a structural shift in the lesson design, and they confuse that with lack of guidance from the teacher, because they do not fully understand, because they have not tried to understand, what is really going on during the course of the lesson.

4. Because the tasks are constructed as puzzles, there is feedback available from the task itself. Students can often discern for themselves whether they are on the right track, or they can look around the room and see what others are doing. For anyone interested in student agency, they should stop talking so much about choice and look to see what students are doing when they are asked to tackle a challenging problem and empowered to monitor their own progress and given the means to self-correct.

5. The accusation that BTC cannot work because it exceeds students’ cognitive load is clearly false. As pointed out above, the teacher is actually putting a great deal of thought, during the lesson itself, to providing hints and extensions to students so that they are able to keep thinking. If their cognitive capacity was exhausted then they would not be able to track their progress, would experience frustration, and would likely withdraw from the task. If you visit a classroom full of students at whiteboards busily making sense of a task and engaged in spirited discussion about the correct way forward, I think the one thing that you cannot argue is that their cognitive load has been exceeded.

I would go further and say that my experience with watching other instructional methodologies in action, such as NGSS, and my experience with teachers in general and their mental models of high quality instruction, is that there is actually very little minimally guided instruction going on in real classrooms, because teachers tend to hold a mental model of good teaching that requires the teacher to provide a lot of help to students, to explain, to support, to scaffold. Indeed, I would go so far as to say that MGI is much less of a pressing issue in American classrooms than the impulse to over-explain, over-scaffold, and to rescue students in such a way that they are required to do less thinking than the instructional design ostensibly intended. This is congruent with the finding in Kirschner, et al., (2006), that teachers who are supposed to be teaching with minimal guidance (which actually is kind of stupid thing to say—that’s actually not teaching) end up scaffolding the lesson for students anyway. With BTC, the scaffolding is built in, but unlike much over-scaffolding that happens in classrooms, where the cognitive demand is actually diminished inappropriately, the scaffolding in BTC is responsive to student needs in the moment.

In addition, there is much in BTC that is affirmatively good practice, and might be employed effectively and profitably by teachers in other subject areas. For example:

1. Putting students in random groups. We have plenty of research that suggests that effective teachers do not group students by perceived ability. This appears to be because a) they have confidence in their ability to teach anyone (Rand, 1977) and b) they are less likely to base their expectations for student achievement on student characteristics such as race, identification as qualifying for special education services, body composition, or attractiveness. Much ability grouping is a vehicle for teacher expectations, which are far from objective, to invade the classroom and impact the quality of instruction students receive based on characteristics that are not in fact indicative of their ability to think (citation). 

2. Formative assessment. There’s a huge amount of research on the effectiveness of formative assessment, which only makes sense: in order to adapt instruction to meet the needs of learners, a teacher, and/or the learners, must know where they are relative to the intended outcomes of instruction, so that actions can be taken to close the distance between where the learners are and where they should be. Practices that provide that information are known as formative assessment. Additionally, as Black and Wiliam (1998) point out, “Many of these studies arrive at another important conclusion: that improved formative assessment helps low achievers more than other students and so reduces the range of achievement while raising achievement overall.” Asking students to make their thinking visible on whiteboards around the room while they are working means that the teacher has a huge amount of easily accessible information on which to base decisions about what to do next—the very definition of formative assessment—and the formative assessment is embedded in the instructional design. I don’t know why the BTC skeptics don’t make the connection between BTC and formative assessment—oh, that’s right, I forgot. They don’t actually know what they are decrying.

3. Feedback. The book Building Thinking Classrooms does not really use the language of feedback, but the practices of feedback are described in Chapter 9. Teachers use the evidence of student work on the whiteboards and student conversation as they think through the problems as formative assessment that they then respond to. That response is feedback. In BTC that feedback can take many forms, and Liljedahl has many techniques for keeping students thinking. These techniques are very similar to those suggested by Wiliam in Embedded Formative Assessment, which is a book I recommend often—a very sophisticated take on instruction.

4. Situated cognition. There’s a great article by David Kirsh (1995) about how experts use space to support their thinking and problem solving, based in part on how chefs work. Again, we’re talking about reducing cognitive load, and creating predictable and strategic use of the environment to support problem-solving, and I think BTC taps into this in clever ways through the use of the whiteboards and how there is consistent practice through the use of specific instructional routines. I could go on about this one, but it feels a bit esoteric, even for me…

5. “Learning happens when people have to think hard.” (Coe, 2013.) And as Willingham (2009) points out, the most general and useful idea that cognitive psychology can offer teachers is to review each lesson plan in terms of what the student is likely to think about (only lightly paraphrased, so the page number is  79.) It is, therefore, exactly what cognitive science calls for when students are asked to think about the content of the learning objective. One of the clever aspects of BTC is that all the students can be thinking about the content all at once; we use the method to demonstrate language arts lessons in which the traditional way of teaching the lesson would be to have the teacher direct questions to the students, but in a BTC classroom, all students can be engaged in the same questions simultaneously.

6. Framing tasks as puzzles. There’s a lovely article by Howard-Jones & Demetriou (2009) about the psychological effects of games and puzzles. It’s full of interesting stuff. For example, there is an “attractiveness of uncertainty” linked to the release of dopamine, which as ChatGPT explained to me, is closely related to the brain’s reward system, i.e. feeling pleasure, feeling good, and feeling motivated. Puzzles are inherently rewarding and motivating. Here’s an interesting finding: students generally prefer low levels of academic uncertainty and when given the choice, will choose tasks well below moderate level of difficulty (which is one of the many reasons why student choice is generally not a good thing (Gagné (1980)). “Interestingly, however, when the same tasks are presented as games, students will take greater risks.” Therefore, the framing of BTC tasks as puzzles to be solved is a very smart and research-based strategy for increasing motivation and engagement.

I am not trying to convince anyone that BTC is a superior method of instruction. Although you would be forgiven for thinking otherwise, that’s not really what I’m trying to do here. What I am trying to do is point out that a) research on how learning happens does not prescribe a single method for how teaching ought to be enacted; but b) teaching methods should certainly be based on what we know about learning and the effectiveness of some methods over others; and c) you really should work hard to understand something before you shred it—I know I haven’t been subtle about that, but I’m not sorry. I have spent a significant amount of time over the years defending Direct Instruction (DI) from detractors who thought that it was all teacher talk and rote memorization but who had never done any research on it or gone to see it in practice (for a meta-analysis on the effectiveness of DI, see Stockard et al., 2018). So I find it funny and ironic and a bit sad that I am now seeking to similarly explain to critics of BTC (many of whom seem to be proponents of DI) that BTC is not all MGI and productive struggle. I would have thought that advocates for a method of teaching that is regularly maligned and misunderstood would have some empathy or at least intellectual curiosity about other instructional methods, but apparently I have made yet another false assumption.

Finally, if I have learned anything over the course of my time in classrooms, it is that almost any teaching method executed well is preferable to one that is executed poorly. One of our problems in education is that we dabble. We ask teachers to implement new programs with insufficient schema-building or opportunity to develop and practice new skills (what Cobb et al, 2018, call pedagogy of exploration and pedagogy of enactment). So don’t think that buying everyone a copy of BTC will solve all of your problems of getting kids excited about math. Clarifying what high quality instruction means, and then providing the support for learning about it and teaching it, are leadership responsibilities. Teachers are doing the best they know how to do with what they have, so if instruction is lacking then that is a failure of direction, clarity, coherence, capacity and support more often than unwilling teachers.

And a sort of coda. I owe a lot of my schema for being able to write this Coaching Letter to Professor Gary McKenzie, whose courses in the research on teaching effects have been invaluable to me over the 30 years (!) since I took them. He was teaching about the import of cognitive science for instruction well before it was trendy, and he was right. I took his classes back when you had to pick up a photocopied course packet from Kinko’s, and I put all the articles in a giant 3-ring binder, which I consulted in order to write this CL since I’ve kept it on the shelf next to my desk all these years. I took a picture of one of my favorites for the top of this CL. I remember being shocked that there was a whole quarry of research about teaching that no one had ever told me about when I was training to be a teacher, even though I got really excellent training, and I’ve been mining it ever since. So this is a thank you note.

I think this is the longest CL ever, so if you’re still reading at this point, thank you for hanging in there. I’m hoping that this CL spurs some discussion, and I look forward to hearing all about it! And if there is anything else I can do for you, please let me know. Best, Isobel

References (I don’t usually include complete citations in a Coaching Letter, but I’m going to here in case anyone wants to chase down the research articles. And I just want to be super clear that I have actually read everything that I’m citing.)

Anderson, R. C., Reynolds, R. E., Schallert, D. L., & Goetz, E. T. (1977). Frameworks for comprehending discourse. American Educational Research Journal, 14(4), 367-381.

Black, P., & Wiliam, D. (1998). Inside the black box: Raising standards through classroom assessment. Phi Delta Kappan, 80(2), 144-148.

Christodoulou, D. (2014). Seven myths about education. Routledge.

Cobb, P., Jackson, K., Henrick, E., & Smith, T. M. (2018). Systems for instructional improvement: Creating coherence from the classroom to the district office. Harvard Education Press.

Coe, R. (2013, June). Improving education: A triumph of hope over experience. Inaugural lecture of Professor Robert Coe. Durham University. 

Gagné, R. M. (1980). Learnable aspects of problem solving. Educational Psychologist, 15(2), 84-92.

Howard-Jones, P. A., & Demetriou, S. (2009). Uncertainty and engagement with learning games. Instructional Science 37, 519-536.

Kirsh, D. (1995). The intelligent use of space. Artificial Intelligence, 73(1–2), 31-68.

Kirschner, P. A., Sweller, J., & Clark, R. E. (2006). Why minimal guidance during instruction does not work: An analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching. Educational Psychologist, 41(2), 75-86.

Liljedahl, P. (2020). Building thinking classrooms in mathematics, grades K-12: 14 teaching practices for enhancing learning. Corwin.

Miller, G. A. (1956). The magical number seven, plus or minus two: Some limits on our capacity for processing information. Psychological Review, 63(2), 81-97.

Stockard, J., Wood, T. W., Coughlin, C., & Rasplica Khoury, C. (2018). The effectiveness of direct instruction curricula: A meta-analysis of a half century of research. Review of Educational Research, 88(4), 479-507.

Sweller, J. (1988). Cognitive load during problem solving: Effects on learning. Cognitive Science, 12(2), 257-285. 

Wiliam, D. (2011). Embedded formative assessment. Solution Tree.

Willingham, D. T. (2009). Why don’t students like school? Jossey-Bass.

Vygotsky, L. S., & Cole, M. (1978). Mind in society: Development of higher psychological processes. Harvard University Press.