Adult brains, prior knowledge and more. In this episode Andy, Emily and Adam talk about working memory. How useful are basic maths facts? Can you decrease mental load? Plus, the difference between rote learning and deeper conceptual understanding.
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Hi, I'm Andy Psarianos.
Hello, I'm Emily Guille-Marrett.
Hi, I'm Adam Gifford.
This is the School of School podcast. Welcome to the School of School podcast.
Hi everyone. Thanks for joining. Today we're talking about working memory? Short-term memory... What were we talking about? So what were we talking about?
There's a lot, I think that neuroscience general, I'm not going to completely geek out on this, but there's so much that comes out now. And I know that is a topic of conversation. It's a really, really interesting topic, particularly in relation to education. I think working memory, it's interesting in that, it's the part of our memory that orders things, processes things as we're working. And I think that this can be a real hurdle if we don't consider this for everyone's learning, not just children's, but everyone's learning. To make it as simple as my understanding will let me make it. Is that if we at have to attend to too many things in real time, just to understand something, our ability to access new learning decreases. So if we're attending to it so I don't know if we've got something a problem, or actually, we'll do a reading.
If I'm reading, if I have to decode too many words, because I don't understand them. So I'm sounding out every word in a sentence. The chances of me understanding that whole sentence and the meaning as it was written by the author is incredibly low. If I only need to decode one word and amongst those, then the chance of me understanding the context of that sentence is hugely increased. So I think it's really important in education that we're aware of this, because if we're having to attend to too many things, if we're not fluent in the majority of the processes that we are using, it really makes it far more difficult to pick up new learning. Now and we see where kids, I've had it before, this poor wee boy, but really felt for him, obviously changed what he did, but he said, "I'm trying really hard and I'm getting my brain to try even harder." I'm thinking, oh mate, if you try, your brain tries any harder, the chances of you learning something new are almost zero because your brain doesn't have anything left.
There's been some conversations I've had with people around prior knowledge. So I don't know, Adam and Andy, how much that's similar in maths, but increasingly people are finding that before you introduce a new subject, maybe so let's say you were going to read a book and it's on a particular topic. There might be some certain things that you need to make sure that children are clear about or comfortable with before you go and start. They start actually reading the book because actually you're giving them a disadvantage without giving them some kind of key information that could just help take that load away when they reach it. Or you're giving them some information that can help them access that information more effectively as they go. I think that's quite interesting.
Yeah, no, that's really interesting that you bring that up. And I think in mathematics, especially that is so important because mathematics is really didactic in nature. And I know that didactics is not something that we often want to talk about in education. When often when people hear the word didactic, they think it's a bad thing, but the reality is that if you don't know how to do something, you won't be able to do the other thing. Right? And in mathematics, that's really, really important. And I don't know that as educators, mathematics educators, I don't know that we know exactly what that is, but we have a good insight into it conceptually. So for example, let me ask you a question, right? As a teacher, should you teach decimals first or fractions?
I'd say fractions.
I would only say fractions, but that's purely cause that's just how I imagine. It's probably wrong, but go on Andy, what would you say?
Well I'm not going to give you the answer. I'm just going to ask you why, why fractions first?
Because I think that, in the very first instance, you have the youngest children who come into school with the language. So there's already a language aspect there. So chances are, there's a half a biscuit. So I think that we're exposed more often to fractions, but maybe that's just because of the way that it lands in our curriculum. That could be the case. So that's a bit chicken and the egg, but I think that those ideas around fractions to start with, that we're talking the same thing. We're talking parts of a number, but it's the language around, I think the initial understanding of fractions, that's what I would start with, fractions. That would be my number one reason.
I was thinking about that in terms of the language, the half and the quarter. If you take three quarters, I don't know somehow it's how it's written as well. The whole and the parts. It feels like there's a way of showing there's this many parts in a hole, and this is how many parts we're talking about sort of visually as a symbol of three quarters or one half seems to make sense in my mind. But that could be because it's my adult brain rather than my child brain. Rather than not 0.75, for example.
How many people actually think about that, right? Like when they're doing their teaching program or, but it's critical, right? It's critical that you get that, right. Because if you don't do one of them before or the other, then you're not really going to understand the other, right? Whether you're doing reading, whether you're doing whatever the point is, is that if you're trying to teach, okay, I can't, I can't help myself. I have to tell you. You're right. You have to teach fractions before you teach decimals. We know that it's been well researched. We know that's a fact, right? If you try to teach decimals and children don't understand the concept of fractions, they're going to really struggle to learn that. You need to have that foundation in order for them to learn decimals, right? They need to have experienced a certain type of thinking before they can address this new learning, right?
It's not even just factual. It's not just having the facts. It's also just conceptual constructs, right? They have to exist in order for you to grasp that at learning. You want to make sure that you can focus as much of the brain onto the thing, the construct that you want them to learn. Not on too many distracting factors at the same time. Right? That's really what this is all about. I think the working memory principles.
So what about facts? People talk about this in the context of you need to know your multiplication tables. This is always the argument, right? It's always about working memory, short term memory, blah, blah, blah. If you don't know your times tables, you're never going to get anywhere in life and all this kind of stuff. What you guys think is that true? Is it just a bunch of bunk?
I feel that times tables is one of the anomalies in a lot of these rules. Like for me, I don't know, maybe my mum was an old-fashioned math teacher. There is an element where you do need to know. I do believe that you need to have a sense of what things mean, but there are some things like times tables where having a fluency in the tables it does give you an advantage to be able to kind of then start learning some of the more complex elements. So, for me, tables kind of sits in, it has its own little place.
I'm a deeply frustrated adult because as I've got older, particularly now I've got kids and I get to work more in education. I realize how much I was taught by road. Not just like tables. I mean like so many things. If you ask me questions, I can tell you the answer. But if there's a point at which my learning...I'm having to relearn myself, even when I'm with my kids now, because the approaches that they're learning, I'm like, "Oh!" It's like light bulb moment. Like that's actually what it was trying to tell me. I didn't necessarily know. I didn't deeply, I didn't have deep knowledge of what that meant. I had a symbolic representation, which I was able to apply. Or I had a, I don't know whether you call it an algorithm or a kind of a means of getting to the answer, because that was the process by which I was told if I did these things I'd get there.
But did I deeply know that? Did I deeply get the concept of what that was? No, I didn't. So I do feel that knowledge and kind of making sure that children have a concrete sense of it as well as that abstract is really critical. So there you go. That's quite a lot in the short space, but those are the things. So tables, I think is different, but hopefully only if it's then applied so that there's a meaning and an understanding behind it as well.
Everyone should feel comfortable with the concept that children should know certain facts. They should remember certain facts, right? I think the point is, if you want them to address certain parts of the curriculum, if you want children to be able to do, for example, column addition, they need to know their addition facts up to 20, right? If they don't, they're going to struggle with the column...They're going to struggle with that algorithm right? Now, should they learn it, should they not learn it, you could have an opinion. The reality is, is they have to learn it because if nothing else, if for no other reason, their curriculum says they have to learn it. So if you were a teacher, you have to teach it. That's the law. Is it the law? I don't know if it's the law or not.
That's your job. That's what you signed up to do. Was to teach the kids that, whether you agree with it or not. There's certain things that you have to do as a teacher. You have to equip them with a certain amount of facts. You don't have to know off the top of their head, what 28 times 45 is. Right? But they need to be able to figure that out, but they should know what seven times eight is. They should just know that. Right. Cause if they don't know it they'll struggle with the other stuff.
I think the other thing too, is that when we look at some of the early knowledge ideas, the number bonds to 10, 20, 100, the multiplication tables, these are things that we do use often in our everyday life. So yeah, of course we've got phones that we can go to, but the reality is if I'm going and I'm taking my two children and another child, and there's a sandwich that costs one pound 25, I want to be able to multiply that by three to see if I've got enough. If I've got a five pound note in my pocket. These are the things that I think we can use all the time. And without that, those basic facts, I think it's restricting. There might be some other things like the area of a rhombus where the reality might be is how often do I use that in my day to day life?
Well, I want to be able to, if I ever do come across that, I want to be able to understand why that's the case and it's association with the area of other shapes and so on and so forth. But I think that those...what I would consider them basic facts. I think it's so important that they become part of our long term memory, just so we can access the new learning regularly. Like Andy saying, when the structure of how we add is presented differently, can I apply that without thinking about it? And the only thing that I need to think about is how do I use this structure? That's the only thing I need to think about. Cause calculation wise is piece of cake. I'm all over it. As long as I can add up to nine and nine, then there's nothing more I need to do here. Likewise, multiply up to nine, nine. Doesn't matter how big the number is. You can make it as big as you want. It's just then it becomes the structure.
The important thing to understand here is that there are certain topics that they are probably best suited to learn by Rote. The alphabet. There's no other way to do it, right? Well, you can't reason your way through the alphabet. The same with counting. You have to learn that by Rote. Is Rote the best way to learn your times tables? It can work, but what you should really do as a teacher is pay attention to what the research says. If you learn it by Rote, there are real serious pitfalls, right? One is that probably a third of the kids won't remember. That's it. That's just what the facts say. So if you're happy to leave a third of the classroom behind, if that's really what you think that's an acceptable result, then by all means, do it that way, right? Or do it only that way.
If you want all the kids to learn, you might have to spend a bit more time doing it the hard way. Which is looking at what the research says and the research by the way is written by a guy called Berutti and it's all well documented. There are stages, right? You got to go through those stages. If you go through those stages, most of the kids will remember them. That's been well researched and this is kind of a nonsense argument.
The point from a memory point of view is, is by the time they get to year four or year five, if they still have to draw little dots on a piece of paper to figure out what three times six is, they're going to struggle. Because they don't have the capacity, their working memory, short term memory, whatever is being preoccupied with these tedious sort of calculations. And they can't address the problem solving aspect of what you're trying to teach them, which is more important anyway. They can't address that bit because they're still trying to figure out what three times six is, right? When they should just know what the answer is. I think that's the point. Yeah?
It is. Let the working memory do the work just so they can learn new stuff, not the stuff that they could have learned some time ago.
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