Ep 53. Using the Instructional Hierarchy to teach math with Brendan Lee
This transcript was created with speech-to-text software. It was reviewed before posting but may contain errors. Credit to Canadian Podcasting Productions.
Using the Instructional Hierarchy to teach math with Brendan Lee (Ep 53)
In this episode, Anna Stokke chats with Brendan Lee, a teacher and educational consultant focused on bridging the gap between educational research and classroom practice. They discuss the instructional hierarchy and how teachers can tailor their teaching based on where students are in their learning journey––whether it’s the acquisition, fluency, generalisation, or adaptation stage. Brendan shares practical strategies and actionable advice that teachers can immediately apply in the classroom to better support student learning. This is an insightful discussion that will leave educators feeling informed, inspired, and ready to take on their next lesson.
Brendan Lee’s website: www.learnwithlee.net
This episode is also available in video at www.youtube.com/@chalktalk-stokke
TIMESTAMPS
[00:00:23] Introduction
[00:03:15] Understanding the Instructional Hierarchy
[00:04:40] The acquisition stage
[00:08:28] Teacher’s Talk Radio
[00:10:39] Students’ struggles in the acquisition stage
[00:12:48] Effective teaching techniques in the acquisition stage
[00:19:37] Think-alouds: The meaning and purpose
[00:23:45] Concrete-Pictorial-Abstract
[00:33:47] Backwards fading method
[00:34:58] Make or break method
[00:36:50] Fluency stage: what teaching techniques work best
[00:47:34] Generalization/adaptation stage
[00:55:11] When to use teaching tools
[01:00:55] Advice for new teachers using the Instructional Hierarchy
[00:00:00] Anna Stokke: Welcome to Chalk & Talk, a podcast about education and math. I'm Anna Stokke, a math professor and your host. Welcome back to another great episode of Chalk & Talk.
For this episode, I recorded both audio and video. So, if you are listening on a podcast platform, but would like to check out the video, I put a link to my YouTube channel in the show notes. My guest in this episode is Brendan Lee, a teacher and educational consultant focused on bridging the gap between educational research and classroom practice.
The discussion is all about giving educators practical advice that they can use in the classroom, particularly keeping the instructional hierarchy in mind. We talk about how teachers can recognize which stage a student is at in the instructional hierarchy, whether it's acquisition, fluency, generalization, or adaptation, and how to tailor instruction accordingly. It's a great conversation, chock-full of practical tips and strategies, and I really hope you enjoy it. Now, without further ado, let's get started.
I am excited to have Brendan Lee with me today and he is joining me from Sydney, Australia. He's a primary school teacher, a school leader, and an educational consultant. He dedicates his time to bridging the gap between educational research and classroom practice.
He has collaborated with organizations such as the Grattan Institute and Think Forward Educators to help bridge that gap, and he serves on the board of Ochre Education. He offers professional learning for teachers, often focused on math, which we love to talk about here on the Chalk & Talk podcast, and he blogs at Learning with Mr. Lee, that's learnwithlee.net, and he is host of the Knowledge for Teachers podcast, which listeners should check out. Welcome, Brendan, welcome to my podcast.
[00:02:17] Brendan Lee: Thank you for having me, it's an absolute pleasure.
[00:02:20] Anna Stokke: So, I thought we'd concentrate on giving some practical suggestions today, that educators can use in the classroom to help with their teaching, particularly teaching math, because you're a teacher and you do work with teachers regularly. So, I thought we'd start with the instructional hierarchy, which I know you love to talk about, and so do I. So, let's briefly walk listeners through the stages of the instructional hierarchy, and we've talked about it on the podcast before, but we should talk about it again, because you can never talk about it too much. And there are four stages, and learners move through these stages when they're taught anything, really, and the stages are acquisition, fluency, generalization, and adaptation.
So, can you remind our listeners what each of those stages means? And let's start with acquisition.
[00:03:15] Brendan Lee: Yeah, look, and I think just before I go into acquisition, I think what's important is probably quite helpful to go through my own journey into actually understanding the instructional hierarchy. And I think a lot of listeners will probably resonate with the sorts of things that I talk about.
Whereas here in Australia, we've got a really strong push for the science of learning at the moment, which is terrific. But it's probably only really coming from that sort of cognitive science point of view, which is really helpful. Things like Cognitive Load Theory, really quite transformational in teachers' knowledge and understanding as to what they should be doing in the classroom and why they might be doing different things.
However, I found that a lot of the cognitive science stuff, the neuroscience, their theories or their bits of information, which can sound really great, but it kind of seems to leave you with wanting to know more. So, you want to know, well, okay, so when exactly do I do this or that? Well, how can we break down that novice to expert continuum? And that's where, for me, the instructional hierarchy really comes into it, is that it actually breaks down that novice to expert continuum, rather than it being sort of this abstract idea of they're closer to the novice end of the continuum or they're closer to the expert. We've now actually got this framework, the instructional hierarchy in the stages of learning that we can use that tells us exactly when you're seeing students behaving like this, then this is what you should do as a teacher.
And so, for the acquisition stage, essentially the goal is that we want students to be able to perform things accurately and independently without assistance repeatedly. And when they're able to do that, then we can move on to the next stage. However, that doesn't mean that we start there.
So, in order to get to that level of independence and accuracy, the teacher actually needs to be providing them with the prompting, the scaffolding, the cues that they actually need and require at that point, because this is new for them. And so, they're struggling to make those connections to their existing bits of knowledge. And so, yeah, we've got to make sure that we are actually supporting them with what they need at that point.
Once we have started to see a high level of accuracy, and that's done independently, and I'll talk about that importance of independent practice later on in this conversation, but once we see that level of accuracy, then we can move into fluency, where the goal is now to maintain that accuracy, but increase the speed of response. So, this is where we're trying to, and when we're talking about speed of response, we're saying two to three seconds. It's not five to six seconds or ten seconds, two to three seconds, really fast response.
They don't have to think about it. And coming back into Cognitive Load Theory, and we understand the limitations of our working memory, right? And so we don't want our students to be having to exhaust all of their thinking on the simple things like what's three plus four, or seven times eight. Like we don't want their working memory to be exhausted on that, when we know that the fun stuff comes in the problem solving.
But often what happens, is we move to that problem solving, which is in that generalization phase. We move there too early. So, our students haven't got that accuracy, they haven't got the fluency, but then we want to start with these problems, and we end up, rather than what we're aiming for, that productive struggle ends up going into, destructive struggle, I like to say.
And yeah, so generalization is definitely where we want our students to be getting to. And so often critics of explicit instruction, they're like, well, what about the problem solving? And I just want to be really clear, we're not saying no to problem solving, okay? We're just saying it's all about the timing of when you do it, and making sure that that prerequisite knowledge is actually there, that foundational knowledge, they've got fluency in. Okay, so then generalization, that is where we are actually getting them to engage with novel problem types, so word problems, problem solving, like I mentioned, before they move into the adaptation.
And adaptation is kind of, they talk about it being continuous and actually has no end point, because essentially, it's when students and learners, they're able to use what they've learnt and they can adapt it now. And I like to use sporting analogies. My background is actually more in sport and as an athlete and PE.
And so, yeah, the analogy I like to use is that, when we're learning skills in sport, whether it's swimming, whether it's soccer or football, whatever it is, we go through these stages and it can look really quite clear because we break down skills, we practice them. And then that generalization is when we're actually able to do it in the game. But the adaptation is when you're able to use the skills that you've got, and now all of a sudden, you're pulling off these new moves that you weren't necessarily taught at training, but you've been able to adapt them purely out of your experiences.
And you've gotten to that level of fluency where you've been able to actually adapt the way that you hold the ball or the way that you move and those sorts of things. The other stage, which is sometimes also mentioned, which I'll just briefly touch on here, is the maintenance phase. And I think that's extremely important as well.
So, no matter what stage of learning you're at, we want to maintain that we don't want to let that go. And this is where all that retrieval practice stuff comes in. And so, we're offering opportunities for students to space out their recall over time.
So, in a nutshell, that's the instructional hierarchy in the stages of learning.
[00:08:28] Anna Stokke: If you're enjoying Chalk & Talk, you might want to check out another podcast I've been listening to lately. It's called Teacher's Talk Radio. They've got a network of around 30 teacher hosts, and they publish episodes daily on all the usual platforms like Spotify, Apple, and YouTube.
They cover anything that's teacher-related, like behaviour, assessment, instructional techniques, even AI. So, give them a follow wherever you get your podcasts, or visit them at ttradio.org. That's Teacher's Talk Radio.
[00:09:04] Anna Stokke: Excellent. Okay, so I'm going to recap. All right, so we start with the acquisition stage, and you can tell the students in the acquisition stage, really, when they're trying to build accuracy, right? So, the student, they may be really, you know, they're in the acquisition stage, they may have trouble doing the skill accurately. So, the idea is to get them to the point where they can perform the skill accurately. However, they may still be slow.
And so, at the fluency stage, you want to get them to a point where they can do the skill rather effortlessly, right, where it’s kind of almost becomes second nature, regardless of really what the skill is. I think every math teacher knows that this sort of thing happens. A student might be actually really fluent and accurate, but then you change the problem slightly, and they have no idea what to do.
Like every math teacher has seen that. And that's kind of where you want to get to that generalization stage, right? So that's that problem solving stage, that generalization and adaptation, they're kind of similar, right? I would say generalization is just when you slightly change the problems and adaptation would require quite a high level of problem solving. So, like you’ve said, we're not trying to skip that stage.
It's just the order in which we do it. We want to make sure that students have that really good foundation, so that they can do the problem solving later on, right? That's what you're saying? Okay, perfect. So, what do you advise teachers, like how can they tell when a student is in the acquisition stage?
[00:10:39] Brendan Lee: I think this is really helpful is that when you're seeing students struggling, so they might be struggling to start, they might not be lacking in confidence in responding, look, I've literally seen, unfortunately, I've seen children in tears, like when we are not using the right tools at the right time.
So, we're asking them to do things that they are not ready for. They know within themselves, they haven't got the prerequisite knowledge to do what you're asking them to do. And it is so many steps away from where they're currently at, that they actually break down in tears.
And I've seen that happen in unfortunately too many classrooms. So, they can also struggle to discriminate between different relevant elements. So, this is why like, Engelman talks a lot about the importance of examples and non-examples.
And this is where it really comes into it is what we're trying to do is we're trying to ensure that they know, they understand the boundaries of the concept that you're trying to teach. So, by giving them examples, multiple examples and non-examples, and being really quite strategic and specific with those examples, we're actually highlighting the different things that they need to be looking out for. And so in that sense, when they're moving forward, they can start to see, all right, this is when I'm going to apply this strategy that I've just been learning.
They might still struggle to complete tasks independently. And so, this is why we've got to use that gradual release of responsibility when they are in that acquisition stage. Because if we just go from modeling straight to independent practice, we're not actually giving them that time to play around with this idea.
And the teacher's not able to give that immediate corrective feedback, which is really important at this stage as well. They might be hesitant even when they do provide the correct answers. So, they're not fully sure as to how they're able to get those.
So sometimes teachers can ask questions like, are you able to explain how you got that answer? But they're doing it too early. So, if you're asking that sort of question, the students are still just grappling with this new idea and to actually unpack it at that sort of level, they're going to need a bit more time with that to understand how they're getting their correct answer. So, they might be accurate, but still slow, okay? So, we're still building up that response speed, right? But that's going to come with more practice.
[00:12:48] Anna Stokke: Okay, great. So, what are some effective teaching techniques that teachers could use in the acquisition stage?
[00:12:58] Brendan Lee: So firstly, I don't know if we mentioned yet, but so this originally comes from Haring and Eaton in 1978. And so, when we're looking at that acquisition stage, they originally spoke about, they identified four different strategies.
So modeling, demonstration, prompting and cueing. And so, like when we look at maths, there's, I guess, lots of specific ways that we can sort of do that. But, even if we're just looking at modeling, modeling can kind of be broken down into two, I guess, categories.
So, we've got one category where we're modeling and that is like, that's live modeling. So that might be the teacher doing something on the whiteboard. It could be the teacher explaining something live.
We might be using concrete materials and we're live modeling that. We might be using a document camera and we're modeling something under the document camera. So that would be live modeling.
There's pros and cons to that. The pros are that the students are able to see really closely what they need to be doing. So, you can go through step-by-step, like this is what you're going to do.
And sometimes if they're going to do it on the mini whiteboard, I might even pull out a mini whiteboard as well to show them precisely how to actually lay it out. We can also do fully completed models as well. So, we can use those.
So, things like worked examples, they could be like a fully completed worked example. We're presenting that to our students. And I guess the pro to that is, well, firstly, it actually takes a load off the teacher's working memory.
Like one of the issues we have in primary education is that unfortunately many primary teachers don't actually have that pedagogical content knowledge that they need. And so, it can be like quite draining, just to actually remember the steps yourself. And there's lots of arguments, well, they should be able to do it.
But unfortunately, this is just where we're at, right? And so worked examples can be really helpful in that sense to ensure that the teacher doesn't actually have to be thinking about step-by-step, what do I have to do? But it's there, okay? And I can actually now just focus on my attention on the students, okay? Are they studying this worked example? Can I see that they're thinking hard about it? And then I might ask them some questions afterwards just to see how they're going. We might do some think-pair-shares to unpack their thinking before moving on to that next step. So yeah, we've got those two sorts of ways of looking at it and even just worked examples.
I've heard Michael Pershing, and he's got a great book on this as well where there's so many different ways that you can break down even just that routine of looking at a worked example and the sorts of self-explanation prompts that we might ask as well to get students to actually think about what they're doing. On top of that, look, when it comes to, using concrete materials, I'll touch on that here. What's really important is that students, we want to be getting to the abstract understanding in maths.
Okay, that's really important. But often we go there too quickly. And there's a number of moments; I'll keep referring back to the curse of knowledge.
So, teachers often suffer from the curse of knowledge. So, this is where, because you are an expert or you know so much, it can be really difficult to get into the heads of a novice who is at that acquisition stage and actually truly know what they need then and there and then know how to sequence a concept in small steps because often it will skip steps. So, we might assume that something like numbers is really simple and easy for students to understand.
So, for instance, a poor proxy of learning can be that many of our students enter school, so whether you call it kindergarten or reception or foundation, they can enter school, and we can get this false sense of security that our students are already really confident with numbers because they can count to 10. Okay, however, that doesn't really tell us that much. Okay, firstly, often they just learn it as a phrase, you know, it's almost like the alphabet song, you know, they learn the alphabet song, they learn how to count to 10, but they don't actually have a strong understanding of that one-to-one correspondence.
And so, we can go straight into that abstract, you know, using the numerals, the symbols too early when our students actually haven't got a strong understanding of that one-to-one correspondence. And so, we skip using the concrete materials. And so, the whole idea with concrete materials is that we want to aim to fade, but we fade, you know, as quickly as we can, but we go as slowly as we must.
And then, you know, using multiple representations whenever you're using them. So, if we are using some sort of concrete material at the same time, we also want to be guiding students' attention towards what's that, you know, the pictorial representation could look like, and then also what the abstract representation can look like. That way we can get there as quickly as possible, because we're continually showing, you know, right now we're using these MAB blocks or we're using the counters.
What you can see here in this tens frame, this can also be shown as this number here, this is what the abstract number looks like, okay, and keep going through that. But yeah, do be intentional with the choice of manipulatives because they can go wrong as, yeah, any primary teacher will be able to tell you. So yeah, use the right manipulative if they don't understand the concept.
It doesn't, you don't have to fade them away just because they're a certain age. Like if students genuinely are not understanding something, then we pull them out and we let them use them. But then as we move forward into, like I guess that guided practice phase, you know, the ‘I do’, like if we're going through that gradual release responsibility and this is ‘I do’, ‘we do’, ‘you do’, right? But what is happening at each stage, it's really important that teachers understand, like this, I guess the nuances in what we're doing slightly differently between each of those.
So, you know, that ‘I do’, it involves those different types of modeling that I was talking about. You know, we want to give them that demonstration. Thinking aloud is extremely important.
Just be really careful with the vocab that you use so that students are actually able to understand what you're saying. Like I've done, activities with teachers where I'll get them to script it to think aloud and they quickly find out just how difficult it is, if you plan to do this live in front of your students because often we don't quite get the language, right? And so that's really important in the think aloud because the whole idea of that ‘I do’ phase is that students should be knowing like what the end goal is, you know? So, what does a good one look like by the end of that ‘I do’ phase, that modeling phase, they should know what a good one looks like. And then we move into that guided practice and guided practice is all about now giving them multiple opportunities to respond.
And we're going to slowly fade away the amount of prompting and scaffolding as we move through so that we can get to that independent practice. Do you want me to talk about some specific kind of guided practice techniques here or yeah?
[00:19:37] Anna Stokke: I'm going to just go back to something you said earlier. And you talked about ‘think alouds’. you know, just because it's kind of educational jargon. So, I just want to make sure that everyone knows what we mean by that. So, you mean the teacher is going through the problem and thinking out loud, they're going through their thinking so that the students can see how they're thinking through it, correct?
[00:19:58] Brendan Lee: The nuance here is that when you're doing your think aloud it's not just simply going through the steps we're going to do this step, then this one, then this one but actually going through the decision-making process. So that's the important part.
So, students need to be able to see inside the heads of an expert and understand the reason why I'm doing this is because of this, yeah. So yeah, definitely a key point there is to just highlight the importance of going through that decision-making process.
[00:20:25] Anna Stokke Okay, perfect. And then I wanted to also just follow up on the concrete pictorial abstract stuff that you kind of brought up a bit.
And so, you mentioned, you know, working with manipulatives, and you talked about the one-to-one correspondence between students being able to understand, you know, like, what does three actually mean? Like, here we have three chips and before moving to like the symbol and that sort of thing. So, I think the manipulative piece is important. But I would also add, I think that sometimes they get stuck on the manipulatives and don't move to the symbolic fast enough.
Like the end goal is absolutely the symbolic, right? That's sort of the power of, of algebra and using symbols in math, because they're easy to manipulate. So, do you have any thoughts on that?
[00:21:14] Brendan Lee: I think this is again, one of those things where if teachers don't actually understand the why behind what you're doing you just fall into the trap of thinking, well, I'm about to teach this concept.
Yeah, I'm going to use these manipulatives without even really thinking about, well, do I actually need to use it? Like if my students already have that concrete understanding of this topic, I don't necessarily need to get them out or I might just quickly use them in my modeling phase. And I'll do this quite often where if I'm not fully sure I'll use it in the modeling and then just get a bit of a gauge, you know, from what my students are showing me that, all right, they've got this. I'm not going to need to get them out for all of them because they have a pretty strong understanding of this already because we do need to take into account the time factor, you know, of any time you get out these manipulatives you're losing a lot of time because they're playing with them.
You know, they're getting them out. We've got to make sure that everyone's got the right amount of whatever it is that we're using. We might have to be playing around with different colors and sorting them out.
All of those different things need to be taken into account. And so, if they don't need them, don't use them. But if they do need them, do use them.
[00:22:21] Anna Stokke: Yes, I agree with you. And they are not computational tools. Absolutely, you do not want to be using manipulatives to do basic arithmetic, right? Like they're just intended to maybe show someone why something works and then move on. But anyway.
[00:22:38] Brendan Lee: Yeah, otherwise they become, you know, dependent on them, our students. And that's the worst thing that can happen, right? Is when you see those students that have been experiencing a lot of failure in maths.
And so, then the only time they do get that success is when they're using the concrete materials or probably almost just as bad is when they're relying on the pictorial representations. I've been in classes where students, they're relying on, breaking down these huge numbers through drawing circles and dots. And then they get really frustrated after doing that for five minutes where they've made some sort of calculation error.
And now all of a sudden, they're literally like tearing up their sheets of paper because they have just invested so much of their cognitive capacity, which is already really quite low on this really inefficient way of doing maths.
[00:23:29] Anna Stokke: Brendan, I'll tell you that I've even seen it on university skills tests. Like diagnostic tests. 64 divided by 8, and the student draws 8 circles and just starts putting tick marks in them until they fill them up.
But let's talk a bit more about worked examples, right? I think, we can't really talk about worked examples too much, right? So, if you have some specific strategies that you can use to do worked examples, and that sort of thing, that might be really helpful. So, if you'd like to talk about that a bit, that would be great.
[00:24:26] Brendan Lee: Yeah, try and stop me, Anna! So worked examples, like, so right from the start, yeah. So, if we're using fully completed worked examples, there's a few different ways that we can use those. So, we can use them in the way where we're just giving that fully completed answer as it is.
We can also do it step by step. So, we're showing them each step along the way and students can study that. But what's important is that we don't just, I guess, dust our hands off and think, oh, our job's done.
We've shown them that fully completed worked example. And I'm not sure about what it's like over in Canada and in the US, but here in Australia, we've got a bit of a tendency to, you know, if we've got a worked example in, say, a textbook, we'll show the worked example in the textbook and we'll guide students to, you know, “Go to page 65, look at the worked example and then complete questions one through to 20 on page 66.” So, there's been no support from the teacher.
There's been no questioning. There's been no checking. There's been no multiple examples. It's just this one example. Look at that. Now, complete some questions, okay? And so the issue with that is that, yeah, we haven't actually guided students' attention towards what we want them to be looking at.
And so, if you're using this fully completed worked example idea, what we want to actually be doing is then backing that up with questioning. So that might be either self-explanation prompts where we've got these planned questions that students then have to either think about, purely just in their head or they might think about them out loud. They can do them in pairs where they're kind of unpacking these ideas.
And then the teacher's able to get an understanding as to where they're at and then we can kind of guide them towards that next step. So that's one way that we can look at worked examples. What's really important there is that the teacher needs to know where students are at.
So, they need to know that the students have that prerequisite knowledge that is required to actually understand that fully completed worked example. Because sometimes we can fall into the trap of giving them that worked example, but then students haven't got the prerequisite knowledge. And so, they're actually not able to answer the following questions.
So, we might have a triangle and we've shown them that fully completed worked example. They need to find out one of the angles. But if they don't know how many degrees in a triangle, they're not going to be able to find that out.
They're not going to be able to work that out. So, moving on from that, then we go into starting to move into that guided practice phase. And one of the things that I find almost essential is example problem pairs.
So that is where we have our worked example on one side of the board, or if we're using slides on one side of your slide, and you've gone through that with your students, but that stays up there. So, rather than moving on to the question that the students actually have to do, we actually keep that up and students can look at that as a way to guide them, when they are completing their problem, which is going to be minimally different. So we're going to give them a minimally different problem, which is almost exactly the same.
So, we might literally change one digit from the question that we have just shown them how to do. And why do we do that? It's because we are not assessing to see whether they can complete these on their own yet. It is literally just giving them an opportunity to practice what we have just shown them how to do.
So, it's more about learning the process that we're trying to show them. So, it might be, we're showing them how to complete like a three-digit addition algorithm or whatever it is. We've shown them how to do that.
We're not changing much. They're now doing the exact same thing, but rather than trying to have to hold what we've done in their working memory, they can now refer back to exactly what we've just shown them how to do. And they can use each of the steps that we've gone through, as a way to guide what they have to do next.
So, that's example problem pairs. Yeah. And as I mentioned, the two kind of principles that I follow for most lessons will be example problem pairs, minimally different questions.
Like that's the same sort of thing. And then guidance fading. Okay. And guidance fading is where essentially like we're starting with a highly scaffolded question. And so, it might be like, if we've got a multi-step problem, we might just get them to do one step. Okay.
And then we go to another question and then we're going to get them to do two steps. And then the next question, they're going to do three steps. And so we use this so that again, they're getting those multiple opportunities to respond.
They're building up their confidence. Sometimes people don't really talk about motivation when it comes to the science of learning, but motivation completely comes into it. We understand the importance of experiencing success, you know, success breeds success.
And so, we want our students to be getting that experience of success early on, so that they're more likely to persist when things do get harder as well. So, we're going through, this guidance fading, and there's a few different ways that we can do this. So, we might do it in a way where we, you know, I call it step and check.
So, we do that one step. So, the teacher does it one step, the students then do that same step, and then we actually check it. So, we might be using mini whiteboards.
So, I've done a step, they do the step. All right, then I'm going to get them to chin their boards. And then I'm checking, all right, is everyone on board? Awesome.
Let's go to the next step. So, then we do the next step. I'll do it, they do it, check it.
The advantage of doing it that way is that rather than waiting until the end of a multi-step problem to check, we're able to kind of get in front of any issues really early on, you know. So, I might say, after that first step, I've got 80% of my kids and they are not, they're not keeping up with me. So somewhere along the lines of my model, of my example, I've lost them.
Rather than trying to push on, I'm actually going to do a re-teach then and there. All right, I'm going to show you another example. Do my think aloud again.
Let's try that again. So rather than pushing on and getting to the end of a multi-step problem where it can be, again, quite frustrating for a student who has just spent the last five, ten minutes on this problem only for the teacher to tell them, “Oh, sorry, you got the first step wrong.” Yeah, that can be really quite frustrating.
We can actually pause and step after each step rather than waiting until the end. And when we're using mini whiteboards, it can actually be, from a teacher's point of view, really difficult to see where students got them wrong. If we're looking at 20, 30 students whiteboards and their work, and it's full, their whiteboard's full, next to impossible to actually diagnose where those trends are in your classroom and who's getting what wrong.
And so, yeah, I couldn't recommend that step and check idea more.
[00:31:04] Anna Stokke: As an example, it could, are you saying it could be something like this? So. let's say it's like a linear equation. Okay, so say it's like 2x plus 3 equals 7. And you do the first step. So, you know, you've already taught your students a little bit about how to solve linear equations, like more basic ones than that.
But okay, so the first step is, I'm going to subtract 3 from both sides. So, I have 2x is 7 minus 3, which is 4. Now here's your problem. 2x plus 5 equals 7. Do the first step.
Is it like that? And everybody does it and holds up their mini whiteboard and they subtract 5 from both sides.
[00:31:41] Brendan Lee: 100%, yep, 100%, yep.
[00:31:43] Anna Stokke: Okay, and you just kind of keep going through like that.
[00:31:45] Brendan Lee: Keep going through, yep.
[00:31:46] Anna Stokke: And so, you might do a few like that. And then the students get to do those problems on their own. And by going through it step by step like that, and it doesn't slow the whole class down either this way, right? Because it's just one step.
[00:32:01] Brendan Lee: Yeah, and once you kind of get that mini whiteboard routine really slick, yeah, it doesn't take long. You're literally spending probably the same amount of time as you would have anyway, because what would have happened if we go by that traditional approach of, here's a question, complete it all on your own? What can end up happening is that you'll have some students who just whiz through it, and then others who are lacking confidence, so they actually take a lot more time.
So, if anything, that probably ends up taking more time than doing the step and check mode, where we're actually able to kind of keep the pace up. And when students are using mini whiteboards, the teacher still needs to be circulating the room. So, it's not like we're just standing at the front and we're just waiting for everyone to finish.
We actually want to be circulating the room. I like to give my one-on-one feedback on the run. So one-on-one feedback on the run, whole class feedback, one and done.
That's kind of my saying when it comes to feedback, so that you can kind of get in front of the student mistakes a lot quicker. And early on, students are going to be lacking a little bit of confidence because they're in that kind of frustrational phase, right? And so, if we can just give them little hints here and there, and I've got my laser from my PowerPoint clicker, and I might just be quickly, I'll just check that one there. So, I'm using my laser, check that one there, check that one.
And that way, rather than them waiting until the end to find out that they got it incorrectly, we can get them to quickly fix that mistake before we actually check anyway. And so, when we check with everyone, almost all of our students are showing the correct response because they've already received feedback. And then we move on to that next step.
[00:33:40] Anna Stokke: Okay, this is great advice. This is such good advice. Okay, have you got anything else on this topic that you want to talk about?
[00:33:47] Brendan Lee: Yeah, look, I guess there's a couple of slight variations on this idea, right? so rather than, so we could do it the opposite way. So backwards fading is almost like the opposite way. So, it's where, and I wouldn't always do this whole class.
I might do this more after I've released some students for independent practice. And I've noticed I've got some students that they just need a bit more time with the teacher, build up their confidence. I find backwards fading really supportive in that sense.
And so, what we do this time is that rather than getting the students to do the first step, they're actually doing the last step. So, the teacher will go through all of the steps with them. So, I'm doing step one, two, three, and four.
And then I'll leave that last step for the students to do. And then we'll do another example. I'll do steps one, two, and three. And then the students do the last two steps. Okay, and then we'll do another one. And so, yeah, it's almost a reverse, like highly scaffolded because they're seeing so many examples with the teacher.
And that's why it's not always necessary for the whole class, but can be, yeah, it's almost like the missing link for that final 10% of kids that might just need a bit more scaffolded support.
The other one as well is, I've got this one from Reed Smith, who is a CEO of Ochre Education. And yeah, it's called Make or Break. And essentially, it's when you know that there's a really common problem area for a certain topic. And so, the one I like to really use it for a lot is when we're talking about regrouping. And so that can be like a tricky topic for many kids, many students.
And so, we can do what's called ‘Make or Break’. And all it is, is I'll just present a series of questions where they have to just tell, me thumbs up or thumbs down, right, regroup or not regroup. And that's it.
So, look at this question, do I regroup? Yes, or no? Thumbs up? Yes? No, we don't regroup. Thumbs down. And I'll just go through a series of those.
And that can really help me very quickly diagnose whether or not students actually have got their heads around this idea, or do we need to go back and revisit this and reteach it?
[00:35:55] Anna Stokke: I like that one. And so, you could use that really with any common misconception that you know that students have, provided you know that that's a common misconception. That actually comes with experience, right? But really a good textbook might tell you that that would be a good problem to use for ‘Make or Break’ as you call it, right? But I don't think we would often see that. So, this is really great.
And so, these are all really great techniques for using in the acquisition stage. How about fluency? What sorts of techniques can you do to get students to become fluent? And just to recap that fluency is really accuracy, plus speed. So, it's being able to do something not only accurately, but being able to do it effortlessly and quickly. So, what are some techniques that teachers could use in that stage?
[00:36:50] Brendan Lee: Yeah, look, firstly, there's probably a couple of missing pieces from many maths classrooms. And so, the first piece I would say in like a lot of, especially, I'm working in primary schools now. I did used to work in high school, but I'm in primary.
And so, in many primary schools who are using explicit instruction really well, they are using it really well to a point, okay? But the point that they miss out on is the independent practice. So, the real life complex primary classroom can be quite hectic. And so you're doing your very best to get through your maths lesson, but you've got something that pops up.
“We've got an assembly in five minutes. Oh, everyone quickly pack up.” All right, and so we've packed up, but we've missed out on independent practice.
And what most teachers will do in that scenario is that they'll just move on to the next lesson the next day. And so, before we get to fluency, one of the issues that we've got to get right is actually giving enough emphasis on the need for independent practice after we've gone through that gradual release of responsibility. We've gone through the ‘I do’, the ‘we do’, that guided practice.
We need to be making sure that we get to independent practice. And now this is where there's a bit of an art, in actually getting this right. And the way I like to do it is firstly, we want to try to teach a whole class as much as possible when it comes to maths.
It can start to get a bit complex when we start to have a really big range of abilities in our classes. And this is when we don't get those foundational concepts right from the start. We end up with students in year four, year three, year five and six.
And we've got some operating at like a year one level. We've got others who are actually zooming ahead and they're actually now ready to engage with high school content. And so, we've got this huge range of abilities.
And so, teachers end up thinking, oh, we've got to differentiate for all of these different levels. And it's really not very effective and it's very difficult for teachers to get right. So, what we want to be trying to do instead is use that gradual release of responsibility.
And then we're keeping everyone on the same content, on the same concept. And it's more about just releasing students at different points. So, once I'm seeing a high success rate from our students in that guided practice phase, I'm releasing them to independent practice.
My big thing for independent practice is that I like to say it needs to be done independently and silently. And the reason for that is, is that if they're talking to another student, while it might be on topic, I actually don't know how much scaffolding and prompting they're getting from their friend. And if that's the case, in my books, they're still in guided practice.
And that's okay, but I actually want to know that they're in guided practice because that's really useful information for me as a teacher. And so, if they're at independent practice, that's literally practicing what we've just been doing in the class, but it's being done independently without any support. So, it's not, you know, teachers, aides, they're not there supporting, again, that would be guided practice.
It is just them doing what they've done independently, silently, and they're practicing, they're just getting those reps in. Because then once we're able to do that accurately, repeatedly without assistance, then we can move on to fluency practice because fluency practice is all about maintaining that accuracy, but now we're really focused on increasing the speed. Look, I know that you've done a couple of great episodes on fluency with Brian Poncy, and you also released one yourself.
And so, I know that you get how important fluency practice is, but I think like just maybe where I might be able to add a bit of value is just in terms of like a whole class, classroom teacher perspective and what they can be doing. Because it's, you know, it sounds great to, you know, we do our assessments, so we're doing our curriculum-based measurements and we've worked out, we've got students at all of these different, I guess, levels in the progressions, right? And so, we've got, I'm a year four teacher and I've got some students who are ready to, so they're at that kind of instructional phase and they're ready to be practicing their times tables, okay? But then I've also got a group of students who have shown through their assessments that they're actually at the frustrational phase for their times tables. And we've actually just got to get our addition and subtraction facts right for numbers to 20, right? And so that's where they're at.
So, we've got these students at different phases of their learning, but this is also where we can start to differentiate, right? Is that we can actually now provide our students with the practice opportunities that they need in our fluency block. And I would, for primary classrooms, I would really just highlight and emphasize the need to have fluency practice every day. And this is just like a mini block within your maths lesson.
So, it's not happening randomly. It's not just happening when we're doing a unit on multiplication and division. It's actually happening every single day.
And it can be as little as two to five minutes a day. It can be 10 minutes a day. Whatever you're able to fit in, like that's what we want to be really, really providing them.
It doesn't even have to be during your maths lesson. Like I know some schools have got it happening after lunchtime because they understand how routines are a great way to settle our students. And so, this is something where we can build in mini routines within the routine.
And because students are experiencing success, they actually now feel, you know, they can start to take, I guess, a bit of responsibility over what they're doing. And so, I guess building on some of the ideas that you spoke about with Brian Poncy and looking at what that can look like from a whole class perspective and a classroom teacher, what they can do. Things like cover, copy, compare.
Like I've put together booklets they can go through where they're able to, yeah, you know, look at the fact, cover it up and then, you know, write it afterwards. And once you build in this routine, they can start to do that independently. So, one of the things that changes between I guess, whole class and what we might call intervention is more just how many new facts we might be getting them to really focus on at any one time.
So, when we're looking at that kind of whole class, we can probably get them to look at, you know, more than one or two new facts at a time. Whereas when we're looking at that intervention, we might just focus on one new idea at a time or one or two ideas at a time. So yeah, cover, copy, compare, you can put together booklets.
You know, I've found ChatGPT can be really quite helpful in just putting together like problem lists. You know, like once you kind of give it a bit of a prompt, I just need all the facts for this times table, whatever it is, that can spit it out rather than you having to, you know, sit there on a computer and type them all up. So yeah, that can be like one.
And like one of the things that like as teachers, we need to consider is again, coming back to that idea of motivation, right? Is that essentially what we want to be doing in fluency practice is just providing students with opportunities to practice. So that can literally be just worksheets, right? But eventually motivation might wane if they're just getting out a bunch of worksheets every single day and working through that for five to 10 minutes. And so, we want to try to mix it up a bit.
So, that's why like I've got a combination of, you know, partner activities, cover, copy, compare, flashcards. Yeah, like our kids use timestamp as rock stars as well. And so we're using all of these different methods, but the whole idea is that they're just getting practice and emphasizing that you can build in external motivators like having a leveled system, you know, giving out certificates when they get through different levels.
We can look at, I'm not sure if you've looked at precision teaching much, but they use what's called standard celebration charts. And essentially all it is, like it's got this really fancy name, but all it is, it's just a way for students to track their progress. And again, it can be really helpful for them to start to take a bit of ownership over their own growth.
And so, all they're doing is they might just get out a stopwatch, they get out one of those practice sheets and they see how many problems they can complete in one to two minutes. They can self-mark and then they just plot themselves on this graph. And they can start.
So, you know, when they start off, they're going to draw a line across. So, they're using a ruler, they draw a line across what their goal is and then they track their progress towards their goal. So, when we do our formal assessments again, which might be in a couple of weeks, it might be in a month's time, they can actually already feel quite confident that they're going to achieve their goal because they've been monitoring their progress as they've been working along.
So yeah, there's some of the ideas when it comes to working in pairs, like we can do things either with, I've done pretty much the same activity with both flashcards and using the cover copy compare sheets. So, we've got partner A, they ask partner B a question, partner B has to answer that question. If they either get it incorrect or they get it correct, but it's slow, we write that down.
And then, so that's going to go in their column of questions to work on. Okay, and then we swap roles. So, it's simply, yeah, ask a question, partner B answers it.
Was it fast enough? Was it correct? Yes, or no? All right, then we're going to write it down if it's too slow or incorrect.
[00:46:08] Anna Stokke: Okay, perfect. And so, when we talk about fluency, a lot of the times we talk about math facts.
And with math facts, we can actually measure it, right? So, what we've said on the podcast in the past is you want to look for 40 to 60 math facts correct per minute. And we would consider that being fluent. I consider fluency with math facts, by the way, to be instantaneous.
Like if I say six times seven, you should say 42, right? But we want fluency in other topics too, right? It's not always as easy to measure, I guess. So, things like, even like factoring polynomials, like when kids move up in the grades, they should be able to do it fairly effortlessly and correctly, right? I think you've made it fairly clear that that comes from practice. It comes from lots and lots of practice.
Like you can't really practice too much. And it's something that you want to be doing every day. And that's how kids get fluent or how anybody gets fluent with any math skill, really.
[00:47:12] Brendan Lee: Yeah, couldn't agree more. And I think that's probably the next stage is for teachers just to start to understand how we can do fluency practice for anything.
But right now, we've probably got to prioritize the fact that, well, we really got to get, just get out our numbers, right? Our basic maths facts, right? And then we can really start to, all right, well, what's the next thing that we could do some fluency practice on?
[00:47:34] Anna Stokke: Exactly. Okay. So, we should move up the hierarchy. All right. So, we spent lots of time on acquisition and fluency because often I think, at least in Canada, in the United States, I think that students get stuck at the acquisition phase, right? At the acquisition stage that they're not actually moving past through the fluency stage, which is an issue. And, but let's say we get to that point, right? Now we're fluent.
Then we're in the generalization or adaptation stage. And what do you think are some good strategies to use in that stage when you're trying to get students to a spot where they can actually use their skills in new settings?
[00:48:15] Brendan Lee: And again, this is one of those things where I would probably say to teachers, try to do this every day. Yeah, try to have problem solving, like with our fluency practice. We want students to be engaged with problem solving every single day.
But the difference between maybe what some other people might talk about when it comes to problem solving is that when I'm talking about it, I mean, problem solving on things that students have already mastered. So, you know, if they are in year five or year six, and they've already mastered the addition and subtraction facts, they've already mastered their multiplication and division facts, we can now get them practicing problems on those that involve those every single day, okay? And so, it doesn't have to be, I think traditionally, what we've thought, right, is that if you've got a unit of work, either we go through a lesson, and by the end of that lesson, we want our students to be problem solving, which is way too early in my eyes. Or at the end of a unit of work, which is probably too late, you know? And so, because we end up, we either miss out on those lessons because we've spent so much time on the start of the unit, and so students end up not doing any problem solving at all, which is kind of what you're talking about before. Or we get them to generalize in the one lesson.
So, we've just taught them this new concept, and then we go through that whole, the phases of the gradual list responsibility really quickly, and then we think at the end, all right, now we want them to problem solve on that. And then what usually happens is that we just end up with all of these students putting their hand up saying, “I don't know what to do”, or they're coming back to the teacher because we've asked them to actually generalize, we confuse the generalization with being independent practice.
So rather than the independent practice being practicing what you've just taught them how to do, it's actually asking them to generalize what the, yeah, that same concept. So yeah, when it comes to what, like Sarah Powell, I know you've spoken to her before, she's done so much great work on how we can actually help our students with addressing word problems. And so, things like having an attack strategy.
So, an attack strategy is just simply following usually the steps of, understand the problem. So that can involve reading the problem, making sure that you can, like you know what the questions are asking you to do. Like we can go through different steps for that.
So, understand the problem, put together some sort of plan. So that might involve some sort of drawing or diagram, a bar model. Then we go into actually answering the question before checking that we got it right.
And so, those four steps, there's all of these different kinds of acronyms that have been thrown out there. There's UPS check, there's so many different ones, but the main thing is that it should have those four different steps in your attack strategy. So that's the first thing.
So, if you're like a school leader, ideally you set up an attack strategy, which is being taught to kids across your whole school. So, you having got different attack strategies being used in different year groups, but we've actually got the one and we were able to kind of look at how students are using that across the different year groups. And so that's the first thing, get that right, teach it.
So, this is like a separate thing that you need to teach. So, we teach that first. We go through what to do at each of those different steps.
So that might be like four or five different lessons because you're breaking down each of those different steps. Then the other thing that we can do, which goes into even more detail is schema-based instruction. So, this is now where we are actually paying attention to the fact that we can start to see a lot of similarities between common types of problems.
So, we can start to see that we've got these part-part-whole questions, and this is what they look like. And so, then we teach students, when you see these sorts of questions, this is what you need to do. Okay, there might be a missing part, there might be a missing whole, depending on what is missing, will tell us what we need to do next.
And when you show them multiple examples of what that can look like, and again, we might throw in some non-examples of what it doesn't look like, students are able to start to see, oh, okay, so these are the common features. And the difference from what we've kind of done in the past of looking at keywords is that there can be a real danger to that because the keyword doesn't always link up to the same operation, okay? And so, there's a big danger of just looking for the keywords and the numbers and punching them in because it's not always going to give us that correct answer. Yeah, so essentially like schema-based instruction, it allows us to go through those different operations.
We then show students, and again, like if you're taking a whole school approach, it's not like we're going to go through all of these in one year, but we're breaking them down and we're starting from, usually from around year two, year three, we might start to introduce schema-based instruction. And then we're actually starting to introduce new types of problems as they progress through based on the relevance for the age group, yes.
[00:53:24] Anna Stokke: Right. And I think you've made that pretty clear. You know, in the generalization adaptation stage, you can use explicit instruction too, right? You give students techniques, you model how to solve problems, for instance, I know a lot of people that perform really well in math contests when they were kids. And the way you get good at math contests is you just study a lot of different types of problems, and you learn the techniques used in those problems, right? And then you can apply them in new settings. So, certainly you can teach people to problem solve, right? Which I think can sometimes be a misconception.
I think sometimes people think that it has to be discovery based, but it doesn't. People usually are kind of taught how to problem solve.
[00:54:16] Brendan Lee: And so, here in Australia, we have like a standardized assessment that all students get assessed on called NAPLAN. And for the numeracy side of it, it is all word problems. Okay, and so if we're not giving students opportunities to practice it, essentially the first time they're exposed to it is when they have to sit in this, fairly high-stakes environment.
And it's no wonder that many of our students struggle with it, is because like, not only do they have to have reading fluency in order to actually understand the question, but then they've got to know well, what sorts of things can I be doing to address this question? So, it is really, really important. And if we can get to that point where classes are engaging with problems every single day, they're engaging with fluency practice every single day, we're not going to see the sorts of gaps that we're currently experiencing in maths classrooms, because they're getting exposure to the practice that they need.
[00:55:11] Anna Stokke: Yeah, I completely agree with you. So, before we kind of wrap up, I thought, you know, you've talked a lot about things like teaching tools that are successful but sometimes used at the wrong time. So, do you want to give a couple of examples of that, what you think might be the most common situations like that?
[00:55:34] Brendan Lee: Yeah, sure. And I think this sort of thinking came about after working with so many different schools and teachers, I guess being a little bit surprised at just the ways that things were being implemented in classrooms. And like, I always just find this really interesting. Like I'm, I guess another area that I've learned a lot about is, it's just around implementation, implementation science and how we actually implement new ideas.
And I find it just so fascinating around, as a professional learning provider, you think that you've been really clear and explicit with the, I guess the guidance that you provided teachers, and then you go into a classroom and you say, oh, that's not being implemented the way that I had intended it to be implemented, right? And so, yeah, this is where, yeah, I guess we get a little bit of knowledge, and we think we know everything that we need to know about it, and then we go ahead and implement it. But the problem with that is that we don't, if we don't get the timing right, and this is why having like a shared understanding as to how learning happens is just so important for teachers to have, because that way we know, like when we're seeing students struggling, that's telling us they're in the acquisition stage, or if you're going by that novice to expert continuum, they're at that novice stage, so I need to be providing them with explicit instruction.
However, like when we go get into the finer details of explicit instruction, we've got all of these, I guess, tools within it. So, we've got things like ‘checking for understanding’. So we can check for understanding through using things like ‘think-pair-share’, or ‘turn and talk’, many whiteboards we've spoken about already. It might be ‘cold calling’ or ‘calling on non-volunteers’, it can be ‘coral responses’, but so all of those techniques can be used incorrectly. So for instance, in general, we might check for understanding too early, so we might check for understanding, and this is when teachers hear about it, “oh, we need to be doing this more”, and then they start checking for understanding at the start of the lesson, during the ‘I do’ phase, we're seeing if they can understand things before they've actually got a really strong grasp of it. Or sometimes before you've even spoken about it at all, and what ends up happening is it's like we're going fishing, you know, so we're fishing for the correct response, when deep down, you know, as a teacher, I actually haven't taught this yet, but oh, I'm going to look silly if I don't get the correct answer, and so I'm going to keep asking. And then I know, oh, little Johnny at the back, he always knows the answers, “Johnny, what's the answer here?” And then, oh, it's not quite right, this is what the correct answer is. And so, we go fishing, and so that's, I guess, the danger of checking for understanding too early.
What we can do instead during that ‘I do’ phase is we could potentially check for listening. You know, so Craig Barton talks about this idea of, we might just get them to repeat what you've just said, or we can even get them to do a correct response, or read a track with me, read along with me, so if you know your ‘I do’ phase, that modeling phase is probably going on a little bit too long, I haven't had any student engagement for, you know, three, four minutes, all right, let's get them involved here, you know, track with me, read with me, let's read this out together, or what did I just say, whatever it is. So rather than checking for understanding at the start, we need to check for understanding at the right time, we might do something like a ‘turn and talk’, where we're asking them to talk, but they actually haven't got the background knowledge to talk about whatever that concept is, so that can be another mistake that we can make. You know, we can ‘cold call’ or ‘call on non-volunteers’ when we haven't set up the right classroom culture, so we haven't got that culture of error that Doug Lemov talks about. And if you haven't got that, and you start ‘cold calling’, students might actually have the correct answer within them, but they're not feeling that psychological safety to share with the class. And so, setting that up, really important.
And then, you know, we might be using these different ideas, but then, because as teachers, we're not fluent with changing our behavior, we rush through it, okay, you know, we don't think about it correctly. So, we might, looking at that ‘cold calling’ idea, we might cold call students and then ask a question straight away, so we haven't allowed any thinking time at all. So, thinking time, really important, we've asked a question, allow a pause point, some thinking time, so that students can actually process what you've asked them to do before they respond.
Another one is, we actually end up, we think we're cold calling, but we're not, we're doing the same as we were doing before, where we say the student's name, and then we ask a question, and so that's defeating the purpose of cold calling, where we actually want to ask a question and then call on that student's name afterwards.
So there’s just a few, like, you know, we can go into more detail where, like, we might ask, oh, actually, this is probably a good one, we were talking about fluency before, the problem with fluency practice, and where we've fallen into the trap of doing this in the past, is putting them under timed pressure before they've actually got accuracy. Okay, and I think this is where timed practice really got a bad name, was, you know, it got this label of ‘drill and kill’, essentially because what was happening was, we were going for whole class fluency practice, but we were timing them before students actually had accuracy. Okay, and so that's where a lot of our students were getting anxiety over timed practice, was because we're putting them under that timed pressure before they actually had the accuracy. So, yeah, they're just a few of the tools that can go wrong when we don't get the timing right.
[01:00:55] Anna Stokke: Yeah, exactly. Okay, so let's wrap up with this because we've talked about the instructional hierarchy a lot today, which I agree is great.
And it does really add something to the discussions about cognitive load theory. I agree with you. So, what's one piece of advice that you'd give to teachers who are new to using the instructional hierarchy?
[01:01:20] Brendan Lee: Yeah, I guess probably the main thing is just to understand how, the reason why it's so valuable is because it can tell us what to do based on what we're seeing in the classroom, okay, so use that data, use the information to then guide you to be responsive in what you're going to do next, okay, so if you're seeing your students struggling, if they're frustrated, that's telling you, you need to give them some support, you know, so whether that's feedback, whether that's scaffolding, prompting, giving them some cues, and then we're going to fade that over time so that they are able to get to that point of independent practice like we spoke about before, but yeah, just instructional hierarchy, so useful because it tells you what to do based on what your students can do, it gives that direct link.
[01:02:03] Anna Stokke: Perfect. Well, thank you so much. You gave us so much useful advice in this episode, and I think everybody's going to find this really helpful. And I really appreciate you coming on to talk to me today.
[01:02:15] Brendan Lee: Awesome, it's been a pleasure, and yeah, hopefully it was useful, just on the instructional hierarchy, I'll give a quick plug, and yeah, this is, I guess, breaking news, I haven't announced it at all yet, but yeah, I'm currently in the process of co-writing a book on the instructional hierarchy with a couple of really super knowledgeable colleagues in Dr. Russ Fox and Karina Stocker, and so yeah, hopefully by the time this is released, we'll have a bit more information around that, but yeah, essentially it's the book which I wish was out there now, and so we just decided to write it, because there's not really a book that actually unpacks the instructional hierarchy from that sort of whole class perspective, which we think would be really useful.
[01:02:53] Anna Stokke: Nice. And you heard it first here. Okay. Thank you.
[01:02:58] Brendan Lee: Thanks, Anna.
[01:02:59] Anna Stokke: Thank you!
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