Retrieving and replicating, Forgetting names, and more. In this episode, Andy, Robin and Adam are joined by Darien Allan, Mathematics Teacher at Collingwood School in British Columbia, Canada to discuss applying research from neuroscience to improve teaching and learning. What does the research tell us? How powerful is the spiral approach? Plus, Darien talks on the value of delivering lesson-opening questions that prompt prior knowledge topics from as far back as a month ago.
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Hi, I'm Andy Psarianos.
Hi, I'm Robin Potter.
Hi, I'm Adam Gifford.
This is The School of School podcast.
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So welcome back to another episode of The School of School podcast. We are here with our usual suspects, Adam and Andy. Hello both.
How you doing Robin?
Hello.
I'm doing well.
Good.
And I'm doing well because we have Darien Allen here today, and Darien teaches at Collingwood School in West Vancouver, British Columbia, Canada. Darien, welcome to the show and wondered if you could give us a little bit of background on you.
Sure. Thank you for having me. I'm happy to be here. I am, as you said, I work at Collingwood School. I teach mathematics. I am a mom, I have a 10-year-old daughter. I've been teaching for 20 years in both public and independent systems in British Columbia. And I could say honestly over my 20 years that it has been a constant journey of learning in various forms, both formal, masters, and doctoral work. But also just informal conversations with colleagues, reading, all sorts of things. So I'll say I have a growth mindset, just to borrow some terminology there, but constant journey of learning.
And part of your learning I know has come from, you did a doctorate and you looked at how students actions and goals can be... Well, you've done your research on it. I won't go into that because that's a whole other topic, except to say that I'm also wondering with the discussion we're having today, if that comes from some of that research where you're looking at applying research from neuroscience to improve teaching and learning? So I think you need to start us off on this.
Okay.
I think you're the wealth of knowledge here.
So, I'll be honest and say that none of this really comes directly from my doctoral research, other than that I have a almost 20 years background in looking at research and understanding how that supports and drives a lot of what we do in teaching. And how it not necessarily doesn't, but the research that exists has not been applied to teaching. And this is the topic today, which is something I actually, I can't remember if I heard it before this year... I did hear it before this year, but I went to a conference in October, and one of my colleagues from another school was presenting on the findings of neuroscience. And this has been known since the nineties. It's partially the work of Robert Bjork. But the book that came out, because this is often what happens is research comes out, it's published in journals, but that's not accessible to most of the population, not because they're not capable of interpreting that, but just because we don't as teachers, that's not go-to is like these academic journals.
So it comes out at some point, somebody writes a popular book I'll say, and that's when it trickles down. And so that's what happened, is that there's actually a few books on how you can apply the findings of cognitive science, cognitive psychology, to education. And so I will talk a little bit about these ideas. And there's basically four that we are trying to build into, and by we, I mean my colleagues at my school, and I know colleagues at other schools are trying to build into our practise to help students learn, retain, understand mathematics better.
I'm really intrigued. Can't wait to hear about it.
Yeah. Okay. So I am not an expert on this, but I will do my best to try and explain it and make sure I'm not making any mistakes here. But the four ideas are these. I'll give you all four and then I'll explain them. So there's the notion of retrieval. Spacing is the second one. Interleaving and feedback driven metacognition. So those four things. And the first thing is when you learn something, you first encode it, you store it, and then you try and retrieve it. So for example, if someone gives you directions, you encode that, you store it. And then when you go to retrieve it, you may or may not be able to do that depending on how much time has gone by, or I'm sure, this happens to me all the time, when you meet someone and you learn their name or you don't learn their name. They tell you your name, and unless you do something where you encode it, you store it, and when you try and retrieve, it's gone.
And so what you actually need to do is practise retrieving it. And I do do this now, where you have to keep trying to test yourself and retrieve it so that you're actually able to when you need to. And so that's the idea there is that students will learn better, or have a better, let's just say retention, or better success of retrieving something if they practise retrieving it. So in the math context, it could be retrieving a fact, but it could be also retrieving a process. Right. How do I factor this? What's the process for doing that? What's this term called? What's this definition? So there's the fact base there, but where you have to practise retrieving it.
The spacing, the spacing comes in when you're practising things over time. So for example, we'll tell students this, I'm not going to do every problem I've been given in one go. I need to space it so that I am actually making myself retrieve it multiple times over time, versus, I'm going to do all this at once and then I'm going to forget about it for a month, because then you haven't practised enough or frequently for it to be easily retrieved. If you're circling back to something, then you're actually spacing it out and you're forcing yourself to retrieve it, rather than, as typically happens in mathematics is, okay, we're going to do fractions, integers, linear relations, and you haven't done fractions since the start of the year. So spacing things out basically just gives them more hits over time and a better success of retrieving it. And this is supported, this is evidence-based research.
Interleaving is mixing up topics. So mixing up closely related topics I should say. So for example, if we're doing operations with integers, mixing up so students don't do, okay, we're going to do 10 addition, 10 subtraction, 10 division, 10 multiplication. It's mixing those up so that they have to practise retrieving again and again and again. Right, which one is this? Interpret, apply, interpret, apply. And so the more often you do that, the better. And this is so prevalent in workbooks. In fact, I've only seen one, and it's a calculus workbook we use where they're constantly putting in questions. I'm sure it exists, I haven't seen it that often. Constantly mixing in previous content, and so you don't have like, okay, we're going to do 20 of these and 20 of these because what that gives students is that sense of, "Oh, right, I get this. I do." And then it's really just they're repeating something they did, and they're not actually having to retrieve something.
And then the last thing is the feedback driven metacognition, which is just giving them the feedback and getting them to think about it. And so one of the things that can actually... And this actually came up. It was probably the last Pro-D I went to before we went out for COVID, before we were put online, was at UBC. It was a biologist, and she presented findings... She put a quiz up. And gosh, the last time I did biology was a long time ago, but put a quiz up and said, just multiple choice, if students get the answer wrong, they are more likely to remember it, versus just, okay, here's a question, here's the answer. So if you... Oh, it's almost priming, priming students at the start of a class with material they might not know.
You could give them the test for it if you had it in units, you could give them a test for the entire unit. And what it does is it primes them to okay, wait. And honestly gives them a touch point like, "Oh yeah. Wait a minute. We had a question like this in the past." And it just gives them something to latch onto.
And I'm guessing Darien, that there's sort of different tiers of this. So I'm thinking, right, I imagine if I went into the classroom tomorrow morning that there's some of these things that I could put into effect just very quickly and sort of succinctly perhaps. But then on a broader level, hoping that programmes that are used or books that are used or resources that are used understand this process as well. So I guess educators will be trying to come at it from the lots of different angles. Would that be fair?
Yeah. And like you said, I mean there's the big picture where if you decide to aspire a curriculum, that is a whole shift. But I mean, I can walk into a classroom tomorrow and all I have to do is come up with maybe three questions based on the content that day and start off the class with that. Or when I assign homework or practise, just tell them, "Okay, I want you to do one of these, then one of these, then one these, and then go back and do another one." It's really just the ordering of it. Or telling students, "I don't want you to do all your homework tonight. I want you to do five minutes tonight, one of each section, and five minutes tomorrow, one of each section", or something like that. So those are quick and relatively easy adaptations. Other things I've heard is to get the spacing piece and getting kids to retrieve things more frequently, or again, is at the start of a class, starting it with three questions, one from last day, one from last week, and one from last month. So where you're bringing in previous material.
Yeah, and just being mindful of that learning journey, right? So what makes a lesson a good lesson isn't just what you're doing right now, it's where it is in context, what you did yesterday, what you did last year, what you're going to do tomorrow, and what you're going to do next year. And you have to be able to tie all those things in. And then in that, understand that the importance of being able to retrieve information that you studied last year, interleaving the various complexities of it. You have to be mindful of all these things in order for a lesson to be good, right? And I guess that's kind of the challenge, that's the challenge for teachers, is how do you... One, you need to know and understand this stuff. You need to know that these are the things you should be considering when you're planning a lesson, that you need to say, "Well, how does this fit in what they did last year, what they did yesterday, what they're going to do next month, and are there opportunities for me to revisit concepts to allow them to interleave them?"
And there's so many learning theories really, that's why teaching is so hard, right? And then you got to start... Because you got to go back to some of the other pivotal kind of research that's happened in education like Piaget with a sort of accommodation and assimilation and what's the difference and how do you teach a lesson so that you're not merely getting them to remember a bunch of stuff, but that they're actually accommodating for in their own understanding. This is interleaving, it's just different language. His work was basically saying that now we know how that works in neuroscience. And we're saying, "Yeah, actually that was observational work. Now we know what the mechanics of it are." We know that it's actually, that's how the brain works if you want. But as a teacher, you need to be mindful and aware of all these things and be able to tie them all together, and it's a lifetime journey for teachers to get better and better at this kind of stuff.
And there are other people who have to play an important role in this, whether it's content creators, so obviously at Maths No Problem, our whole world is about trying to be as mindful about all this stuff and then create content that allows teachers to do this, to help them save time so they can spend more of their time planning the lesson as opposed to trying to find the examples that will do these things for them. That's our role to play in it, and that's our responsibility, and it takes a tremendous amount of collaboration. What's the saying? "It takes a village to raise a child." It's so true. We all have to work together. And I think you alluded to part of the problem Darien, which is all too often what happens is that the research, although it's there, it largely gets ignored, not because people don't want... It's not that they don't want to know it, it's just they don't even know it exists or it's not in a place where it's accessible to them. A research paper isn't going to make it to the average classroom teacher, right?
Just to go back to the four pieces, I'm just curious, is there one that's more of a stumbling block than the others? I don't know. Do you find that teachers, if given direction on how to implement this, it's kind of like you would start the class with three questions, that kind of thing. Or, is there always a piece of it? Is it the metacognition piece or something that people are kind of like, "Oh, I'm not quite sure how to present this."
The stumbling block here isn't so much any one of these pieces, and it's not even them as a whole. I mean, things don't get implemented for many, many, many reasons. These are relatively, I think, relatively easy, which doesn't mean that they happen in every classroom or every day. The big piece here is actually... One of the big pieces here is the student piece. And what students experiences is that if they're doing these things and they are doing the interleaving practise, that feels harder, because if you are doing 10 questions and those 10 questions are all the same, by the time you get to the end of the 10, you generally feel pretty successful. And what we find, and this is why it's so frustrating for students, they're like, "But I understood it, and I don't understand it on the test." And that reason is because they've really only retrieved it once or twice while they're doing those 10, and then they're just replicating.
And we find that when students use something like they do horizontal copy, and you've got an example here, and they repeat the steps versus having to start from scratch and carry something through vertically and you're constantly having to force yourself to retrieve the next step. And that's what is, I guess maybe frustrating for students is that this is harder. It feels harder, you don't feel as successful. But the research shows they actually are more successful. I think the results were if you were to take a student a month after they'd finished a course or finished some content, a month later, students who had done the interleaving and the spaced retrieval would remember, I think it was somewhere around 66%. They would get 66% on an exam, the same exam they'd written a month ago. And I think the non-spaced is like 30%. It really is significant.
The evidence speaks for itself that the students who did the spacing, and it wasn't even... They didn't even spiral. It wasn't that. Spiralling is just one way to make this all work. It seems to fit quite well, but it's not the only way. You can do this in a unit based classroom. Just using these four, the retrieval, this spaced practise, the interleaving, and the feedback driven metacognition is really just helping students know what they know and what they don't know. The tough piece there is actually the student piece because they don't feel as successful when they're doing it this way. But they are more successful.
It's a mindset thing, right? It's like that... My interpretation is that practise needs to not just be repetitive, but it needs to be a little bit more varied. So there needs to be some variation in the practising , because you want to create an environment of struggling because the struggle is where the learning happens. If it's just repetitive kind of muscle memory kind of work, you're not actually learning. You may be indoctrinating what you already know a little bit more, but you're not actually learning. And it gets, I suppose, less sticky. While if you're struggling, there tends to be more remembering going on when you have to struggle. It's kind of what you said. People are more likely to remember mistakes than they are... You said that early on. If they make a mistake, they'll remember more from that experience because there's a struggle element to it. It doesn't feel comfortable, right?
No. If you're giving an example from say a... You're just reading a passage. Students should only read their notes once really, if they're studying. And this is the thing, the other way that students think they're learning math is to, "I read all my notes. I did all the practise questions again." Or I mean, bring it into socials or any other humanities. They read it, and then you just need to test yourself. The examples given in the [inaudible 00:20:38] are about people learning lines, to these amazing actors who really just constantly are testing themselves. And then, okay, you go back when you have to, but it's not like, "Okay, I'm just going to read and memorise this." It's, "I'm going to read it, and then I'm going to test myself." And you will... I mean, it's way easier to remember something if you understand it and you can build connections. And so that's kind of where that piece comes in.
I think this could be a much longer podcast because I think we're barely scratching the surface, but we're going to have to have you back for the next one Darien, part two. It's fascinating because I always... And when I'm listening to you, I think about my own kids and their learning in the classroom, because I've heard them say some of the things you've said that your students say. I may have to get them to listen to this episode. Anyway, it's been great having you on, and we certainly hope we can get you back on again.
Great. No, I'm really enjoying it. Thank you.
Thanks for coming.
Thank you for joining us on The School of School podcast.
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