Episode 236: Is Mastery a buzz word? What does it actually mean?

Andy Psarianos

Welcome back to another super exciting episode of the school of school podcast. We've got our regulars here, Adam and Robin, as well as me, Andy. Please say hi, you guys.

Robin Potter

Hi you guys. Yeah I got you, I knew you were going to.

Adam Gifford

I was going to say that, hi Andy.

Andy Psarianos

Yeah, this is a very exciting, very exciting day today. We're recording again and I'm particularly excited because you know I finally invested in some AirPods and I'm not wearing my big sort of like you know. Yeah. Yeah. So so my big Mickey Mouse ears right so.

Adam Gifford

Aren't they good? Aren't they excellent?

Robin Potter

You are! That's amazing. Your ears aren't that bad, Andy.

Andy Psarianos

I wonder if Disney could sue us for saying Mickey Mouse ears.

Robin Potter

Or that you just said the D word. I don't know.

Adam Gifford

Probably.

Andy Psarianos

I said the D word. my god. Okay, that's it. That'll be the end of the school of school podcast

Adam Gifford

I missed that, what was that? didn't me. I said it again. Sorry, sorry, sorry.

Robin Potter

There we go.

Andy Psarianos

Alright, so the latest trend here on the school's cool podcast has been doing these like short and snappy kind of episodes.

And today we're talking about really what are the pillars of mastery. like first of all mastery is this idea that, know, lot of people talk about maths mastery, but the reality is maths mastery, there's no defined term of what maths mastery is. In England everybody says we teach to mastery or maths mastery or whatever, but interestingly the word doesn't even show up in the curriculum, right? So I don't know where the word came from. Well I know where the word came from, but anyway. So what are we talking about? talking right now, we're talking about like all the different things

That when we talk about mastery what are we talking about and that's when I say we it's us

That may not be somebody else might have different opinion about what mastery means. Cause like I said, there's no official definition of mastery, but today what we're going to talk about, we already talked about problem solving in another podcast. Now we're to talk about relational understanding, which is another pillar, what I would call pillar of mastery. And you know, why we need to think about relational understanding versus relational understanding versus, instrumental understanding. And those, it's not my terminology. That was a terminology that Richard Schemp used. And that's kind of what talking about. So what are we talking about? What is instrumental understanding versus relational understanding? Why do we need to be paying attention to this? Who wants to start that off?

Adam Gifford

We so need to be paying attention to this. So I'll use a definition and do jump in with each of them. The instrumental understanding. So when we talk about understanding, it's really interesting, it? Because you say, I understand something. And clearly, the fact that you've just defined two different types of understanding suggests strongly that there's a significant difference, or at least a difference. So we'll get to the significance. We'll let the listeners decide.

Robin Potter

That's definitely, that's definitely one for Adam. Yes.

Andy Psarianos

Hmm.

Andy Psarianos

Yeah.

Adam Gifford

So instrumental understanding, sort of how to do it without understanding. So this happens, this pops up all the time in mathematics where there's a trick or perhaps a formula or something that you just do it. You don't question it, you just do it, but you have no idea about how it works, why it works, when you should use it. You just know that at that instant, that's what you're supposed to use because you get told that. Relational understanding.

Andy Psarianos

Mm-hmm.

Adam Gifford

You know how to do it. So in both instances, maybe you know how to do it in that instance, by the way. You know how to do it, but you know why it works. So you understand how it works, why it works, and that gives you a better insight into something else that we've touched on, whether the episode has been aired or not at this stage. So that generalization, being able to spot something that's similar and say,

I wonder if I can do this or you see where it's built off. The two are significantly different. One is very limited. You've got to make sure that the conditions to use it are exactly the same or so close that you can recognize, yes, this is the same one that I was told just to flip it, twist it, kick it, do something with it, invert, but I don't know why.

Robin Potter

Amen. Yeah.

Adam Gifford

I don't know why. And if that situation changes even slightly, then you're at sea, man. You've got to learn something brand new. So again, I'll hand over at that point.

Robin Potter

That's right. But I just, just...

Andy Psarianos

Yeah, it's rules without rules without reason is basically what it is, right?

Adam Gifford

Hmm.

Robin Potter

Yeah, yeah. And I think that's the way I grew up doing math. know, I'm thinking about all the equations that I was told. If you use this equation, you'll get the right answer. Yeah, and it worked. But now if they said to me, OK, now Robin, explain why you're using that equation. Maybe I could explain part of it, but maybe not. Well, I got the right answer, but.

It's because my teacher told me I had to use this equation when we were talking about this.

Andy Psarianos

Well, that's right. So, instrumental understanding is just knowing how to do a procedure, right? In order to get the result, the end result. You know, call it the answer or whatever, right? But without any understanding whatsoever as to why it works or whatever. And obviously,

It kind of it's good. It's good if like if you can imagine a world where we didn't have spreadsheets, right or calculators and You were an accountant, right or an economist or whatever somebody had to work with numbers a lot right like and you had a lot of rows and columns of things to add up and so you have to take you know, like this number and multiply by this and do this and then end up with that

Right? And then do it again for the next number. Do it again for the next number. And then sum all those numbers up. Like if that was your job, right? Yeah, you needed to know it the most efficient way. You needed to know how to do it and to do it efficiently, right? And that was a really, really important skill once upon a time. I don't think anybody's job looks like that anymore. I don't think anybody does that kind of work anymore. And in that old world, right?

One could obviously imagine that instrumental understanding was really, really important skill. You needed people to be human calculators. Actually, there was a job. It was a job description. What is your job? I am a calculator. That used to be a job, right? Okay, those people don't exist anymore. So that's kind led us into this thing. Like if really super efficient algorithms for adding and subtracting and doing procedural stuff and whatever. Great.

Relational understanding is knowing what to do and why. Okay, so this is the important thing to understand. It's knowing what to do and why. Instrumental understanding is just really knowing what to do but having no idea why, right? So, work together. Like you need to have the instrumental understanding as part of your relational understanding but it's not one or the other. It's like basically what we're saying is

Andy Psarianos

instrumental understanding is not enough, you have to have the relational bit as well. Okay, now we could argue about, there's lots of arguments that go online about how do you learn relational understanding? Do you start with instrumental understanding or do you start with a relational bit or do you teach it through problem solving? We're not gonna get into that because that's a really long winded.

Conversation but just for an analogy, you know, I like to use music as an analogy, right? You could teach someone how to read music For example, right read it and play so say you play the piano You put she any bit of sheet music in front of that person and they could play it right That's one skill That doesn't make them a composer Right

You don't have to understand any of the laws or rules of music in order to be able to do that. But if you want to create a

a musical piece that follows, you know, the sort of like then knowing

the laws of music is almost, well, it's, whether you it, know it, yeah, it's necessary. You just need to understand it, right? You need to know that, hey, these notes are on the same scale, and this is, you know, and these scales are related. This is a minor, a relative minor scale, and this is a Aeolian mode, and all this kind of stuff. Like, we don't have to get into the jargon of it, but, you know, it's kind of like that's important, right? Because if you want to be a composer, and you want to compose for an orchestra,

Robin Potter

necessary.

Mm-hmm.

Andy Psarianos

Right? There are a lot of instruments. They're not all playing the same thing. Right? You got to put something together that's going to sound pretty good. You need to kind of understand the rules of music. So being a player is not the same skill as being a composer. It's a completely different skill. So mathematician is a composer. Right? And yeah. So you know, really good...

Robin Potter

Yeah.

Robin Potter

That's a good analogy. Yeah.

Adam Gifford

Okay.

Robin Potter

Certainly not.

Mm-hmm.

And the rest of us are just those people that can do a small amount of the work but cannot expand on it. Yeah.

Andy Psarianos

Yeah, exactly. Well, it's really efficient. Some players are really efficient, but they have no idea why what they're playing sounds good or it sounds horrible or whatever. They're just really efficient at...

Adam Gifford

But I think I think in that analogy as well, you're limited by the sheet music in front of you. So so so you're only going to be able to play what's given to you. That's the other thing. So you're completely limited. So if you were just to ask to go and play with another group over here, improvise, do whatever you're at sea. If you if no one gives you new music, all you're going to do is be really good at these pieces, like really good at it fast, accurate.

Andy Psarianos

Yeah.

Robin Potter

Right.

Yes.

Andy Psarianos

That's right.

Adam Gifford

Brilliant. And anyone listening would go musician. Absolutely incredible musician. And that's a bit like, I don't know. I was reading some research the other day about the times tables test. It's the first time the times tables test that that cohort's gone through to the SATs. I've read analysis that's come out. I think it was from the Royal Society. If I've got that wrong, certainly people who have worked in the primary committee in the Royal Society. No correlation. People that were fantastic at the times tables in year four.

Some of them have done really poorly in SATs. Some of them who did poorly in the year four times tables did really well. Some that did well, did well. Some that did poorly, did poorly. But they cannot. They've stripped it back, tried to find it every different way. But I guarantee you in year four, there'll be plenty of people who will listen to some of those children who can just do it like lightning and assume they're your mathematicians.

Andy Psarianos

No. There's no evidence.

Adam Gifford

they're the people who are going to be be spot on and it's flawed.

Andy Psarianos

Yeah, that's right. That's right. So what's the takeaway? What do we need to know? You need to know how to do it. That's kind of a given, right? Like you have to know how to do it. But more importantly, you have to know when to apply what you know and choose the right thing to do in the right set of circumstances. And that's important. And

just you know in my mind one of the things that I like to tie this into is this wonderful word that does show up in the English National Curriculum, it shows up in a lot of curriculums, is this word fluency.

And fluency is not about instrumental understanding. Fluency is about relational understanding, right? You wouldn't say someone is fluent because they know how all the grammar of a language and they know how to spell all the words. That doesn't make them fluent in a language. That makes them good at spelling and good at grammar. Kind of like playing the piano. But...

Adam Gifford

Yeah.

Andy Psarianos

If you say someone is fluent in the language, it means that they know how to use those things. When to use them, when to use the word bigger versus the words larger versus the word more versus the word whatever, right? That's being fluent. That's being able to reason, communicate clearly and that requires relational understanding knowing what to do and why not just knowing what to do without without reason yeah and that's what it's all about.