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Hello everyone and welcome back 
to another episode of Teach 

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Sleep Repeat. 
My name is Dylan and my name's 

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Hayden, and this week we're 
going to be diving into our 

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favourite subject. 
You know what it is? 

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It's math. 
We're going to be talking 

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fluency, reasoning and problem 
solving, defining them and also 

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going over some of the 
misconceptions around them. 

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We'll take a look at how to 
structure a really quality maths

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lesson and sequence of learning,
as well as being able to use 

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schemes without them becoming 
limiting and frustrating. 

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And make sure you stick around, 
because we'll be giving some 

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sneak peek information about 
what we've been up to behind the

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scenes in the Mass world. 
Oh, how exciting. 

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Let's go. 
All right, so I think before we 

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dive into this, we should just 
give some context. 

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Listeners will know how much we 
love maths. 

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They will know how involved 
we'll have maths and a whole 

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career. 
However, I just want to make 

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this really clear for anyone 
maybe who's watching or 

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listening for the first time or 
isn't quite sure about why we 

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feel like we can almost be the 
experts here talking about 

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maths, our careers. 
I for me, I think it's defined 

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by maths. 
Like I loved being a primary 

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school teacher because you could
teach all the subjects, but my 

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passion and what I was really 
interested in and what I thought

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I did really well was teach 
maths. 

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Same for you. 
I was a primary maths teacher, 

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Yeah. 
And I had to teach some other 

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subjects as well. 
That's, that's the way I see it.

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My family literally asked like 
they got when I was just 

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throughout my career. 
They're like, Oh yeah, how how's

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the old maths teaching? 
I was like, do you do know? 

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I do actually teach other stuff 
as well, even though I only talk

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about maths. 
I do also teach English and 

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Geography everything. 
Else, yeah. 

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And I think when we trained the 
university, you know, our main 

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focus was maths as well. 
Like we literally had maths 

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specialist input from Gina 
Donaldson. 

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And Gina, I don't know if you're
listening to Gina Donaldson, but

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you are genuinely the reason why
I felt like I could become an 

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expert in maths and I felt like 
I could pass it on to the 

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children because she inspired 
me. 

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Like she was unbelievable as a 
tutor. 

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It was at Canterbury 
Christchurch University, 10 out 

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of 10. 
And having done her course, I 

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felt equipped almost straight 
away because again, we trained 

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in 2014, 2015, around the time 
of this new curriculum. 

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So we were in this really odd 
position where in university we 

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were being taught how to teach 
maths in this almost new mastery

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way, but embedded in the new 
curriculum from the start. 

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So when we went into school, we 
almost had a head start in that 

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respect, I think big time. 
And it was like, no, this is 

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just how you teach maths. 
And this whole idea of, oh, new 

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maths different to what I did 
before, we had none of that 

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really, because it was just 
that's how we were learned and. 

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Having now taught for 10 years, 
I can't believe how important 

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that was. 
I also had Gina so big up 

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transformational in terms of 
changing my just eradicating my 

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misconceptions about maths and 
how I very much thought of like,

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yeah, it's just you see it 
online all the time now. 

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People being like, don't teach 
the kids multiple methods, just 

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do this one way. 
It always works and then they 

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can get the questions right in 
the test. 

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There are so many reasons I 
could argue against that and 

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we'll go into it and we talk 
about fluency and all the other 

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bits, but Gina really just 
immediately from from day one 

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was like, Yep, here is a more 
holistic way to think about how 

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people learn maths really well 
and and it just shaped my shaped

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my maths and this. 
Is why it's better and This is 

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why it's good. 
And then when we went into 

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school, very quickly you became 
maths lead of of the school 

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where I worked. 
I remember you becoming maths 

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lead and I was on the hub, the 
team, but you were the leader 

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for that. 
And then when we ended up in our

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school that we worked in 
together, just at the end of our

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teaching journey, we both LED 
maths together, kind of Co LED 

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it. 
You're my assistant to the maths

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lead. 
I was the maths lead. 

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So you were very much just kind 
of below me. 

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But yeah, we've LED maths in 
school for years and years and 

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years and years. 
And one of my big passions, and 

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This is why we're doing this 
episode, is to just help other 

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teachers understand maybe some 
of the terminology, fluency, 

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reasoning, problem solving, what
it means, what it might look 

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like in a lesson, why it's 
important, which ones we should 

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weight more heavily, what it 
might look like in a classroom. 

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And importantly, what the 
misconceptions are as to what 

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good maths teaching actually 
might look like. 

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Which I think embedded in a lot 
of schools now for reasons where

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they want to help their children
as much as possible and want to 

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meet the national curriculum 
aims, they're actually doing 

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things that I think are 
potentially bad practise when it

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comes to maths in general. 
So hopefully we can flesh some 

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bits out, talk about what 
different words mean literally 

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in this in the curriculum, and 
then yeah, dive into what a good

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lesson might look like, how it 
might structure things and 

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basically let our passion shine,
no doubt. 

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No doubt that's what you're 
saying, because we love maths 

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and we could just talk about 
this for hours. 

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Precisely that. 
So let's start off, I think it's

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important that we everything we 
do is rooted in the national 

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curriculum aims. 
So I'm going to talk about the 

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aims specifically for the maths 
curriculum now in primary 

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school. 
And it's split up into three 

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chunks. 
And these three chunks are 

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things people will have heard of
at some point in their training 

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or just in their delivery of 
maths lessons in primary school,

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and that is fluency, reasoning 
and problem solving. 

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So let's read them through. 
Now this is from the national 

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curriculum. 
The National Curriculum for 

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Mathematics aims to ensure that 
all pupils, and that's really 

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important, all pupils, we'll 
come back to that number one, 

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become fluent in the 
fundamentals of mathematics, 

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including through varied and 
frequent practise with 

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increasingly complex problems 
over time so that pupils develop

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a conceptual understanding and 
the ability to recall and apply 

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knowledge rapidly and 
accurately. 

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It goes on to then say #2 to 
reason mathematically by 

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following a line of inquiry, 
conjecturing relationships and 

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generalisations and developing 
an argument, justification or 

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proof using mathematical 
language. 

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And thirdly, can problem solve 
by applying their mathematics to

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a variety of routine and non 
routine problems with increasing

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sophistication, including 
breaking down problems into a 

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series of smaller, simpler steps
and persevering in seeking 

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solutions. 
Excellent. 

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Shall we dive in then? 
Should we break these down? 

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Should we just go into fluency 
now and really just talk about 

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what fluency is? 
Again, some of the 

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misconceptions and just yeah, 
our top tips and what it looks 

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like in a lesson, how to embed 
it into lessons. 

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Yeah. 
Because when people say fluency,

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I think you can sometimes 
simplify in your head as do you 

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know your timetables. 
Yeah. 

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Can you add up? 
Can you subtract? 

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And I think that's part of 
fluency. 

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I think that's really important.
And one thing we'll be 

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referencing throughout this, I 
think it's a fantastic blog on 

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3rd Space Learning by Neil 
Ormond. 

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He did a whole blog about 
reasoning, problem solving, and 

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fluency. 
And a lot of what he says 

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resonates with the way I think 
we think about math as well. 

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So we'll be referencing that 
too. 

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We'll leave a link down in the 
description to that whole blog. 

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If you wanted to read, I would 
recommend it. 

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But fluency, to me, fluency it's
being able to understand 

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mathematical facts and know them
quickly, to understand concepts 

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and know them quickly and 
mathematical language and to 

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understand what they mean. 
And for me, being fluent in 

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something means practising doing
the maths, understanding the 

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words or knowing the concepts. 
So it becomes second nature and 

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that's when you become fluent. 
So fluency is something you 

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should be working towards 
becoming. 

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Are you fluent in addition and 
subtraction at the year 4 level,

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yes or no? 
The answer for most children 

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will be no. 
And we're working towards 

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becoming fluent. 
So when we say what does fluency

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look like or varied fluency or 
mixed fluency in a maths lesson,

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it's ensuring that children are 
exposed to ability to practise 

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things and not be scared of 
practising things over and over 

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because you need to be able to 
do the maths. 

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Do they understand the language 
being used in that topic? 

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And I would say being exposed to
doing the maths, but in many 

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different representations. 
So I think a lot of people would

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say, and maybe you can clarify a
bit more about all this, a lot 

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of people would say that fluency
equals arithmetic. 

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So just going a bit further from
your, you said fluency might be 

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just times tables, but I think 
you can expand that to a genuine

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misconception, which is that 
it's just arithmetic. 

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So do you think when it comes 
down to things like key stage 1 

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to arithmetic papers, or just 
generally arithmetic papers in 

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your ear group, do you think 
that embodies entirely fluency 

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because ultimately it's all the 
methods you need to know to do 

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maths? 
So what I'd say to people is 

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arithmetic is part of fluency. 
It's one string to the bow. 

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It's it's really, really, really
important. 

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You could even say it's 
potentially the most important 

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part of fluency in my opinion. 
And I think we could argue that.

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And I think you might be right 
to say that. 

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I think it's the actually being 
able to literally manipulate 

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number using the four operations
is the most fundamentally 

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important part of maths. 
And then what I worry about 

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sometimes and what I see in 
schools is it's kind of brushed,

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brushed aside or rushed through 
or sort. 

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Yeah, that's important, but we 
need to reason and problem 

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solve. 
No, no, no, you literally cannot

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reason and problem solve if you 
can't do the maths. 

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So let's talk about arithmetic 
in particular. 

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I think that is vital and it 
very much links to the kind of 

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thing we're working on now. 
We're building platform to to 

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help teachers and children 
become fluent and specifically 

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to begin with get better at 
arithmetic. 

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Another sneaky yeah. 
Another sneaky is or. 

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Basically, it's true because I 
kind of want to talk about both,

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because we're obviously 
extremely passionate about this 

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and I will, I genuinely think 
just backing on what you're 

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saying, I think arithmetic, 
particularly as part of fluency,

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fluency in general, I would say 
is absolutely the most 

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fundamentally important part of 
maths, genuinely. 

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And I do feel like because we 
can also say the end goal of 

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maths is problem solving, I do 
think we conflate the importance

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levels of them. 
It's like, yeah, the end goal is

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problem solving, but fluency is 
the most important bit because 

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you can't do it without it. 
It's literally the foundation of

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the house you're building. 
You have to get it right. 

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There's way more to it, you 
know, but if you think about the

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classic pyramid example, I think
even first place learning has a 

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couple of different examples of 
that. 

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It kind of is, you know, 
crudely, it's the massive bit at

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the bottom, fluency, and that 
involves majority of that is 

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arithmetic. 
Yeah, we've got to get it right.

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And I think that that's really 
important and that's the link. 

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We're going to be drawing these 
links throughout this and you'll

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see why will maybe come back to 
it once we've defined, you know,

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reasoning and problem solving. 
Why actually this is the most 

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important part. 
Fluency is the most fundamental 

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part of if you're teaching 
primary mathematics properly, 

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you have to get this right. 
And if you are glazing over it 

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to go through more quickly to 
reasoning and problem solving 

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without becoming secure in your 
fluency, you're doing your 

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children at the service because 
who can problem solve if they 

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can't once they've figured out 
what to do, actually do it. 

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It's the most important thing. 
And just going back to what you 

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said about fluency and we said 
arithmetics part of fluency. 

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So I can imagine people might be
out there thinking, well, what 

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do you mean part? 
What's the rest? 

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00:10:07,120 --> 00:10:10,040
For example, think of your part 
whole models, think of schemes 

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00:10:10,040 --> 00:10:13,680
like White Rose learning, White 
Rose maths that a lot of a lot 

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00:10:13,680 --> 00:10:16,760
of schools use out there and 
what questions might look like 

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00:10:16,760 --> 00:10:19,600
1-2, three and four. 
And I can imagine sometimes as a

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00:10:19,600 --> 00:10:23,280
teacher, I've known teachers who
become frustrated that, oh, 

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00:10:23,360 --> 00:10:25,200
they've only done 4 questions 
like this, then suddenly they've

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00:10:25,200 --> 00:10:27,080
got a part hole model, then 
suddenly they've got a bar 

234
00:10:27,080 --> 00:10:28,760
model. 
Then suddenly they've got an 

235
00:10:28,760 --> 00:10:30,920
inverse operation and suddenly 
the presentation looks different

236
00:10:30,920 --> 00:10:32,440
and the missing answer boxes in 
a different place. 

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00:10:33,120 --> 00:10:36,840
That's down to you as a teacher.
I think good schemes give lots 

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of opportunities for fluency 
like this. 

239
00:10:39,240 --> 00:10:42,280
But you as a teacher need to 
understand what fluency is and 

240
00:10:42,280 --> 00:10:45,640
why it's important and almost 
hierarchically move through 

241
00:10:45,640 --> 00:10:48,200
fluency in a way that's still 
sensible. 

242
00:10:48,320 --> 00:10:51,440
Because I think sometimes with 
fluency people here, OK, I kind 

243
00:10:51,440 --> 00:10:53,600
of get what you're saying now, 
Dylan, fluency is this like 

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00:10:53,600 --> 00:10:56,800
ability to have lots of 
different representations of 

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00:10:56,800 --> 00:10:58,840
questions and being able to 
apply. 

246
00:10:58,840 --> 00:11:01,360
Maybe let's just talk about 
addition to lots of different 

247
00:11:01,360 --> 00:11:02,640
ways. 
But oh, OK, even though this is 

248
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a pothole model, I'm adding, 
even though this is maybe a bar 

249
00:11:05,600 --> 00:11:08,800
model, I'm adding, this might be
just literally written as 

250
00:11:08,800 --> 00:11:10,840
arithmetic, but I'm adding that 
is fluency. 

251
00:11:10,920 --> 00:11:14,120
But it doesn't mean you have to 
just randomly do them off the 

252
00:11:14,120 --> 00:11:17,280
bat. 
Big part of fluency is can you 

253
00:11:17,280 --> 00:11:19,680
do the maths in the 1st place? 
Can you literally add 2 numbers 

254
00:11:19,680 --> 00:11:22,560
together? 
OK, Then we can expand it to, to

255
00:11:22,560 --> 00:11:25,560
some ideas of maybe, OK, look, 
maybe not just arithmetic now, 

256
00:11:25,560 --> 00:11:27,400
but it might be shown in a 
different way. 

257
00:11:27,400 --> 00:11:28,720
Yeah. 
And then there's even another 

258
00:11:28,720 --> 00:11:31,320
step of fluency, which is do you
know how many sides the square 

259
00:11:31,320 --> 00:11:33,200
has exactly? 
That's not reasoning on problem 

260
00:11:33,200 --> 00:11:34,600
solving. 
Do you, do you know how many 

261
00:11:34,600 --> 00:11:36,160
centimetres are in a metre? 
These are. 

262
00:11:36,160 --> 00:11:39,000
This is when we talk about the 
known facts, the things you just

263
00:11:39,000 --> 00:11:40,680
have to know. 
You just have to know the 

264
00:11:40,680 --> 00:11:43,000
definition of some words. 
You need to know what perimeter 

265
00:11:43,000 --> 00:11:44,760
means. 
That's not reasoning on problem 

266
00:11:44,760 --> 00:11:45,880
solving. 
It's not arithmetic either. 

267
00:11:45,880 --> 00:11:47,520
Exactly. 
It's not arithmetic, but it is 

268
00:11:47,520 --> 00:11:50,720
fluency and it comes under that 
umbrella and This is why fluency

269
00:11:50,720 --> 00:11:52,520
is vital. 
If you don't know what words 

270
00:11:52,520 --> 00:11:56,320
mean, mathematical vocabulary, 
if you can't do the maths and if

271
00:11:56,320 --> 00:11:59,200
you don't understand the 
concept, you can't do maths. 

272
00:11:59,640 --> 00:12:03,360
It's like, I can't get across 
enough how I feel like fluency 

273
00:12:03,360 --> 00:12:06,880
is maths and the reason people 
push back and they say, well, no

274
00:12:06,880 --> 00:12:08,880
problem solving is maths, 
correct? 

275
00:12:09,440 --> 00:12:12,680
It overlaps. 
We can't see it as separate 

276
00:12:12,680 --> 00:12:14,200
things that we just do 
separately. 

277
00:12:14,680 --> 00:12:17,000
It's it's one in the same. 
And the way the aims of the 

278
00:12:17,000 --> 00:12:19,640
curriculum are written down and 
the way sometimes schemes of 

279
00:12:19,640 --> 00:12:22,720
work present things and the way 
sometimes we're taught how to 

280
00:12:22,720 --> 00:12:25,640
teach a maths lesson. 
I feel like fluency just gets 

281
00:12:25,840 --> 00:12:28,240
lumped in as like, yeah, you do 
that for a bit and then we do 

282
00:12:28,240 --> 00:12:30,560
some reasoning, problem solving.
What I'm trying to get here is 

283
00:12:30,560 --> 00:12:34,400
with the definition of fluency 
is it is fundamentally what a 

284
00:12:34,400 --> 00:12:38,680
maths lesson should be and then 
you work towards so if you're 

285
00:12:38,680 --> 00:12:40,160
reasoning and problem solving 
which we'll. 

286
00:12:40,160 --> 00:12:43,320
Come on to moving through the 
the flow chart in my head when 

287
00:12:43,320 --> 00:12:46,200
I'm thinking about the three 
elements of maths, you know, 

288
00:12:46,240 --> 00:12:49,280
fluency, reason, problem solving
is I think to myself, are the 

289
00:12:49,280 --> 00:12:52,040
kids fluent in the maths that 
I'm thinking of right now? 

290
00:12:52,040 --> 00:12:54,040
Yes or no? 
If the answer is yes, then I'll 

291
00:12:54,040 --> 00:12:56,520
start thinking, oh cool. 
I wonder if I can expose them to

292
00:12:56,520 --> 00:12:59,240
some opportunities to solve some
problems now where they can use 

293
00:12:59,240 --> 00:13:01,080
their reasoning skills and they 
can apply this fluency. 

294
00:13:01,240 --> 00:13:04,920
And if the answer is no, my 
genuine thought is either, OK, 

295
00:13:04,920 --> 00:13:08,480
cool, can I do some more fluency
with them until they become 

296
00:13:08,480 --> 00:13:10,320
fluent? 
Maybe it's maybe it is just 

297
00:13:10,320 --> 00:13:11,520
straight arithmetic. 
If they're really, really 

298
00:13:11,520 --> 00:13:13,600
struggling even with the method 
at this point, maybe it's just 

299
00:13:13,600 --> 00:13:15,200
they're struggling with 
different representations. 

300
00:13:15,200 --> 00:13:17,720
They're not they've not been 
exposed enough yet to different 

301
00:13:17,720 --> 00:13:18,800
ways of seeing. 
They've got they're really good 

302
00:13:18,800 --> 00:13:20,120
at the method. 
They're just not very good at 

303
00:13:20,240 --> 00:13:22,320
recognising, Oh, that's when I 
need to use that method 

304
00:13:22,400 --> 00:13:25,080
definitions, definition equally,
stuff like that. 

305
00:13:25,080 --> 00:13:27,600
That's outside arithmetic. 
And if and, but even still, if 

306
00:13:27,600 --> 00:13:30,400
the answer's no, I might still 
think, I still, I would like to 

307
00:13:30,400 --> 00:13:32,800
expose my children to a bit of 
problem solving, but I might use

308
00:13:32,800 --> 00:13:34,960
something that fluent in, in 
something else, which we'll come

309
00:13:34,960 --> 00:13:36,640
to, I guess, when we talk more 
about problem solving. 

310
00:13:36,640 --> 00:13:39,640
But the, the fundamental part of
what I'm saying here is I always

311
00:13:39,640 --> 00:13:41,560
think to myself, are they fluent
or are they not? 

312
00:13:41,800 --> 00:13:43,320
You know, that's my first 
thought. 

313
00:13:43,400 --> 00:13:46,600
It's not just does the lesson 
struct to tell me I need to be 

314
00:13:46,600 --> 00:13:48,880
doing some reasoning on this 
objective today and some problem

315
00:13:48,880 --> 00:13:50,360
solving. 
That's not the way to think 

316
00:13:50,360 --> 00:13:52,040
about maths because I they need 
to be fluent. 

317
00:13:52,080 --> 00:13:53,480
That's the point. 
If they're not fluent, don't do 

318
00:13:53,480 --> 00:13:55,160
it. 
It's such a good point and let's

319
00:13:55,160 --> 00:13:57,080
move on to let's move on to 
reasoning now. 

320
00:13:57,080 --> 00:13:58,520
So we talked about, we talked 
about fluency. 

321
00:13:58,920 --> 00:14:03,320
Reasoning is, is to me really 
bizarre and unique. 

322
00:14:03,320 --> 00:14:04,920
Hardest one to define. 
I think so. 

323
00:14:04,920 --> 00:14:07,880
And I think, I think I can kind 
of define it, but I feel like 

324
00:14:08,200 --> 00:14:10,720
the old fashioned way of 
thinking of these as 3 pillars 

325
00:14:10,720 --> 00:14:12,360
of maths. 
I don't think it's helpful. 

326
00:14:12,680 --> 00:14:14,800
There's I feel like there's a 
very old fashioned way we think 

327
00:14:14,800 --> 00:14:16,600
of yeah, you've got your 
fluency, then you've got your 

328
00:14:16,600 --> 00:14:18,360
reasoning questions, then you've
got your problem solving 

329
00:14:18,360 --> 00:14:19,080
questions. 
Yeah, sure. 

330
00:14:19,080 --> 00:14:21,000
And what I'm trying to do is we 
go through this, I think we're 

331
00:14:21,000 --> 00:14:22,640
trying to just eradicate that 
thought process. 

332
00:14:22,880 --> 00:14:24,480
Don't think of them as separate 
pots. 

333
00:14:24,840 --> 00:14:28,360
Because to me, reasoning is the 
ultimate version of you reason 

334
00:14:28,760 --> 00:14:30,920
all of the time, all of the 
time. 

335
00:14:31,080 --> 00:14:33,560
So reasoning again, let's think 
about what reasoning actually is

336
00:14:33,880 --> 00:14:36,640
to define it. 
I'm going to be taking from Neil

337
00:14:36,640 --> 00:14:39,400
Ormond in this in this blog 
because I think the way he puts 

338
00:14:39,400 --> 00:14:41,280
things down on paper is a 
really, really clear way of 

339
00:14:41,280 --> 00:14:43,160
thinking about it. 
Reasoning and maths is the 

340
00:14:43,160 --> 00:14:47,440
process of applying logical 
thinking to a situation to 

341
00:14:47,440 --> 00:14:50,120
derive the correct problem 
solving strategy for a given 

342
00:14:50,120 --> 00:14:52,600
question. 
Put more simply, mathematical 

343
00:14:52,600 --> 00:14:55,480
reasoning is the bridge between 
fluency and problem solving. 

344
00:14:55,800 --> 00:14:58,920
It allows pupils to use the 
former accurately to carry carry

345
00:14:58,920 --> 00:15:01,360
out the latter. 
And I think that's such a nice 

346
00:15:01,360 --> 00:15:05,120
way of thinking about it is you 
can't just think about reasoning

347
00:15:05,120 --> 00:15:06,760
as have I done reasoning 
questions today. 

348
00:15:07,280 --> 00:15:09,480
Reasoning is the art of 
thinking. 

349
00:15:10,040 --> 00:15:13,160
It's the art of of actually 
doing maths. 

350
00:15:13,480 --> 00:15:15,280
And I'd argue there's an overlap
of fluency. 

351
00:15:15,680 --> 00:15:17,880
Clearly there's an overlap here 
with problem solving because we 

352
00:15:17,880 --> 00:15:20,440
have to reason and think about 
what's what we're going to pick 

353
00:15:20,440 --> 00:15:22,040
to solve a problem or come on to
problem solving. 

354
00:15:22,440 --> 00:15:25,480
But also, I think with fluency, 
I think picking efficient 

355
00:15:25,480 --> 00:15:28,680
methods, that's reasoning, 
thinking, oh, what if I had to 

356
00:15:28,680 --> 00:15:31,080
explain to someone why this 
method is more efficient than 

357
00:15:31,080 --> 00:15:33,200
that method? 
That is definitely reasoning. 

358
00:15:33,360 --> 00:15:36,680
And it's the kind of thing I'd 
be doing during my fluency part 

359
00:15:36,680 --> 00:15:38,280
of my lesson. 
I wouldn't be thinking, oh 

360
00:15:38,280 --> 00:15:39,920
Christ, no, I can't possibly 
reason now. 

361
00:15:40,120 --> 00:15:42,080
I mean, my fluency part of my 
lesson, we're just practising. 

362
00:15:42,080 --> 00:15:46,120
No, no, reasoning is everything.
And I think quality reasoning 

363
00:15:46,120 --> 00:15:48,680
happens to all children all of 
the time, no matter what they're

364
00:15:48,680 --> 00:15:50,360
doing. 
Because at any point as a 

365
00:15:50,360 --> 00:15:51,760
teacher, you can be asking 
questions. 

366
00:15:51,760 --> 00:15:54,360
Why doing that? 
What's the benefit of doing 

367
00:15:54,360 --> 00:15:56,200
that? 
Why have you exchanged there in 

368
00:15:56,200 --> 00:15:57,040
that question? 
Yeah. 

369
00:15:57,240 --> 00:15:58,920
Yeah. 
Well, that's weird because on 

370
00:15:58,920 --> 00:16:00,200
the other table they did this 
method. 

371
00:16:00,200 --> 00:16:01,480
Do you think that's better or 
worse? 

372
00:16:01,880 --> 00:16:03,800
They're still doing. 
Why have you used inverse here 

373
00:16:03,960 --> 00:16:05,640
Exactly. 
You know, even just that you 

374
00:16:05,640 --> 00:16:06,480
said. 
I agree, by the way. 

375
00:16:06,480 --> 00:16:08,440
I think reasoning is very much. 
It's the glue. 

376
00:16:08,520 --> 00:16:09,240
Yeah. 
And it does. 

377
00:16:09,240 --> 00:16:11,600
It ranges all the way from 
fluency all the way into problem

378
00:16:11,600 --> 00:16:12,040
solving. 
Yeah. 

379
00:16:12,040 --> 00:16:14,200
I can think of the most basic 
version of this where you could 

380
00:16:14,200 --> 00:16:16,160
just where you could just about 
say, yeah, actually there's a 

381
00:16:16,160 --> 00:16:17,760
bit of a reasoning going on 
here, which is right. 

382
00:16:17,920 --> 00:16:19,880
You've taught the kids the 
arithmetic of adding two 

383
00:16:19,880 --> 00:16:21,280
numbers. 
They know the method. 

384
00:16:21,280 --> 00:16:23,200
They know how to line it up and 
do the addition and when 

385
00:16:23,200 --> 00:16:26,120
something says this, add this, 
they can do it, right? 

386
00:16:26,320 --> 00:16:28,320
And then you present them. 
This is all with influence. 

387
00:16:28,320 --> 00:16:30,680
You still based on all these 
definitions when you then 

388
00:16:30,680 --> 00:16:33,040
present them an inverse question
where it's blank. 

389
00:16:33,200 --> 00:16:36,240
Take away a number equals a 
number and you know, as a 

390
00:16:36,240 --> 00:16:38,360
teacher, oh, they've actually, 
even though it says the 

391
00:16:38,360 --> 00:16:40,600
subtraction symbol in this 
question, they've got to add 

392
00:16:40,600 --> 00:16:42,560
those two parts together to get 
back to that total. 

393
00:16:43,040 --> 00:16:44,840
They're still using the exact 
same method you taught. 

394
00:16:44,840 --> 00:16:47,200
There's nothing different about 
the method and the arithmetic 

395
00:16:47,200 --> 00:16:48,560
that they've got to use to solve
this. 

396
00:16:49,200 --> 00:16:52,000
But technically they've got to 
think just a little bit more 

397
00:16:52,120 --> 00:16:54,840
than the last ones of oh, wait, 
am I supposed to be subtracting 

398
00:16:54,840 --> 00:16:56,840
here? 
Or oh, wait, it's laid out this 

399
00:16:56,840 --> 00:16:58,800
way, which means I need to use 
inverse, which means I'm still 

400
00:16:58,800 --> 00:17:00,080
using addition. 
Great, I can do that. 

401
00:17:00,600 --> 00:17:03,640
That to me is like the smallest 
increment where I can think of 

402
00:17:03,640 --> 00:17:05,599
where it's like you could say 
there's a bit of reasoning 

403
00:17:05,599 --> 00:17:08,079
happening there now, but that's 
very much fluency. 

404
00:17:08,079 --> 00:17:09,800
So that kind of just backs up my
idea. 

405
00:17:09,800 --> 00:17:11,760
This idea that reasoning really 
is the glue. 

406
00:17:12,079 --> 00:17:13,560
It happens all the way through 
fluency. 

407
00:17:13,560 --> 00:17:15,640
It happens all the way up to 
just complete problem solving. 

408
00:17:15,880 --> 00:17:17,839
It's kind of everywhere. 
It's like you said, it's not 

409
00:17:17,839 --> 00:17:20,839
really like a, a separate thing 
isolated. 

410
00:17:20,839 --> 00:17:23,280
You've got your fluency, then 
you've got this thing explicitly

411
00:17:23,280 --> 00:17:25,000
called reasoning, and then 
you've got this thing explicitly

412
00:17:25,000 --> 00:17:26,480
called problem solving. 
It doesn't work like that. 

413
00:17:26,560 --> 00:17:29,160
I think that the reason why I 
think this has happened and 

414
00:17:29,160 --> 00:17:32,000
developed over time is because I
do think there are some 

415
00:17:32,000 --> 00:17:34,920
questions which are you can't 
refute that it's it's a 

416
00:17:34,920 --> 00:17:37,880
reasoning question. 
They do exist, like they they 

417
00:17:37,880 --> 00:17:40,240
can exist in terms of explaining
your method. 

418
00:17:40,560 --> 00:17:42,240
You've seen these questions a 
million times in all these 

419
00:17:42,240 --> 00:17:45,120
schemes where it says, you know,
think, think like Tiny from 

420
00:17:45,120 --> 00:17:47,280
White Rose maths, right? 
Tiny's done this. 

421
00:17:47,480 --> 00:17:49,880
Where has he gone wrong? 
Yeah, that's that's fun, that 

422
00:17:49,880 --> 00:17:50,360
is. 
Reasoning. 

423
00:17:50,360 --> 00:17:51,960
Explain your reasoning. 
Explain your reasoning. 

424
00:17:51,960 --> 00:17:55,640
It is literally reasoning, yeah,
but again, you've literally 

425
00:17:55,640 --> 00:17:58,400
can't do that reasoning unless 
you understand the process. 

426
00:17:58,400 --> 00:18:00,280
Yeah, you've got to be fluent in
the thing he's talking about. 

427
00:18:00,280 --> 00:18:02,440
Exactly how can you possibly do 
that? 

428
00:18:02,640 --> 00:18:05,600
And then that's when good 
teaching in the moment of doing 

429
00:18:05,600 --> 00:18:09,120
fluency, it is embedding these 
reasoning questions as you go. 

430
00:18:09,320 --> 00:18:11,440
Because then what the children 
can do when it comes to that 

431
00:18:11,440 --> 00:18:14,080
reasoning question is they think
back to when they explain to 

432
00:18:14,080 --> 00:18:15,800
their teacher or they explain to
their partner. 

433
00:18:15,800 --> 00:18:18,720
And the power of talk and the 
power of reasoning whilst doing 

434
00:18:18,720 --> 00:18:21,040
fluency means they can now 
access that question. 

435
00:18:21,280 --> 00:18:24,000
They are all interlinked. 
It is not a separate thing. 

436
00:18:24,200 --> 00:18:26,640
You should not be just getting 
kids just to practise maths, 

437
00:18:26,640 --> 00:18:28,240
practise maths, practise maths, 
practise maths. 

438
00:18:28,600 --> 00:18:32,040
Let's do some reasoning. 
No, no, no, it's embedded in the

439
00:18:32,040 --> 00:18:34,600
very moment of learning the 
process. 

440
00:18:35,120 --> 00:18:38,080
You can have reasoning going on 
all of the time and the best 

441
00:18:38,080 --> 00:18:41,160
teachers do that. 
And that's where I think it's 

442
00:18:41,160 --> 00:18:42,800
absolutely right that we have 
these different names in the 

443
00:18:42,800 --> 00:18:45,280
curriculum. 
But I just hoping to get through

444
00:18:45,280 --> 00:18:48,880
to people that you, you don't 
have to isolate them. 

445
00:18:49,000 --> 00:18:51,560
And if you do, I think it's at 
the detriment of your maths 

446
00:18:51,560 --> 00:18:53,760
teaching. 
So think about the last one, 

447
00:18:53,920 --> 00:18:56,880
problem solving. 
I'm going to start off by saying

448
00:18:56,880 --> 00:18:59,760
to me, I said about earlier how 
fluency is maths, right? 

449
00:18:59,960 --> 00:19:01,840
Yeah, I'm going to say some 
people might think I'm being 

450
00:19:01,840 --> 00:19:03,680
hypocritical here or 
contradicting myself. 

451
00:19:04,080 --> 00:19:07,560
Problem solving is math 
hypocrite, actually, because I, 

452
00:19:07,560 --> 00:19:13,280
I think to me, if you, if you 
think about why we teach 

453
00:19:13,280 --> 00:19:15,360
fluency, right, it's not for 
fun. 

454
00:19:16,200 --> 00:19:18,640
I personally used to love adding
up numbers when I was younger 

455
00:19:18,640 --> 00:19:19,720
because I just liked the 
patterns. 

456
00:19:19,800 --> 00:19:21,320
Yeah. 
I enjoy it, feels good to get it

457
00:19:21,320 --> 00:19:22,480
right. 
Off it felt good and it's right 

458
00:19:22,480 --> 00:19:24,680
or wrong and I quite liked that.
OK, and you could say oh, that's

459
00:19:24,680 --> 00:19:26,040
fluency. 
No, no, the point of being 

460
00:19:26,040 --> 00:19:29,680
fluent and the point of 
reasoning is to apply this and 

461
00:19:29,680 --> 00:19:32,320
have a bridge to problem 
solving. 

462
00:19:32,760 --> 00:19:36,600
What is maths if not a way to 
understand and solve problems in

463
00:19:36,600 --> 00:19:38,920
the real world? 
That, that is literally it. 

464
00:19:39,200 --> 00:19:42,360
I've got to catch that bus so 
that I get to my meeting at this

465
00:19:42,360 --> 00:19:44,320
time. 
The bus takes this long, it's 

466
00:19:44,320 --> 00:19:46,600
only every 15 minutes. 
What time do I have to leave my 

467
00:19:46,600 --> 00:19:48,160
home? 
That's problem solving. 

468
00:19:48,200 --> 00:19:50,240
Yeah, I've got this much budget 
for the month. 

469
00:19:51,000 --> 00:19:53,560
I spend this much on my 
outgoings that I can't get rid 

470
00:19:53,560 --> 00:19:55,200
of. 
There's a grey area of ones that

471
00:19:55,200 --> 00:19:57,240
I can. 
What can I get rid of and then 

472
00:19:57,240 --> 00:19:59,960
be below and have enough money 
to pay my water bill. 

473
00:20:00,480 --> 00:20:03,200
This. 
This is maths. 

474
00:20:03,240 --> 00:20:07,320
This is what I think school 
should be gearing towards. 

475
00:20:07,440 --> 00:20:10,800
I think there is a place for 
logical thinking that maybe 

476
00:20:11,040 --> 00:20:12,600
we're not going to use this in 
our real life. 

477
00:20:12,600 --> 00:20:14,640
So why are we doing that? 
Because it's a process of 

478
00:20:14,640 --> 00:20:17,120
problem solving. 
The idea of your brain solving a

479
00:20:17,120 --> 00:20:20,880
problem and being logical is a 
transferable skill and even. 

480
00:20:21,000 --> 00:20:23,040
Within this moment you might 
argue you'll never use this 

481
00:20:23,040 --> 00:20:25,760
again, but you definitely will 
use the process of understanding

482
00:20:25,760 --> 00:20:27,960
how to solve this problem. 
That's what problem solving is 

483
00:20:27,960 --> 00:20:30,960
for me, and it has to be a 
mixture of them and problem 

484
00:20:30,960 --> 00:20:32,920
solving. 
Let's define it. 

485
00:20:33,240 --> 00:20:36,760
And I completely agree with what
I read about this, which was 

486
00:20:36,760 --> 00:20:40,600
it's easier sometimes to say 
what problem solving isn't so, 

487
00:20:40,640 --> 00:20:44,240
so we've got this here. 
So problem solving is not 

488
00:20:44,240 --> 00:20:47,840
necessarily just about answering
word problems in maths. 

489
00:20:48,000 --> 00:20:51,880
If a child already has had 
available method to solve a 

490
00:20:51,880 --> 00:20:54,480
problem, problem solving has not
occurred. 

491
00:20:54,880 --> 00:20:58,520
Problem solving in maths is 
finding a way to apply knowledge

492
00:20:58,840 --> 00:21:01,760
for children who are fluent by 
the way and skills you have 

493
00:21:01,760 --> 00:21:04,320
learnt to answer unfamiliar 
types of questions. 

494
00:21:04,400 --> 00:21:06,280
That's the main bit, isn't it? 
That's the biggest bit. 

495
00:21:06,280 --> 00:21:09,240
I want everyone to focus on 
unfamiliar questions. 

496
00:21:09,480 --> 00:21:13,640
It's not technically problem 
solving if it's not a unique 

497
00:21:13,640 --> 00:21:15,480
situation for you to be solving 
this problem. 

498
00:21:15,480 --> 00:21:17,600
The question if it's if we're 
thinking about questions with 

499
00:21:17,600 --> 00:21:21,200
children, the questions that are
being shown should be unfamiliar

500
00:21:21,200 --> 00:21:23,080
to them. 
If you've modelled on the board 

501
00:21:23,720 --> 00:21:26,360
a particular problem and then 
what you've done is you've 

502
00:21:26,360 --> 00:21:28,600
changed the numbers and you've 
given them the same problem five

503
00:21:28,600 --> 00:21:30,320
more times on a worksheet and 
said have a go. 

504
00:21:30,320 --> 00:21:32,480
But like sometimes what word 
problems do, it'll be the same. 

505
00:21:32,720 --> 00:21:35,520
It'll be the same method, but 
just different, different 

506
00:21:35,520 --> 00:21:38,600
contexts in the word problems 
that and you're saying this is 

507
00:21:38,600 --> 00:21:39,720
the problem solving part of the 
lesson. 

508
00:21:39,720 --> 00:21:42,240
It's not, it's not problem 
solving at all because you've 

509
00:21:42,240 --> 00:21:45,120
solved the problem for them on 
the board, which is what do I 

510
00:21:45,120 --> 00:21:47,200
do? 
How do I get from A to B? 

511
00:21:47,200 --> 00:21:49,920
How do I get from not knowing 
what to do to knowing the method

512
00:21:49,920 --> 00:21:51,800
that solves it? 
And then you're just giving them

513
00:21:51,800 --> 00:21:54,440
more arithmetic practise at that
point because they know, they 

514
00:21:54,440 --> 00:21:56,000
know they know what to do 
because you've solved the 

515
00:21:56,000 --> 00:21:58,320
problem for them. 
So yeah, problem solving is A is

516
00:21:58,320 --> 00:22:03,360
A, I'd say is the most like 
people get it wrong the most. 

517
00:22:03,360 --> 00:22:05,720
I think, I think I've spoke over
my career, I've spoken to 

518
00:22:05,720 --> 00:22:08,120
teachers about maths and problem
solving is the one where I find 

519
00:22:08,120 --> 00:22:11,160
myself being that guy that 
corrects people the most about 

520
00:22:11,160 --> 00:22:12,640
because they're like, Oh yeah, 
I've done some. 

521
00:22:12,640 --> 00:22:14,280
Problem solving Friday. 
Yeah, I've done problem solving 

522
00:22:14,280 --> 00:22:16,000
Friday. 
We do it every week, we do. 

523
00:22:16,440 --> 00:22:18,720
What I'll do is I'll have maybe 
5 different problems, I'll model

524
00:22:18,720 --> 00:22:20,320
just one of each one on the 
board for them and then they 

525
00:22:20,320 --> 00:22:21,560
crack on. 
So that's not problem solving. 

526
00:22:21,600 --> 00:22:23,240
Yeah, problem solving needs to 
be unique. 

527
00:22:23,360 --> 00:22:25,920
It's fundamentally part of what 
what it is, and you can't 

528
00:22:25,920 --> 00:22:27,640
problem solve unless you're 
fluent in the maths that 

529
00:22:27,640 --> 00:22:29,400
underpins it. 
I'm just going to add to what 

530
00:22:29,400 --> 00:22:30,920
you said there because it's so 
interesting. 

531
00:22:30,920 --> 00:22:32,640
I completely agree with what 
you're saying about problem 

532
00:22:32,640 --> 00:22:34,240
solving. 
Has to be new, has to be unique.

533
00:22:34,440 --> 00:22:38,000
But realistically, there are 
points, certainly in problem 

534
00:22:38,000 --> 00:22:40,840
solving lessons, where things 
can't be completely unique all 

535
00:22:40,840 --> 00:22:42,840
of the time, right? 
If you are literally doing a 

536
00:22:42,840 --> 00:22:46,160
small step on additional 
subtraction, the kids may well 

537
00:22:46,560 --> 00:22:48,240
it's gonna be addition. 
Right, they know what? 

538
00:22:49,080 --> 00:22:52,480
I mean, so I don't necessarily 
think that in their situations 

539
00:22:52,480 --> 00:22:55,800
problem solving can't happen. 
I think it's harder and I think 

540
00:22:55,800 --> 00:23:00,080
there's still a place for 
modelling the steps in the 

541
00:23:00,080 --> 00:23:02,800
process of problem solving. 
So we talk about there like what

542
00:23:02,800 --> 00:23:04,400
if you're at the front of the 
board and you model how to 

543
00:23:04,400 --> 00:23:05,840
answer this question, the kids 
go and do it. 

544
00:23:05,840 --> 00:23:08,720
It's not problem solving. 
Yeah, I slightly push back at 

545
00:23:08,720 --> 00:23:12,920
that a little bit in terms of, I
think the way you model it with 

546
00:23:12,920 --> 00:23:16,240
everyone involved asking 
questions, reasoning, getting 

547
00:23:16,240 --> 00:23:18,640
the kids to explain themselves, 
thinking why we might try this 

548
00:23:18,640 --> 00:23:21,920
method or we might try that 
method that is vital in teaching

549
00:23:21,920 --> 00:23:24,360
problem solving. 
So I think there is a huge place

550
00:23:24,360 --> 00:23:26,400
for that. 
And you can absolutely say even 

551
00:23:26,400 --> 00:23:28,600
though my children didn't get 5 
unique questions they'd never 

552
00:23:28,600 --> 00:23:31,040
seen before, therefore they 
didn't problem solve, I'd be 

553
00:23:31,040 --> 00:23:33,480
saying no, no, no, no, no. 
Because I think really good 

554
00:23:33,480 --> 00:23:36,600
problem solving teaching comes 
from really good modelling of 

555
00:23:36,600 --> 00:23:39,600
what problem solving is, 
involving your class in that and

556
00:23:39,600 --> 00:23:43,160
then letting them have a go. 
And it might be that you model 

557
00:23:43,160 --> 00:23:45,240
them halfway there and you say 
right, you'd, what do you think 

558
00:23:45,240 --> 00:23:47,440
the last thing might be then? 
That's definitely problem 

559
00:23:47,440 --> 00:23:49,040
solving. 
But they don't necessarily have 

560
00:23:49,040 --> 00:23:51,760
to do everything from the start,
all of the time off the cuff for

561
00:23:51,760 --> 00:23:53,800
it to be good problem solving. 
I completely agree and I hope 

562
00:23:53,800 --> 00:23:55,920
that that I don't think you 
think that's a contradiction at 

563
00:23:55,920 --> 00:23:57,160
all, by the way. 
I think that's just an extra 

564
00:23:57,160 --> 00:23:59,360
point and that the easiest 
analogy I can make is honestly 

565
00:23:59,360 --> 00:24:00,920
to writing. 
Think of modelling writing. 

566
00:24:00,920 --> 00:24:04,280
It's exactly the same when you 
model writing to children, when 

567
00:24:04,280 --> 00:24:06,520
you expect children to do 
writing, by the way, you don't 

568
00:24:06,520 --> 00:24:08,920
just say off you go. 
Them modelling writing is 

569
00:24:08,920 --> 00:24:10,680
essential to them becoming good 
at writing. 

570
00:24:10,680 --> 00:24:13,000
But when you model that first 
paragraph or those first few 

571
00:24:13,000 --> 00:24:15,440
sentences on the board and 
they're all copying those 

572
00:24:15,440 --> 00:24:18,000
sentences or doing extremely 
similar sentences in their book,

573
00:24:18,000 --> 00:24:20,480
because you've heavily modelled 
it, you don't count that. 

574
00:24:20,480 --> 00:24:22,240
But it's independent write, 
independent writing. 

575
00:24:22,920 --> 00:24:25,400
But the rest of it, you've shown
them some skills that they can 

576
00:24:25,400 --> 00:24:27,760
transfer now and then when 
they're applying it to unique 

577
00:24:27,760 --> 00:24:30,040
situations, which is the rest of
their writing or in math 

578
00:24:30,040 --> 00:24:31,880
situation, it might just be 
other problems now. 

579
00:24:31,920 --> 00:24:33,000
Yeah, that are equally. 
Yeah. 

580
00:24:33,000 --> 00:24:33,960
OK. 
It's all within addition, 

581
00:24:33,960 --> 00:24:35,000
subtraction. 
They know they're going to 

582
00:24:35,000 --> 00:24:36,840
probably be doing some adding 
and subtracting, but it's. 

583
00:24:36,840 --> 00:24:38,480
Got to work out what. 
The problems are still unique, 

584
00:24:38,480 --> 00:24:38,960
Yeah. 
How? 

585
00:24:38,960 --> 00:24:40,520
How much they're adding, How 
many times they're adding, 

586
00:24:40,520 --> 00:24:42,640
Whether they're subtracting, 
Whether there's going to be? 

587
00:24:42,800 --> 00:24:45,120
And context can be important. 
Different words, different 

588
00:24:45,120 --> 00:24:46,160
language. 
Exactly right. 

589
00:24:46,320 --> 00:24:48,720
Less than sold. 
Yeah, they they all mean 

590
00:24:48,720 --> 00:24:49,960
subtract. 
But this is still different 

591
00:24:49,960 --> 00:24:51,840
problem solving, because you're 
still accessing what words might

592
00:24:51,840 --> 00:24:53,920
mean, because you're. 
Exactly right. 

593
00:24:53,920 --> 00:24:57,000
So I absolutely fundamentally 
agree you should still be 

594
00:24:57,000 --> 00:24:59,640
modelling two children how to 
solve different types of 

595
00:24:59,640 --> 00:25:03,280
problems, but also giving them a
chance to independently solve 

596
00:25:03,280 --> 00:25:06,720
new unique problems. 
Even if you know that it's using

597
00:25:06,720 --> 00:25:09,760
their the same problem solving 
skills but there's still unique 

598
00:25:09,760 --> 00:25:11,720
problems for them. 
Yeah, I want to, I want to. 

599
00:25:11,720 --> 00:25:12,920
We're going to, we're going to 
talk in a second. 

600
00:25:12,920 --> 00:25:15,840
I think more about how what that
can look like. 

601
00:25:15,880 --> 00:25:18,520
If you're worried that your kids
aren't fluent yet, can we talk 

602
00:25:18,520 --> 00:25:19,720
about that? 
Maybe we'll do some scaffolding,

603
00:25:19,880 --> 00:25:22,760
but I really want to push on 
because I think it's something 

604
00:25:22,760 --> 00:25:26,280
that our listeners who maybe 
don't quite understand problem 

605
00:25:26,280 --> 00:25:29,280
solving completely in this way 
can really grasp onto. 

606
00:25:29,280 --> 00:25:31,840
And it's your comparison with 
independent writing. 

607
00:25:31,920 --> 00:25:35,840
I think that is such a good 
comparison because for a couple 

608
00:25:35,840 --> 00:25:37,840
of reasons. 
First reason I think about, I 

609
00:25:37,840 --> 00:25:40,640
think about what's the hardest 
thing for children to do in in 

610
00:25:40,640 --> 00:25:43,880
school, in primary school, 
because fundamentally adding 2 

611
00:25:43,880 --> 00:25:46,520
digit numbers together is quite 
easy and we can show that in 

612
00:25:46,520 --> 00:25:48,480
five to 10 minutes and children 
can practise it and they might 

613
00:25:48,480 --> 00:25:49,560
not get it straight away, but 
most. 

614
00:25:49,560 --> 00:25:51,400
Arithmetic is fairly 
straightforward. 

615
00:25:51,400 --> 00:25:52,920
Exactly that where and 
everything. 

616
00:25:52,920 --> 00:25:54,640
What's the hardest thing kids do
in school? 

617
00:25:54,640 --> 00:25:57,360
It's solving problems in maths 
and it's doing independent 

618
00:25:57,360 --> 00:26:00,560
writing and I think we are so 
much further along on 

619
00:26:00,800 --> 00:26:05,280
independent writing in terms of 
it being more understood that of

620
00:26:05,280 --> 00:26:07,760
course I'm not going to get my 
kids to write 2 paragraphs of 

621
00:26:07,760 --> 00:26:09,120
writing if they can't even do a 
sentence. 

622
00:26:09,560 --> 00:26:11,920
Of course I'm not going to ask 
my children to apply what a 

623
00:26:11,920 --> 00:26:14,800
front front of the verb you're 
writing in their work if I don't

624
00:26:14,800 --> 00:26:16,880
already know they can do it and 
I've not introduced the idea of 

625
00:26:16,880 --> 00:26:20,840
adding information to them. 
This in independent writing, 

626
00:26:20,840 --> 00:26:23,040
it's so common that you're like,
of course I'm going to model. 

627
00:26:23,280 --> 00:26:25,800
How can I possibly expect the 
children to have some really 

628
00:26:25,800 --> 00:26:28,760
good independent writing if I as
the expert has not modelled to 

629
00:26:28,760 --> 00:26:31,680
them what it looks like. 
This is what problem solving is.

630
00:26:31,840 --> 00:26:35,640
You don't just in your English 
lessons just say, ohh, by the 

631
00:26:35,640 --> 00:26:38,520
way, kids, we're just gonna do 
of independent writing now where

632
00:26:38,640 --> 00:26:40,360
you need to workout what to do 
here. 

633
00:26:40,360 --> 00:26:42,400
And I'm, I'm going to be judging
you based on whether you put 

634
00:26:42,400 --> 00:26:45,520
some, some independent clauses 
in here or not, or I'm going to 

635
00:26:45,520 --> 00:26:47,440
be looking for the this type of 
determiner. 

636
00:26:47,840 --> 00:26:51,040
No, it's very structured. 
You as the teacher are leading 

637
00:26:51,040 --> 00:26:52,720
them there and you let them have
a go. 

638
00:26:52,880 --> 00:26:54,120
And if they get it wrong, it 
doesn't matter. 

639
00:26:54,160 --> 00:26:56,200
We're going to do it again. 
If they get it wrong, it doesn't

640
00:26:56,200 --> 00:26:56,840
matter. 
We're going. 

641
00:26:56,880 --> 00:26:58,920
To put in opportunities to 
become fluent in those 

642
00:26:58,920 --> 00:27:00,960
fundamental writing strategies 
first. 

643
00:27:01,160 --> 00:27:02,560
But you've done a lesson. 
You've done lessons on 

644
00:27:02,560 --> 00:27:03,960
determinism. 
Whatever you said front of the 

645
00:27:03,960 --> 00:27:05,440
verbals. 
Yeah, that because you'll think,

646
00:27:05,440 --> 00:27:06,360
right, They're fluent in these 
now. 

647
00:27:06,360 --> 00:27:08,360
And now hopefully they can apply
it to this problem solving. 

648
00:27:08,360 --> 00:27:10,400
I mean, independent writing 
situation. 

649
00:27:10,400 --> 00:27:12,640
Yeah, it's so true. 
Isn't how English I think does 

650
00:27:12,640 --> 00:27:16,080
understand the process a bit 
more of fluency to the end goal 

651
00:27:16,080 --> 00:27:18,120
which is independent writing 
more than maths? 

652
00:27:18,120 --> 00:27:21,240
In understands fluency to the 
end goal which is problem 

653
00:27:21,240 --> 00:27:22,640
solving. 
I think they're a bit more 

654
00:27:22,840 --> 00:27:24,680
confused in maths. 
It can be, I think they can be. 

655
00:27:24,680 --> 00:27:26,200
I think, I think it's easier to 
understand. 

656
00:27:26,440 --> 00:27:27,800
I still think schools don't 
always get it right of 

657
00:27:27,800 --> 00:27:30,400
independent writing, but I do 
think sometimes it can be A tag 

658
00:27:30,400 --> 00:27:31,680
on a bit like problem solving 
is. 

659
00:27:31,840 --> 00:27:34,040
So we do a few weeks of learning
and then we do an independent 

660
00:27:34,040 --> 00:27:36,360
writing every few weeks. 
I think both of them have to be 

661
00:27:36,360 --> 00:27:39,760
interweaved a lot more. 
And let's move on to now 

662
00:27:39,840 --> 00:27:42,600
something you said there, which 
which I thought was fascinating 

663
00:27:42,600 --> 00:27:48,200
about when to problem solve, 
because I think we can speak now

664
00:27:48,200 --> 00:27:49,600
about we've got these three 
pillars. 

665
00:27:50,080 --> 00:27:53,080
And, and it very much felt like 
at the start of my career when 

666
00:27:53,080 --> 00:27:55,640
this was first being introduced 
because fluency and problem 

667
00:27:55,640 --> 00:27:58,480
solving, this idea of mastery 
and everyone doing like really 

668
00:27:58,480 --> 00:28:01,240
pushing themselves. 
I want to start by saying I 

669
00:28:01,240 --> 00:28:03,840
think it's vital. 
Every child problem solves, 

670
00:28:04,280 --> 00:28:06,960
every child reasons and every 
child becomes fluent in maths. 

671
00:28:07,120 --> 00:28:10,880
I think that's vital. 
But we're thinking about of 

672
00:28:10,880 --> 00:28:14,280
these three pillars, I don't 
think it should look like a 33% 

673
00:28:14,280 --> 00:28:17,360
split absolutely in your lesson,
and I think that's bad practise 

674
00:28:17,960 --> 00:28:21,280
and dive into that and then 
we'll talk about what good 

675
00:28:21,280 --> 00:28:23,080
problems on my. 
Level Well, I even say that in 

676
00:28:23,080 --> 00:28:25,840
that split analogy, whatever the
split is that you think is 

677
00:28:25,840 --> 00:28:27,760
optimal for your class, even 
that doesn't work on the 

678
00:28:27,760 --> 00:28:29,400
individual level. 
Different children have 

679
00:28:29,400 --> 00:28:31,880
different splits, genuinely, 
because different children will 

680
00:28:31,880 --> 00:28:35,640
require some children require a 
lot more time at the fluency 

681
00:28:35,640 --> 00:28:38,400
stage to become fluent. 
And if we, if we accept the 

682
00:28:38,400 --> 00:28:42,000
idea, this flow diagram of when 
you're fluent in something, you,

683
00:28:42,080 --> 00:28:44,040
you can then start applying it 
to problem solving. 

684
00:28:44,600 --> 00:28:47,160
Then by definition, obviously 
some children take, it takes 

685
00:28:47,160 --> 00:28:48,440
them longer to become fluent in 
something. 

686
00:28:48,440 --> 00:28:50,400
So by definition, they're 
getting problem solving 

687
00:28:50,400 --> 00:28:52,320
opportunities at different 
points on that objective. 

688
00:28:52,600 --> 00:28:54,920
But there's another layer to 
this, because it doesn't mean, 

689
00:28:54,920 --> 00:28:55,920
which is the point you're 
getting at. 

690
00:28:56,120 --> 00:28:58,680
It doesn't mean then that those 
kids that take a lot longer to 

691
00:28:58,680 --> 00:29:00,960
become fluent, you can't just 
say, Oh, we've run out of time 

692
00:29:00,960 --> 00:29:02,840
again and no problem. 
They never get any problem 

693
00:29:02,840 --> 00:29:04,480
solving because we never get 
that fluency. 

694
00:29:04,480 --> 00:29:06,400
Finished yeah and didn't hate on
the podcast. 

695
00:29:06,400 --> 00:29:07,960
Said I can't just give them 
problem solving. 

696
00:29:08,840 --> 00:29:11,240
They're just not getting there 
ever with the fluency is not 

697
00:29:11,240 --> 00:29:12,000
true. 
How do we solve? 

698
00:29:12,160 --> 00:29:14,560
What you can do is problems You 
can. 

699
00:29:15,320 --> 00:29:18,080
You can give them problem 
solving opportunities with 

700
00:29:18,200 --> 00:29:20,640
objectives that are not 
necessarily the exact unit 

701
00:29:20,640 --> 00:29:22,160
you're doing right now at the 
exact level. 

702
00:29:22,240 --> 00:29:25,760
It could be something from 
before you find something they 

703
00:29:25,760 --> 00:29:27,640
are fluent on. 
I've seen examples where 

704
00:29:28,240 --> 00:29:31,120
children are just maybe 
significantly behind their age 

705
00:29:31,120 --> 00:29:33,080
expected standard in maths. 
It doesn't. 

706
00:29:33,080 --> 00:29:34,400
They can't do any problem 
solving. 

707
00:29:34,400 --> 00:29:37,120
It just means you might need to 
drop back a year group or even 2

708
00:29:37,120 --> 00:29:40,280
year groups and find something 
they are fluent in and provide 

709
00:29:40,280 --> 00:29:42,880
them problems that allow them to
utilise that fluency. 

710
00:29:42,880 --> 00:29:45,840
So that's everyone gets a chance
to problem solve. 

711
00:29:46,480 --> 00:29:48,960
It just might not be at the same
level or the same level of 

712
00:29:48,960 --> 00:29:50,680
fluency underpinning that 
problem solving. 

713
00:29:51,040 --> 00:29:52,120
So you've got to find the 
balance. 

714
00:29:52,120 --> 00:29:54,280
It sounds almost slightly 
contradictory. 

715
00:29:54,280 --> 00:29:55,960
I get it because it's, I'm in 
one breath. 

716
00:29:55,960 --> 00:29:58,560
I'm saying keep going with the 
fluency until they're until 

717
00:29:58,560 --> 00:30:00,120
they're definitely fluent 
because then you can problem 

718
00:30:00,120 --> 00:30:02,560
solve on it. 
But I'm also saying, but do also

719
00:30:02,560 --> 00:30:04,360
building opportunities to 
problem solve. 

720
00:30:04,600 --> 00:30:06,760
So there's got to be sometimes 
where you think, OK, we've done 

721
00:30:06,760 --> 00:30:08,920
a lot of fluency, but I am going
to now build in, I'm going to 

722
00:30:08,920 --> 00:30:11,520
dedicate some time to do a 
little bit of problem solving 

723
00:30:11,520 --> 00:30:14,720
because I want them to be, I 
can't not do problem solving at 

724
00:30:14,720 --> 00:30:16,400
all ever. 
So I need to build in some time,

725
00:30:16,480 --> 00:30:19,080
time and what that ends up 
transcending to sometimes in a 

726
00:30:19,080 --> 00:30:20,880
lot of schools, we've seen this 
over our whole careers. 

727
00:30:21,120 --> 00:30:23,440
People then go to the final 
version of this and they go, OK,

728
00:30:23,440 --> 00:30:25,400
cool. 
So we'll put a policy in place 

729
00:30:25,600 --> 00:30:29,480
where everyone does a bit of 
fluency in their lesson and then

730
00:30:29,480 --> 00:30:31,200
they do a bit of reasoning and a
bit of problem solving. 

731
00:30:31,200 --> 00:30:32,480
If we do that and every lesson, 
don't worry. 

732
00:30:32,480 --> 00:30:34,960
Teachers, I know that children 
are at different paces, so I'll 

733
00:30:34,960 --> 00:30:36,360
let you do different amounts of 
them. 

734
00:30:36,360 --> 00:30:39,040
But everyone has to have 
fluency, reasoning and problem 

735
00:30:39,040 --> 00:30:42,080
solving in their lesson. 
Teacher A you can do 50% 

736
00:30:42,200 --> 00:30:44,360
relevancy, 15 reason problem 
solving, TGB. 

737
00:30:44,360 --> 00:30:45,840
You've got class find a bit 
tricky. 

738
00:30:45,840 --> 00:30:49,080
You can do 60% fluency and then 
just 40% reason problem solving,

739
00:30:49,080 --> 00:30:50,640
but everyone's got to do it. 
Yeah, it. 

740
00:30:50,760 --> 00:30:53,920
Doesn't work, No. 
I think this is hopefully if we 

741
00:30:53,920 --> 00:30:56,480
are really establishing these 
definitions at the start, it 

742
00:30:56,480 --> 00:30:59,800
just becomes common sense that 
this can't happen and it doesn't

743
00:30:59,800 --> 00:31:01,920
have to happen. 
And I remember as we were 

744
00:31:01,920 --> 00:31:04,600
preparing for Ofsted as maths 
leads master came in, we had a 

745
00:31:04,600 --> 00:31:08,040
very successful maths Ofsted and
we get very successful data in 

746
00:31:08,040 --> 00:31:09,400
maths and all the schools that 
we've ran. 

747
00:31:09,400 --> 00:31:12,320
So we know this works and we 
were, we were looking up things 

748
00:31:12,320 --> 00:31:16,560
and it said like, it can 
actually be seen as bad practise

749
00:31:16,840 --> 00:31:19,840
for problem solving to be 
shoehorned into every single 

750
00:31:19,840 --> 00:31:22,320
lesson. 
Because if you're doing that, 

751
00:31:22,480 --> 00:31:26,080
you're not doing problem solving
for the right reasons. 

752
00:31:26,360 --> 00:31:28,520
You're doing it for coverage 
because you're worried it needs 

753
00:31:28,520 --> 00:31:31,960
to be seen. 
Problem solving can happen twice

754
00:31:31,960 --> 00:31:34,360
a week. 
Problem solving can be can be a 

755
00:31:34,360 --> 00:31:37,320
whole lesson. 
It can be half a lesson once a 

756
00:31:37,320 --> 00:31:39,440
week. 
It can be every day. 

757
00:31:39,560 --> 00:31:42,800
It can be okay. 
It's not hard and fast raw. 

758
00:31:43,040 --> 00:31:45,240
And if you're thinking about 
what problem solving has to look

759
00:31:45,240 --> 00:31:47,880
like and what fluency looks like
and what we might see is like a 

760
00:31:47,880 --> 00:31:51,760
generic split. 
I think for me, the vast 

761
00:31:51,760 --> 00:31:54,640
majority of your maths teaching 
should be around fluency. 

762
00:31:55,080 --> 00:31:58,480
You have to get that right. 
You have to, it's as simple as 

763
00:31:58,480 --> 00:31:59,440
that. 
You have to teach the 

764
00:31:59,440 --> 00:32:02,120
curriculum, you have to get 
through things and children need

765
00:32:02,120 --> 00:32:03,800
to be able to do maths. 
They were thinking about 

766
00:32:03,800 --> 00:32:06,560
reasoning as being able to 
understand concepts, procedures 

767
00:32:06,600 --> 00:32:09,280
and language. 
That is by far if you just think

768
00:32:09,280 --> 00:32:13,120
about it for a second, you can't
do the rest unless you have 

769
00:32:13,120 --> 00:32:14,920
that. 
So the vast majority of your 

770
00:32:14,920 --> 00:32:17,240
time in your lessons should be 
on fluency. 

771
00:32:17,440 --> 00:32:18,840
The reasoning happens all the 
time. 

772
00:32:19,360 --> 00:32:21,840
I wouldn't even, I honestly 
wouldn't even be saying to 

773
00:32:21,840 --> 00:32:24,160
someone, oh, you need to have a 
reasoning chunk in your lesson. 

774
00:32:24,600 --> 00:32:27,600
It would just be so built into 
my planning, to my questioning, 

775
00:32:27,640 --> 00:32:31,200
to my, to my fluency and to my 
teaching that fluency is 

776
00:32:31,200 --> 00:32:33,360
happening all the time in 
whether I'm I'm sorry, that 

777
00:32:33,360 --> 00:32:35,200
reasoning is happening all the 
time, whether I'm doing fluency 

778
00:32:35,200 --> 00:32:38,800
or problem solving. 
Reasoning is thinking like it 

779
00:32:38,800 --> 00:32:40,000
doesn't even need to be a 
separate thing. 

780
00:32:40,240 --> 00:32:44,800
And then I could either think to
myself, OK, my children aren't 

781
00:32:44,800 --> 00:32:46,040
quite fluent in this. 
I'm going to carry on. 

782
00:32:46,680 --> 00:32:49,520
You might think, oh, my children
are getting fluent in this, but 

783
00:32:49,720 --> 00:32:52,400
there's something else I want to
recap and do and and keep them 

784
00:32:52,400 --> 00:32:54,200
fluent in that. 
And you might even think to 

785
00:32:54,200 --> 00:32:55,720
yourself, I think it's time for 
some problem solving. 

786
00:32:55,960 --> 00:32:58,440
And that might be my kids are 
fluent in this year for stuff 

787
00:32:58,440 --> 00:32:59,800
I'm doing. 
Oh, rub my hands again. 

788
00:32:59,800 --> 00:33:02,920
But let's try a problem where I 
know the cognitive load won't be

789
00:33:02,920 --> 00:33:04,320
on the processes and the 
understanding. 

790
00:33:04,320 --> 00:33:05,240
So you're going to do it at your
full? 

791
00:33:05,240 --> 00:33:06,240
Level. 
So I'm going to do at your full 

792
00:33:06,240 --> 00:33:07,760
level. 
However, I might well have a 

793
00:33:07,760 --> 00:33:10,080
class or even a group of 
children where I think, do you 

794
00:33:10,080 --> 00:33:13,200
know what you guys are fluent in
Year 4, you're going to do it at

795
00:33:13,200 --> 00:33:15,440
this year 4 level. 
You guys aren't. 

796
00:33:15,440 --> 00:33:18,120
But there's no way I can deprive
your problem solving because 

797
00:33:18,120 --> 00:33:19,840
that's what maths is. 
It's that your name in the 

798
00:33:19,840 --> 00:33:22,080
curriculum. 
Let's just dip back a little 

799
00:33:22,080 --> 00:33:26,840
bit, but the art of problem 
solving, the ability to look at 

800
00:33:26,840 --> 00:33:29,160
and try and use your reasoning 
to know what to do. 

801
00:33:29,760 --> 00:33:33,920
The techniques involved, the 
types of question, whether it's 

802
00:33:33,920 --> 00:33:37,760
missing number, word, problem, 
finding all possibilities, trial

803
00:33:37,760 --> 00:33:39,960
and improvement. 
Whatever the strategies might 

804
00:33:39,960 --> 00:33:42,200
be, everyone can use those 
strategies. 

805
00:33:42,640 --> 00:33:45,640
Everyone in any class can do 
trial and improvement. 

806
00:33:45,880 --> 00:33:48,000
It might be that ones in the 
context of something much more 

807
00:33:48,000 --> 00:33:50,680
simple for them to understand. 
It might be another one is much 

808
00:33:50,680 --> 00:33:52,480
trickier to know. 
That's what you've got to do. 

809
00:33:52,800 --> 00:33:54,680
But part of the problem solving 
is figuring out you got to do 

810
00:33:54,680 --> 00:33:57,720
that and then doing it. 
But you can fundamentally have 

811
00:33:58,280 --> 00:34:01,320
any amount of children with any 
level doing problem solving a 

812
00:34:01,320 --> 00:34:03,440
mass, and it's vital. 
And it doesn't have to be 

813
00:34:03,440 --> 00:34:04,920
shoehorned in. 
It doesn't have to be the same 

814
00:34:04,920 --> 00:34:07,280
amount of time every day. 
It just needs to be a whole 

815
00:34:07,280 --> 00:34:09,800
picture. 
And I think that's where you can

816
00:34:09,800 --> 00:34:11,560
fall into that trap of tick box,
tick box, tick box. 

817
00:34:11,560 --> 00:34:13,199
Because I want to just see that 
everyone's doing the right 

818
00:34:13,199 --> 00:34:14,040
thing. 
I want to make sure it's all 

819
00:34:14,040 --> 00:34:15,560
right. 
Yeah, it's got to be holistic, 

820
00:34:15,719 --> 00:34:18,600
because actually tick boxes by 
definition can force you to do 

821
00:34:18,600 --> 00:34:20,280
it wrong. 
Exactly what what happens a lot 

822
00:34:20,280 --> 00:34:22,719
in that situation, just to be 
extremely clear, is when you are

823
00:34:22,719 --> 00:34:25,320
doing the tick box situation, 
you are then in a position 

824
00:34:25,320 --> 00:34:28,000
possibly where you're showing 
kids problem solving 

825
00:34:28,000 --> 00:34:30,560
opportunities and they're simply
just not fluent in the maths 

826
00:34:30,560 --> 00:34:31,840
yet. 
And and therefore is it's a 

827
00:34:31,840 --> 00:34:33,360
complete waste of time. 
Because what you end up doing is

828
00:34:33,360 --> 00:34:35,400
you end up modelling it all on 
the board, taking away the 

829
00:34:35,400 --> 00:34:37,880
problem solving element and end 
up inadvertently doing more 

830
00:34:37,880 --> 00:34:40,080
fluency, which probably 
realistically is not the worst 

831
00:34:40,080 --> 00:34:41,760
thing in the world because they 
clearly need more of that. 

832
00:34:41,760 --> 00:34:43,760
But it would be maybe more 
effective to have just been 

833
00:34:43,760 --> 00:34:45,280
carrying on with the way you're 
doing fluency. 

834
00:34:45,760 --> 00:34:47,880
A really good idea very quickly 
on problem solving, because I 

835
00:34:47,880 --> 00:34:52,520
love this as like a function is 
to to take the numbers out of 

836
00:34:52,520 --> 00:34:54,520
the question. 
Because sometimes by taking 

837
00:34:54,520 --> 00:34:56,639
numbers out of the question, 
you're kind of getting rid of 

838
00:34:56,639 --> 00:34:59,080
that difference there of like, 
oh, are you working at you 2 

839
00:34:59,080 --> 00:35:01,320
level, your four level, your 
five level of addition, let's 

840
00:35:01,320 --> 00:35:03,480
say? 
Because no, what that then 

841
00:35:03,480 --> 00:35:06,720
becomes is then the children are
simply solving the problem. 

842
00:35:06,720 --> 00:35:09,920
And the question is simply just 
what do I have to do here? 

843
00:35:10,400 --> 00:35:12,520
What what is the, what is the 
like? 

844
00:35:12,520 --> 00:35:15,440
What do these words mean? 
Are you fluent in the vocabulary

845
00:35:15,440 --> 00:35:17,560
we've learnt? 
Oh, you are brilliant. 

846
00:35:17,560 --> 00:35:19,640
That means you've been exposed 
to a bunch of vocabulary. 

847
00:35:19,800 --> 00:35:22,360
What do you think it might mean 
for a delivery to be shipped 

848
00:35:22,360 --> 00:35:24,920
somewhere? 
That is not, that is not the 

849
00:35:24,920 --> 00:35:26,840
word ad. 
That is not the symbol ad. 

850
00:35:27,080 --> 00:35:30,160
That is you think I'm really 
thinking to tell, OK, I kind of,

851
00:35:30,160 --> 00:35:31,560
I can use my phone, become 
fluent in this. 

852
00:35:31,560 --> 00:35:34,360
I understand these words mean, I
think we need to add, we don't 

853
00:35:34,360 --> 00:35:37,320
even have the number, but but 
the act of that and that this 

854
00:35:37,320 --> 00:35:38,880
can be reasoning and problem 
solving. 

855
00:35:38,880 --> 00:35:40,960
This is where it overlaps. 
You can explain to stuff. 

856
00:35:40,960 --> 00:35:42,960
I think it means add because the
shop would have more of it. 

857
00:35:43,120 --> 00:35:43,960
Yeah. 
Oh, interesting. 

858
00:35:43,960 --> 00:35:45,200
What does the question say at 
the end? 

859
00:35:45,360 --> 00:35:47,600
The question says how much does 
the shop at the end of the week?

860
00:35:47,760 --> 00:35:49,040
Oh, interesting. 
So is there something else in 

861
00:35:49,040 --> 00:35:50,200
the question that might happen 
in the week? 

862
00:35:50,200 --> 00:35:53,240
This is like as close as it gets
to actually extracting pure like

863
00:35:53,240 --> 00:35:55,240
problem solving and reason 
because you're almost taking out

864
00:35:55,240 --> 00:35:56,360
the bit where they actually do 
the maths. 

865
00:35:56,360 --> 00:35:57,600
At this point. 
You can take my numbers. 

866
00:35:57,760 --> 00:35:59,400
I actually learned that. 
Hilariously, if we're begging up

867
00:35:59,400 --> 00:36:01,920
people like Gina Donaldson, I 
actually learned that from 

868
00:36:02,080 --> 00:36:03,680
originally right at the 
beginning of my career, Gareth 

869
00:36:03,680 --> 00:36:06,520
Metcalf, who we had on this 
podcast two years ago now. 

870
00:36:06,520 --> 00:36:08,400
It's crazy to think that one of 
our earlier episodes, go and 

871
00:36:08,400 --> 00:36:10,960
find it. 
He's an unbelievably talented 

872
00:36:11,000 --> 00:36:13,800
mathematics teacher. 
He creates incredible resources 

873
00:36:13,800 --> 00:36:16,640
that I see reasoning, I see. 
I see problem solving as well. 

874
00:36:16,800 --> 00:36:18,720
Really, really good. 
But I first picked that up from 

875
00:36:18,720 --> 00:36:19,880
him. 
I went to one of his training at

876
00:36:19,880 --> 00:36:21,080
many years ago. 
I was like, Oh my God, yeah, 

877
00:36:21,400 --> 00:36:23,200
just another, It's just another 
string to your bow, isn't it? 

878
00:36:23,200 --> 00:36:25,520
There's so many little things 
and tools and tricks and ways 

879
00:36:25,520 --> 00:36:29,440
you can expose children to 
isolated skills, as well as just

880
00:36:29,440 --> 00:36:31,440
opportunities to just straight 
up problem solve, as well as 

881
00:36:31,440 --> 00:36:33,880
opportunities to just practise a
method and arithmetic, as well 

882
00:36:33,880 --> 00:36:36,080
as opportunities for them to 
become fluent by showing them 

883
00:36:36,600 --> 00:36:38,880
five different ways of looking 
at an arithmetic question. 

884
00:36:38,880 --> 00:36:40,040
That's just ever so slightly 
different. 

885
00:36:40,040 --> 00:36:42,400
There's a bit of very fluency in
there where they're using slight

886
00:36:42,400 --> 00:36:44,280
elements of reasoning, but it's 
not problem solving because 

887
00:36:44,280 --> 00:36:46,520
ultimately it's just two numbers
and you're either adding or 

888
00:36:46,520 --> 00:36:48,720
subtracting them or multiplying 
and dividing them. 

889
00:36:49,040 --> 00:36:52,080
You've got all these little 
levels and I just think you have

890
00:36:52,080 --> 00:36:54,600
to genuinely to be a really good
maths teacher, I think you just 

891
00:36:54,600 --> 00:36:57,280
have to be aware of all of 
these, these layers and elements

892
00:36:57,280 --> 00:37:01,480
and aware of differences between
reasoning, problem solving and 

893
00:37:01,480 --> 00:37:04,160
fluency and how they are, like 
you said, they are both pillars 

894
00:37:04,160 --> 00:37:06,880
in terms of the way we account 
for them and we, we, they're 

895
00:37:06,880 --> 00:37:09,640
three separate aims, but they're
also not pillars in the idea 

896
00:37:09,640 --> 00:37:12,360
that they're completely separate
things all the time, that they 

897
00:37:12,360 --> 00:37:15,240
flow for each other. 
Reasoning flows through fluency 

898
00:37:15,360 --> 00:37:17,320
and problem solving. 
And just having this grand 

899
00:37:17,320 --> 00:37:19,720
awareness of all these things in
maths is what makes you a really

900
00:37:19,720 --> 00:37:21,240
good maths teacher. 
And I think without these 

901
00:37:21,240 --> 00:37:24,560
things, what can sometimes 
happen is if you, it's the 

902
00:37:24,560 --> 00:37:27,160
classic, what I think a lot of 
people say that when I was at 

903
00:37:27,160 --> 00:37:30,400
school, this is what we did. 
We got wrote, taught a method 

904
00:37:30,560 --> 00:37:33,160
that works. 
When I see this number times 

905
00:37:33,160 --> 00:37:35,840
this number written like that, 
this is the method that works. 

906
00:37:35,840 --> 00:37:37,600
Just do that. 
Why are we bothering teaching 

907
00:37:37,600 --> 00:37:39,800
kids different methods? 
Is that what we're teaching kids

908
00:37:39,800 --> 00:37:41,520
different methods? 
Because when the problem isn't 

909
00:37:42,040 --> 00:37:45,280
shown exactly like that, they 
then don't know what to do 

910
00:37:45,480 --> 00:37:47,880
because they were never really 
taught to think about it. 

911
00:37:48,120 --> 00:37:50,000
They were just taught. 
If you see this, do you can 

912
00:37:50,000 --> 00:37:52,400
teach a computer to do that. 
If you see this, apply this 

913
00:37:52,400 --> 00:37:53,840
method. 
It doesn't always work. 

914
00:37:54,200 --> 00:37:57,480
And to to just jump on that and 
finish off that's still 

915
00:37:57,480 --> 00:38:00,160
important to do exactly. 
It's still, well, not even 

916
00:38:00,560 --> 00:38:01,760
people who are saying why don't 
you just do that? 

917
00:38:01,760 --> 00:38:03,320
I was like, mate, I do. 
Yeah, that's what. 

918
00:38:03,360 --> 00:38:06,120
Fluency and arithmetic is yeah, 
that's really, really important.

919
00:38:06,120 --> 00:38:08,280
You're not wrong. 
You are not wrong. 

920
00:38:08,400 --> 00:38:10,240
That is really important. 
But you know what I'm also going

921
00:38:10,240 --> 00:38:12,200
to do? 
Just expose them to a different.

922
00:38:12,200 --> 00:38:13,560
Way show them a different way. 
Exactly. 

923
00:38:13,560 --> 00:38:15,080
The most simple one I always 
think of right. 

924
00:38:15,080 --> 00:38:18,440
And this is something we're 
building into our, our best 

925
00:38:18,440 --> 00:38:20,800
software for maths that we're 
passionately building right now,

926
00:38:20,960 --> 00:38:23,120
which is really, really focused 
at the moment on arithmetic. 

927
00:38:23,120 --> 00:38:25,280
And it will expand wider into 
fluency and more. 

928
00:38:25,400 --> 00:38:27,200
Yeah. 
One of the easiest things that 

929
00:38:27,200 --> 00:38:29,880
we've we've done is can you move
the equal sign to the other 

930
00:38:29,880 --> 00:38:31,000
side? 
Because I can tell you in my 

931
00:38:31,000 --> 00:38:33,960
career how many times where 
especially earlier on where I 

932
00:38:33,960 --> 00:38:37,440
maybe didn't consider this, I'd 
show every single question as A 

933
00:38:37,640 --> 00:38:41,560
* B equals or A+B equals. 
And it'll always be arithmetic 

934
00:38:41,560 --> 00:38:44,120
and then equals at the end. 
And the kids genuinely thought 

935
00:38:44,120 --> 00:38:48,520
equals meant this is the answer.
They thought it meant the symbol

936
00:38:48,520 --> 00:38:49,640
where you put your answer next 
to it. 

937
00:38:50,000 --> 00:38:51,920
And they didn't really 
understand what equals actually 

938
00:38:51,920 --> 00:38:53,240
meant. 
And as soon as you then took the

939
00:38:53,240 --> 00:38:56,800
exact same question, A * B 
equals and you put blank equals 

940
00:38:56,800 --> 00:39:00,040
a * B, they were like, oh, have 
I got Oh my God, what do I do? 

941
00:39:00,440 --> 00:39:01,760
Have I got to use? 
Have I got to use inverse? 

942
00:39:02,280 --> 00:39:05,080
Because because they don't know,
they haven't been exposed to the

943
00:39:05,080 --> 00:39:09,720
variety of fluency enough. 
They know the method and I will 

944
00:39:09,720 --> 00:39:11,760
practise that method. 
I'll make sure they are fluent 

945
00:39:11,760 --> 00:39:15,000
in the method itself, but I'll 
also make sure they're fluent in

946
00:39:15,000 --> 00:39:18,320
a wider sense in this is some 
different ways to even represent

947
00:39:18,320 --> 00:39:20,160
this arithmetic, Yeah. 
Yeah, like. 

948
00:39:20,160 --> 00:39:23,000
Precisely. 
And that is just fundamental to 

949
00:39:23,000 --> 00:39:26,560
the way we're building this app.
This software that we're 

950
00:39:26,560 --> 00:39:29,360
building is like, it's not just 
methods, even though it's 

951
00:39:29,360 --> 00:39:31,520
unbelievably important. 
It's also here's some different 

952
00:39:31,520 --> 00:39:35,120
ways you might see the same 
arithmetic question, but still 

953
00:39:35,120 --> 00:39:37,120
applying the same method. 
And it's important kids are 

954
00:39:37,120 --> 00:39:38,920
exposed to it, by the way. 
So yeah, use this. 

955
00:39:39,080 --> 00:39:41,920
And, and the great thing is with
this and fluency in general, I 

956
00:39:41,920 --> 00:39:44,640
think the, the really important 
thing about knowing facts, for 

957
00:39:44,640 --> 00:39:47,040
example, and becoming fluent at 
something is you are doing it 

958
00:39:47,040 --> 00:39:49,240
quite frequently as well. 
You're doing quite frequently, 

959
00:39:49,240 --> 00:39:51,240
not necessarily for ages and 
ages in terms of obviously you 

960
00:39:51,240 --> 00:39:52,960
need to teach a lesson and have 
varied fluency in there. 

961
00:39:53,160 --> 00:39:55,160
But then when when like I've 
maybe I've taught additional 

962
00:39:55,160 --> 00:39:58,760
subtraction and this kind of 
links in to be to be fair with 

963
00:39:58,760 --> 00:40:01,720
schemes and stuff in general. 
Which is, you know, it's very 

964
00:40:01,720 --> 00:40:04,040
common now to block things. 
Maybe we can talk about that a 

965
00:40:04,040 --> 00:40:05,920
little bit where you might block
your learning. 

966
00:40:05,920 --> 00:40:08,560
And what we mean by blocks is 
there are essentially two ways 

967
00:40:08,560 --> 00:40:11,360
traditionally that you might 
teach maths. 1 is a spiral 

968
00:40:11,360 --> 00:40:13,160
curriculum and 1 is a block 
curriculum. 

969
00:40:13,520 --> 00:40:16,160
In a spiral curriculum, let's 
take additional subtraction. 

970
00:40:16,160 --> 00:40:18,160
Let's say you've got six weeks 
of that you need to do in year 

971
00:40:18,160 --> 00:40:20,320
4. 
In a spiral curriculum. 

972
00:40:20,320 --> 00:40:22,960
You do it for two weeks before 
Christmas, you do it for two 

973
00:40:22,960 --> 00:40:24,960
weeks before Easter, and then 
you do it for two weeks before 

974
00:40:24,960 --> 00:40:26,800
summer. 
And the idea being you come back

975
00:40:26,800 --> 00:40:28,080
and maybe you get deeper each 
time. 

976
00:40:28,720 --> 00:40:31,480
The block curriculum would be 
you do all six weeks before 

977
00:40:31,480 --> 00:40:34,480
Christmas in a row because 
you're really diving deep into 

978
00:40:34,480 --> 00:40:36,960
it and getting those 
opportunities where for the 

979
00:40:36,960 --> 00:40:39,040
first week and a half I didn't 
really get a chance to problem 

980
00:40:39,040 --> 00:40:40,960
solve too much. 
But my goodness me, because I'm 

981
00:40:40,960 --> 00:40:42,840
doing it for six weeks, we're 
going to dive in. 

982
00:40:42,880 --> 00:40:44,600
They're going to become really 
fluent and get those 

983
00:40:44,600 --> 00:40:47,520
opportunities. 
I think block curriculum really 

984
00:40:47,520 --> 00:40:50,960
lends itself to be able to apply
what we've talked about today 

985
00:40:51,120 --> 00:40:52,600
better. 
I think it's a good thing. 

986
00:40:52,600 --> 00:40:55,840
Truly mastering maths? 
To truly master it, I do think 

987
00:40:55,840 --> 00:40:59,080
it has a massive drawback, which
again goes against is one thing 

988
00:40:59,080 --> 00:41:01,160
we've said which is fluency 
needs to be done all the time. 

989
00:41:01,320 --> 00:41:02,920
You need to be revisiting it all
the time. 

990
00:41:03,320 --> 00:41:06,960
And that's where a block 
curriculum loses its power if 

991
00:41:06,960 --> 00:41:09,960
you don't do something about it.
Because then those children 

992
00:41:09,960 --> 00:41:12,880
doing six weeks of additional 
subtraction might get really 

993
00:41:12,880 --> 00:41:15,720
deep and by November they are 
unbelievable, but they're not 

994
00:41:15,720 --> 00:41:17,760
going to do additional 
subtraction until next November 

995
00:41:17,760 --> 00:41:19,320
when they come back to it for 
the next year group. 

996
00:41:19,600 --> 00:41:22,160
So maybe you could talk talk a 
little bit about this as like, 

997
00:41:22,520 --> 00:41:25,400
why is it still important, even 
though maybe we have this idea 

998
00:41:25,400 --> 00:41:28,600
of mastery to become fluent in 
something and thinking about our

999
00:41:28,720 --> 00:41:31,960
platform, even about arithmetic 
testing every week and becoming 

1000
00:41:31,960 --> 00:41:34,400
really good at doing your maths.
Why? 

1001
00:41:35,080 --> 00:41:37,760
How can we square that with what
schemes do now, which is? 

1002
00:41:37,760 --> 00:41:40,040
Block so there's something 
really important that we need to

1003
00:41:40,040 --> 00:41:42,640
understand about block 
curriculums, which is they are 

1004
00:41:42,680 --> 00:41:45,680
mapping coverage of your main 
lesson objective. 

1005
00:41:46,040 --> 00:41:49,880
And I think sometimes it's easy 
to forget that that might not be

1006
00:41:49,880 --> 00:41:52,080
the be all and end all of the 
entirety of your maths lesson. 

1007
00:41:52,520 --> 00:41:55,560
A really good maths lesson, and 
this is to, in my opinion, is 

1008
00:41:55,560 --> 00:41:59,200
the best practise, is that there
is a significant different chunk

1009
00:41:59,200 --> 00:42:01,680
of the allocated time that you 
have to teach maps that is 

1010
00:42:01,680 --> 00:42:04,520
dedicated to your lesson 
objective and that very much be 

1011
00:42:04,800 --> 00:42:07,200
following your, your curriculum 
map. 

1012
00:42:07,280 --> 00:42:10,720
OK, your your block curriculum, 
but there should be a, another 

1013
00:42:10,720 --> 00:42:13,400
significant part of your lesson,
maybe smaller than the main bit,

1014
00:42:13,640 --> 00:42:17,920
which is dedicated to not that 
main lesson objective, but other

1015
00:42:17,920 --> 00:42:19,720
things. 
So mostly fluency. 

1016
00:42:19,720 --> 00:42:21,240
It could even be problems. 
We'll come to that later. 

1017
00:42:21,240 --> 00:42:25,600
But a part of your lesson is 
dedicated to recapping parts of 

1018
00:42:25,600 --> 00:42:27,800
fluency that you've looked at in
the past so that you're not 

1019
00:42:27,800 --> 00:42:30,680
leaving at a year, year. 
It's we should never be in a 

1020
00:42:30,680 --> 00:42:33,840
situation where you're actually 
leaving an objective an entire 

1021
00:42:33,840 --> 00:42:36,920
year before it's remotely talked
about or touched on again. 

1022
00:42:36,920 --> 00:42:39,760
That is bad practise. 
And I, and I hate the idea that 

1023
00:42:39,760 --> 00:42:42,520
anyone looks at block curriculum
and says, well, that encourages 

1024
00:42:42,520 --> 00:42:45,320
this, therefore it's bad. 
It doesn't actually encourage 

1025
00:42:45,320 --> 00:42:46,280
it. 
It's really just mapping out 

1026
00:42:46,280 --> 00:42:48,280
your main lesson objectives. 
You should be building as a 

1027
00:42:48,280 --> 00:42:50,440
school, you should be building 
in time. 

1028
00:42:50,520 --> 00:42:53,320
I think what do we have about 20
to 25 minutes. 

1029
00:42:53,320 --> 00:42:57,040
We had this dedicated section, 
which is is nothing to do with 

1030
00:42:57,040 --> 00:42:59,800
the main lesson objective. 
It could be, if you want it to 

1031
00:42:59,800 --> 00:43:02,160
be, it could be, it could be 
linked, it could be we're pre 

1032
00:43:02,160 --> 00:43:04,680
teaching a skill that we think 
that's going to be useful. 

1033
00:43:04,680 --> 00:43:07,240
And by pre teaching, I'm 
literally talking about, let's 

1034
00:43:07,240 --> 00:43:09,800
say you're doing rounding. 
And you know, if you, I would 

1035
00:43:09,800 --> 00:43:12,320
say the same example, it's the 
easiest one to think of because 

1036
00:43:12,320 --> 00:43:14,840
it's so like tangible when 
you're teaching rounding, like 

1037
00:43:14,840 --> 00:43:16,960
obviously you need kids to know 
multiples of 10 or if you're 

1038
00:43:16,960 --> 00:43:19,320
rounding the nearest 10, they 
they intrinsically need to know 

1039
00:43:19,320 --> 00:43:21,000
what multiples of 10 are when 
you're teaching rounding. 

1040
00:43:21,000 --> 00:43:24,080
So you might be doing a pre 
teaching in starters leading up 

1041
00:43:24,080 --> 00:43:26,000
to this rounding unit where 
you're reminding them of 

1042
00:43:26,000 --> 00:43:27,280
multiples of 10. 
If you feel that's what they 

1043
00:43:27,280 --> 00:43:29,760
need, that's what I'd call as 
pre teaching teaching, but and 

1044
00:43:29,760 --> 00:43:31,440
you've also got reteaching in 
that time. 

1045
00:43:31,440 --> 00:43:34,680
It could be that you know what 
we finished this unit on 

1046
00:43:34,720 --> 00:43:36,320
addition, subtraction. 
We use that example a lot. 

1047
00:43:36,960 --> 00:43:41,040
And a month later, I just, I 
just wasn't satisfied fully that

1048
00:43:41,040 --> 00:43:42,760
they were fluent, as fluent as 
I'd like them to be. 

1049
00:43:43,080 --> 00:43:45,120
And you know what, I'm going to 
use some of this time outside of

1050
00:43:45,120 --> 00:43:48,000
my main listing objective in 
later blocks across the year to 

1051
00:43:48,000 --> 00:43:51,360
reteach some smaller parts of, 
of, of those of those small 

1052
00:43:51,360 --> 00:43:53,600
steps, those elements of those 
lessons I'm going to reteach. 

1053
00:43:53,800 --> 00:43:56,200
And the big one, the thing we do
the most is, is just genuinely 

1054
00:43:56,240 --> 00:43:58,120
just recapping. 
It's been a bit of time. 

1055
00:43:58,120 --> 00:44:01,480
I want to make sure I'm covering
and I'm going over and making 

1056
00:44:01,480 --> 00:44:03,520
sure because fluency has to be 
done all the time and they're 

1057
00:44:03,520 --> 00:44:05,120
building on it. 
I'm going to go back to old 

1058
00:44:05,120 --> 00:44:07,000
objectives and I'm going to and 
I'm going to recap this. 

1059
00:44:07,000 --> 00:44:10,880
Why is it difference to reteach?
Reteach is I guess is from 

1060
00:44:10,880 --> 00:44:12,640
mindset, right? 
So reteaching is specifically, I

1061
00:44:12,640 --> 00:44:14,320
feel like they weren't fluent, 
they weren't there, they weren't

1062
00:44:14,320 --> 00:44:15,800
quite there. 
And I and I want to make sure 

1063
00:44:15,800 --> 00:44:18,000
I'm getting them to this a 
certain standard recapping. 

1064
00:44:18,000 --> 00:44:20,800
They could be absolutely there, 
but it's very important that 

1065
00:44:20,800 --> 00:44:22,440
it's still, yeah, refreshing 
their mind. 

1066
00:44:22,440 --> 00:44:25,600
In that recap, obviously you're 
saying that they're still 

1067
00:44:25,600 --> 00:44:28,520
fluent. 
Do you think in this, in this 

1068
00:44:28,520 --> 00:44:30,480
like chunk? 
Because I used it a lot to be 

1069
00:44:30,480 --> 00:44:32,400
like, cool, well, I can reason 
in problem Solver now as well, 

1070
00:44:32,400 --> 00:44:34,520
yeah. 
Would that come into recapping 

1071
00:44:34,520 --> 00:44:35,880
for you or like going over 
stuff? 

1072
00:44:35,880 --> 00:44:38,880
Again, it would do yeah. 
So, so for me that is down to 

1073
00:44:39,200 --> 00:44:41,160
all honesty like the the make up
of your class as well. 

1074
00:44:41,160 --> 00:44:44,320
So I've had classes before where
genuinely, because we are 

1075
00:44:44,320 --> 00:44:47,680
struggling with the fluency so 
much and yeah, I was building a 

1076
00:44:47,680 --> 00:44:49,960
problem solving opportunities in
the class, but fluency was a 

1077
00:44:49,960 --> 00:44:51,400
much bigger issue than maybe 
other times. 

1078
00:44:51,920 --> 00:44:56,160
That time for me became almost 
exclusively more time to recap 

1079
00:44:56,160 --> 00:44:58,960
and reteach and preteach fluency
things. 

1080
00:44:58,960 --> 00:45:01,520
And very, very rarely, whereas 
I've had other classes where 

1081
00:45:01,680 --> 00:45:04,240
because they're so fluent, it 
doesn't take me long to recap 

1082
00:45:04,240 --> 00:45:05,640
things to make sure they're 
still up there. 

1083
00:45:05,640 --> 00:45:07,720
It's like bouncing off the 
limiter of like, they're right 

1084
00:45:07,720 --> 00:45:09,600
up there really, really 
understanding, really super 

1085
00:45:09,600 --> 00:45:11,120
fluent. 
So I'd be like, cool, I've got 

1086
00:45:11,120 --> 00:45:14,480
some opportunities here to to 
now recap or reteach some 

1087
00:45:14,480 --> 00:45:16,120
opportunities from to problem 
solve as well. 

1088
00:45:16,120 --> 00:45:17,960
Because actually that is always 
that is the end goal. 

1089
00:45:17,960 --> 00:45:20,400
And I can and that's like, I can
make that infinitely hard. 

1090
00:45:20,400 --> 00:45:21,760
You can't complete problem 
solving. 

1091
00:45:22,200 --> 00:45:24,600
It just goes on forever. 
So yeah, lots of different 

1092
00:45:24,600 --> 00:45:26,520
things you can do. 
But my main point here, maybe 

1093
00:45:26,520 --> 00:45:29,640
you can dive into it more, is 
you've got your main lesson 

1094
00:45:29,640 --> 00:45:31,080
objective and you've got your 
coverage. 

1095
00:45:31,280 --> 00:45:35,160
And as part of your lesson, 
you've got exclusively a special

1096
00:45:35,160 --> 00:45:37,520
part of your lesson that is 
designed for recapping, re 

1097
00:45:37,520 --> 00:45:39,840
teaching, pre teaching, whatever
else you need to do. 

1098
00:45:39,840 --> 00:45:41,680
Yeah, I think it's vital. 
I think it's the way to make 

1099
00:45:41,680 --> 00:45:43,520
schemes work like this. 
I don't think they work 

1100
00:45:43,520 --> 00:45:45,160
otherwise. 
And I think I'm going to 

1101
00:45:45,160 --> 00:45:47,200
slightly change what you said. 
I don't think it necessarily has

1102
00:45:47,200 --> 00:45:50,440
to be part of your lesson. 
I quite, I quite like thinking 

1103
00:45:50,440 --> 00:45:52,160
of them as literally separate 
things. 

1104
00:45:52,400 --> 00:45:54,120
I can think of my maths lesson 
when I'm going through the 

1105
00:45:54,120 --> 00:45:57,600
curriculum that has the majority
of that is fluency and it has to

1106
00:45:57,600 --> 00:45:59,320
because I'm teaching them how to
do the maths. 

1107
00:46:00,200 --> 00:46:02,280
I've had people message us 
saying I'm really frustrated. 

1108
00:46:02,280 --> 00:46:04,840
My head teacher says every 
single lesson needs to have this

1109
00:46:04,840 --> 00:46:06,200
much reasoning and this much 
problem solving. 

1110
00:46:06,200 --> 00:46:07,920
It's annoying me. 
I'm like, I I get why that's 

1111
00:46:07,920 --> 00:46:10,200
annoying because it would annoy 
me because when I'm teaching the

1112
00:46:10,200 --> 00:46:13,480
curriculum, I have to teach you 
how to do the thing. 

1113
00:46:13,800 --> 00:46:15,760
And part of that is going to be 
reasoning, problem solving. 

1114
00:46:15,760 --> 00:46:17,640
Reasoning comes for everything. 
Part of it will be problem 

1115
00:46:17,640 --> 00:46:19,360
solving. 
But the majority of my lesson is

1116
00:46:19,360 --> 00:46:21,280
fluency because I'm teaching you
how to do the maths. 

1117
00:46:21,600 --> 00:46:25,560
This separate thing here, the 
reason I love it so much and I, 

1118
00:46:25,600 --> 00:46:28,200
I thought it was the best thing 
we ever did for maths in our 

1119
00:46:28,200 --> 00:46:31,600
school was introducing this as a
hard, hard separate thing. 

1120
00:46:31,680 --> 00:46:33,480
Protected time. 
It's protected time. 

1121
00:46:33,480 --> 00:46:37,040
It is literally protected time 
where you get 20 to 25 minutes. 

1122
00:46:37,440 --> 00:46:40,760
And I used it for times tables 
because I was in year 4 big 

1123
00:46:40,760 --> 00:46:42,800
focus on times tables. 
I did a lot of times tables in 

1124
00:46:42,800 --> 00:46:45,120
there. 
I did a lot of recapping stuff 

1125
00:46:45,360 --> 00:46:48,440
if I finished my block and I was
like, I, I had a set that maybe 

1126
00:46:48,440 --> 00:46:49,800
needed more support in maths, 
let's say. 

1127
00:46:50,240 --> 00:46:52,320
And I finished my block and I 
thought, do you know what? 

1128
00:46:53,240 --> 00:46:55,720
OK, I might sometimes choose to 
just do it for another week or 

1129
00:46:55,720 --> 00:46:57,200
two. 
And that's also fine. 

1130
00:46:57,200 --> 00:46:59,320
You've got to be flexible. 
But I might think, you know, I 

1131
00:46:59,320 --> 00:47:00,640
really just need to move on 
actually. 

1132
00:47:00,640 --> 00:47:02,600
So I'm going to move on. 
Lots of them got it, but some of

1133
00:47:02,600 --> 00:47:04,520
them didn't. 
Then I'd use that time to go 

1134
00:47:04,520 --> 00:47:06,400
over that, become more fluent. 
Reteach some bits. 

1135
00:47:06,400 --> 00:47:09,920
Literally, I would use a lot of 
that time to do some problem 

1136
00:47:09,920 --> 00:47:12,320
solving because I found myself 
with my class who needed more 

1137
00:47:12,320 --> 00:47:15,000
fluency. 
I really started to resent the 

1138
00:47:15,000 --> 00:47:17,000
fact that I felt like I wasn't 
doing enough problem solving 

1139
00:47:17,000 --> 00:47:18,560
with them in those lessons. 
So I thought, you know what I'm 

1140
00:47:18,560 --> 00:47:20,080
going to, I'm going to make sure
I do this in this time. 

1141
00:47:20,080 --> 00:47:21,760
You nail the fluency in the 
lesson and. 

1142
00:47:21,760 --> 00:47:23,880
Nail it. 
Yeah, I'm reacting to the kids. 

1143
00:47:23,880 --> 00:47:25,360
Like there might be some 
lessons, like you said, where 

1144
00:47:25,360 --> 00:47:27,360
I'm doing it all the time in my 
lessons because the kids are 

1145
00:47:27,360 --> 00:47:28,880
fluent. 
My kids weren't quite fluent. 

1146
00:47:28,880 --> 00:47:30,480
So I thought, you know what, I 
can do my extra time. 

1147
00:47:30,760 --> 00:47:32,600
I'm going through the curriculum
with them and I need to do that 

1148
00:47:33,000 --> 00:47:35,400
in this time. 
I absolutely went on to the year

1149
00:47:35,400 --> 00:47:37,800
2 curriculum, downloaded 
PowerPoints of reasoning, 

1150
00:47:37,800 --> 00:47:39,960
problem solving questions that 
based on what they, what they're

1151
00:47:39,960 --> 00:47:41,280
called. 
And I went, you know what? 

1152
00:47:41,440 --> 00:47:44,520
Yeah, my kids absolutely can 
count that. 

1153
00:47:44,520 --> 00:47:45,600
They can do that. 
That's fine. 

1154
00:47:45,600 --> 00:47:47,440
They're struggling the year for 
objectives, but they can count 

1155
00:47:47,440 --> 00:47:48,960
in twos. 
Let's look at some problem 

1156
00:47:48,960 --> 00:47:51,160
solving questions that use 
counting in twos. 

1157
00:47:51,320 --> 00:47:55,160
So my kids are no longer 
thinking, oh God, I don't know, 

1158
00:47:55,160 --> 00:47:57,520
because I don't know how to do 
the maths and I'm already 

1159
00:47:57,560 --> 00:47:59,600
thinking about these numbers are
too big. 

1160
00:47:59,600 --> 00:48:02,280
I don't really understand. 
No, no, the, the maths itself is

1161
00:48:02,280 --> 00:48:03,960
fine. 
They can put all of their effort

1162
00:48:03,960 --> 00:48:06,640
into thinking, what do I have to
do to solve this problem? 

1163
00:48:06,880 --> 00:48:09,360
And I, I found that chunk of 
time invaluable. 

1164
00:48:09,360 --> 00:48:11,280
And we had to make it really 
clear to everyone. 

1165
00:48:11,360 --> 00:48:15,240
That's 20 to 25 minutes a day. 
And a chunk of that would always

1166
00:48:15,240 --> 00:48:17,240
be practising known facts 
because you have to know, you 

1167
00:48:17,240 --> 00:48:19,200
know, facts and that's fluency. 
And the chunk would be 

1168
00:48:19,200 --> 00:48:21,160
reasoning, problem solving or 
preteaching like you just said. 

1169
00:48:21,360 --> 00:48:24,920
But what was really powerful I 
found because it's what I would 

1170
00:48:24,920 --> 00:48:26,760
have wanted, which is why we 
introduced it in our school. 

1171
00:48:27,080 --> 00:48:29,360
It was all power to the teacher.
Yeah, it was not. 

1172
00:48:29,440 --> 00:48:32,400
I was not coming around and 
saying have you done your 10 

1173
00:48:32,400 --> 00:48:34,560
minutes reason problem solving 
in this little section? 

1174
00:48:35,080 --> 00:48:37,120
I couldn't care less. 
I said to the professional, as 

1175
00:48:37,120 --> 00:48:40,760
the teacher, you are their 
teacher and you teach them 50 

1176
00:48:40,760 --> 00:48:42,080
minutes every single day of 
maths. 

1177
00:48:42,320 --> 00:48:43,960
What are you not giving them 
enough of? 

1178
00:48:44,120 --> 00:48:46,560
What do they need more of? 
What do you decide? 

1179
00:48:46,760 --> 00:48:49,360
If you had another 20 minutes, 
what would you do with the kids?

1180
00:48:49,360 --> 00:48:51,440
Yeah, yeah, yeah. 
Oh, that's interesting. 

1181
00:48:51,560 --> 00:48:53,880
Do that. 
And that is your. 

1182
00:48:53,920 --> 00:48:58,120
And my kids made so much more 
progress because I could be so 

1183
00:48:58,120 --> 00:49:00,840
targeted in that time. 
And just just flipping that a 

1184
00:49:00,840 --> 00:49:03,880
bit, people thinking, well, my 
maths lesson's shorter. 

1185
00:49:03,880 --> 00:49:05,440
You just said your maths lesson 
was 50 minutes. 

1186
00:49:05,680 --> 00:49:07,560
Yeah, because I wasn't obsessed 
with getting through reasoning, 

1187
00:49:07,560 --> 00:49:10,360
problem solving and and doing my
fluency all in one lesson. 

1188
00:49:10,640 --> 00:49:12,760
It can be shorter. 
It's a very small step. 

1189
00:49:12,920 --> 00:49:16,120
The curriculum can be condensed.
50 minutes is genuinely A 

1190
00:49:16,200 --> 00:49:17,600
suitable amount of time. 
It is. 

1191
00:49:17,600 --> 00:49:20,280
I remember thinking so short, 
remember going for an hour to 50

1192
00:49:20,280 --> 00:49:21,880
minutes once and I was like, Oh 
my God, is it possible? 

1193
00:49:21,880 --> 00:49:23,880
How can I possibly teach maths? 
And it's because I was locked in

1194
00:49:23,880 --> 00:49:26,520
that mindset of I have to do 
XYZI, have to get all these 

1195
00:49:26,520 --> 00:49:28,000
elements in. 
It's not a good maths lesson. 

1196
00:49:28,280 --> 00:49:30,400
It's just not true. 
Just take them on the journey. 

1197
00:49:30,600 --> 00:49:33,920
The whole lesson can be fluency.
And I know there's multiple 

1198
00:49:33,920 --> 00:49:37,360
years of my career where I felt 
like I would look terrible if 

1199
00:49:37,360 --> 00:49:39,520
someone looked at my lesson. 
I looked at the book afterwards 

1200
00:49:39,600 --> 00:49:41,680
and I'd only been working on 
fluency in that lesson. 

1201
00:49:42,040 --> 00:49:45,160
And I wish I could go back and 
be like, no, if, if that's what 

1202
00:49:45,160 --> 00:49:47,440
they needed because they were 
not ready. 

1203
00:49:47,520 --> 00:49:50,040
And you felt like it wasn't 
appropriate to do problem 

1204
00:49:50,040 --> 00:49:51,800
solving in this lesson yet. 
And you didn't want to go back 

1205
00:49:51,800 --> 00:49:53,320
to the previous year because 
you're like right in the middle 

1206
00:49:53,320 --> 00:49:56,440
of this little journey and you 
just wanted to finish off making

1207
00:49:56,440 --> 00:49:59,520
sure they're really fluent. 
Then that's what you need to do.

1208
00:49:59,520 --> 00:50:01,560
And that is OK. 
You didn't need to do that 

1209
00:50:01,560 --> 00:50:03,600
reasoning, problem solving that 
you planned because you got told

1210
00:50:03,600 --> 00:50:06,120
to push it into a starter in 
another week. 

1211
00:50:06,360 --> 00:50:08,440
Maybe you don't even use it or 
maybe use it in tomorrow's 

1212
00:50:08,440 --> 00:50:10,080
season, whatever. 
But that's, that was the right 

1213
00:50:10,080 --> 00:50:11,280
choice. 
You adapted on the spot and they

1214
00:50:11,280 --> 00:50:13,120
needed to become fluent. 
And there's one thing I will 

1215
00:50:13,120 --> 00:50:14,880
just say, and we'll clarify this
right now because it sounds like

1216
00:50:14,880 --> 00:50:16,600
we're being, I feel like we're, 
don't people think we're being a

1217
00:50:16,600 --> 00:50:18,520
bit wishy wishy of like, Hey, 
you just do everything ever, 

1218
00:50:18,520 --> 00:50:21,920
ever, all the time. 
One thing I absolutely did just 

1219
00:50:21,920 --> 00:50:25,200
nail and hammer all the time in 
my status was at the end of the 

1220
00:50:25,200 --> 00:50:27,920
day, arithmetic. 
I would say at at minimum, 

1221
00:50:27,960 --> 00:50:32,720
minimum once per week, my extra 
2025 minutes was dedicated to 

1222
00:50:32,800 --> 00:50:36,000
recapping or reteaching very 
specifically at the fluency 

1223
00:50:36,000 --> 00:50:38,040
level, some arithmetic. 
And that yeah, that might 

1224
00:50:38,040 --> 00:50:40,840
include, I've presented it in, 
in its inverse format or I've 

1225
00:50:40,840 --> 00:50:42,720
put the equal sign on the other 
side just to give them that bit 

1226
00:50:42,720 --> 00:50:45,360
of variety. 
But ultimately it was, I need us

1227
00:50:45,360 --> 00:50:47,080
to re practise this method 
because I taught this to you a 

1228
00:50:47,080 --> 00:50:49,040
month ago. 
We haven't divided decimals by 

1229
00:50:49,040 --> 00:50:51,360
numbers in a while because 
realistically that's one of 19 

1230
00:50:51,360 --> 00:50:54,600
objectives by the by year 6. 
Here's here's 5 questions 

1231
00:50:54,600 --> 00:50:56,080
dividing decimals. 
Can we remember it? 

1232
00:50:56,280 --> 00:50:58,720
You've forgotten it. 
Cool. 22nd recap. 

1233
00:50:58,720 --> 00:51:00,960
Because you were fluent. 
You were here before you were 

1234
00:51:00,960 --> 00:51:02,960
super fluent. 
You've just dropped down a tiny 

1235
00:51:02,960 --> 00:51:03,840
bit. 
I'm just getting you back up 

1236
00:51:03,840 --> 00:51:04,560
there. 
Do you remember that? 

1237
00:51:04,560 --> 00:51:05,640
Oh yeah, I remember that now. 
Brilliant. 

1238
00:51:05,640 --> 00:51:06,800
We've practised it for 10 
minutes. 

1239
00:51:07,000 --> 00:51:11,600
Move on. 
So arithmetic embedded in in my 

1240
00:51:11,600 --> 00:51:14,080
starters all the time. 
I did it every single day in 

1241
00:51:14,080 --> 00:51:16,160
year 4, like every single day. 
It was, it was not even a 

1242
00:51:16,160 --> 00:51:18,000
question. 
Like my kids got to the point 

1243
00:51:18,000 --> 00:51:19,880
where they're like, oh, here it 
is the five questions again. 

1244
00:51:19,920 --> 00:51:21,600
Because I do 5 arithmetic 
questions every day. 

1245
00:51:21,960 --> 00:51:24,120
Some days it might just be 
addition. 

1246
00:51:24,480 --> 00:51:27,120
Some days it might just be 
addition with different digits 

1247
00:51:27,400 --> 00:51:29,080
because I know for a fact it's a
misconception. 

1248
00:51:29,080 --> 00:51:30,320
They can't learn at their 
numbers properly. 

1249
00:51:30,640 --> 00:51:33,880
Some days it might be a mixture 
where I've said, actually, you 

1250
00:51:33,880 --> 00:51:35,200
know what? 
We've done so much work over the

1251
00:51:35,200 --> 00:51:37,320
last couple weeks. 
Here are 5 questions with five 

1252
00:51:37,320 --> 00:51:40,560
different question types. 
It's still arithmetic, but now 

1253
00:51:40,680 --> 00:51:43,960
you're showing me your fluency 
and your reasoning because you 

1254
00:51:43,960 --> 00:51:45,080
need to work out what to do each
time. 

1255
00:51:45,360 --> 00:51:47,600
It's not just doing the process 
to process, not reading it, 

1256
00:51:47,600 --> 00:51:50,040
understanding the symbols. 
It's still a part of reasoning. 

1257
00:51:50,040 --> 00:51:54,000
It's still fluency, but it's 
that really important skill that

1258
00:51:54,000 --> 00:51:56,600
children need to be able to do 
math quickly and accurately. 

1259
00:51:56,720 --> 00:51:59,240
They have to be fluent. 
And arithmetic is the perfect 

1260
00:51:59,240 --> 00:52:02,520
example of that. 
You have to be accurate. 

1261
00:52:02,520 --> 00:52:05,280
And I'd say it to my children 
and I'd, I'd be saying it in a 

1262
00:52:05,280 --> 00:52:08,080
way where like it's a really 
nice supportive thing where I'd 

1263
00:52:08,080 --> 00:52:11,840
say to them, I know for a fact 
when we finish year 4, every 

1264
00:52:11,840 --> 00:52:15,280
single person in this room 
would, will be able to, I say, 

1265
00:52:15,280 --> 00:52:18,440
will will be able to answer 
every single question on your 

1266
00:52:18,440 --> 00:52:20,720
repeated paper. 
You might make a mistake, that's

1267
00:52:20,720 --> 00:52:23,480
fine. 
You might get there and rush 

1268
00:52:23,480 --> 00:52:26,120
through something or miss an 
exchange, That's OK. 

1269
00:52:26,480 --> 00:52:29,560
But I know through my coverage 
and my daily practise and my 

1270
00:52:29,560 --> 00:52:33,320
fluency that I know everyone in 
the room can answer that 

1271
00:52:33,320 --> 00:52:34,880
question. 
And that's all I want to get to 

1272
00:52:34,880 --> 00:52:36,280
guys. 
And then we'd be doing a 

1273
00:52:36,280 --> 00:52:38,520
repetite at the end of the year,
it's out of 40 and my class 

1274
00:52:38,520 --> 00:52:41,720
would be averaging 35 and the 
odd mistake. 

1275
00:52:41,880 --> 00:52:44,360
But there wouldn't be anything 
that a child goes, yeah, I've 

1276
00:52:44,360 --> 00:52:46,320
never seen that before because I
do it every day. 

1277
00:52:46,640 --> 00:52:48,120
I'm not remember at all. 
Exactly. 

1278
00:52:48,120 --> 00:52:50,680
And that's where this, this idea
of our maths platform has kind 

1279
00:52:50,680 --> 00:52:52,880
of come from. 
It's like, OK, how can we make 

1280
00:52:52,880 --> 00:52:55,680
it easy for teachers to do this?
Because I know the power of 

1281
00:52:55,680 --> 00:52:58,680
doing arithmetic every single 
day and getting fluent in being 

1282
00:52:58,680 --> 00:53:01,400
able to actually do the maths. 
But a teacher might not quite 

1283
00:53:01,400 --> 00:53:02,960
get the nuances of the different
questions. 

1284
00:53:03,080 --> 00:53:05,640
They might not quite understand 
maybe why there's, you know, 2 

1285
00:53:05,640 --> 00:53:07,960
exchanging in this question or 
going past the bridging past the

1286
00:53:07,960 --> 00:53:10,840
zero makes it harder, etcetera. 
And even if there are teachers 

1287
00:53:10,840 --> 00:53:13,560
who get that, it can be time 
consuming and frustrating to 

1288
00:53:13,560 --> 00:53:16,320
make sure you get coverage. 
And it can be time consuming and

1289
00:53:16,320 --> 00:53:19,600
annoying to get every individual
child's data and be like, well, 

1290
00:53:19,600 --> 00:53:20,920
that child can't do this, this 
and this. 

1291
00:53:21,040 --> 00:53:22,160
This child can't do that and 
that. 

1292
00:53:22,160 --> 00:53:23,120
But it's a different one as 
well. 

1293
00:53:23,120 --> 00:53:25,840
They can't do. 
Our platform is going to be 

1294
00:53:25,840 --> 00:53:29,160
something where you can really 
easily harvest this information 

1295
00:53:29,160 --> 00:53:30,600
from the children. 
They can practise it. 

1296
00:53:30,760 --> 00:53:33,000
They can do it every day. 
They get what they need. 

1297
00:53:33,000 --> 00:53:36,320
It's adaptive to them. 
And it's going to be so powerful

1298
00:53:36,680 --> 00:53:38,800
to get children better 
arithmetic. 

1299
00:53:38,800 --> 00:53:40,400
And it's something they don't 
have to do for an hour a day. 

1300
00:53:40,400 --> 00:53:42,120
They can do it for 10 minutes. 
Yeah, yeah, yeah. 

1301
00:53:42,120 --> 00:53:45,120
They can do a test, they can do 
a bit of practise on what they 

1302
00:53:45,120 --> 00:53:46,920
need. 
And the teachers can go in and 

1303
00:53:46,920 --> 00:53:48,520
say, actually I want this, this 
and this question. 

1304
00:53:48,680 --> 00:53:51,360
Generate me 10 done. 
Yeah, it's it's going to be. 

1305
00:53:51,360 --> 00:53:55,640
So I'm so gassed about it 
because anyone listening to this

1306
00:53:55,640 --> 00:53:57,800
who kind of gets what we're 
saying here about arithmetic, a 

1307
00:53:57,800 --> 00:53:59,200
lot of people already message 
about it. 

1308
00:53:59,480 --> 00:54:01,720
Message us and just let us know 
if it's something that interests

1309
00:54:01,720 --> 00:54:04,400
you because it's going to be so 
powerful. 

1310
00:54:04,560 --> 00:54:08,920
And the reason we're doing it is
not because we're saying teach 

1311
00:54:08,920 --> 00:54:10,760
to a test. 
You just got to be able to do 

1312
00:54:10,760 --> 00:54:13,000
arithmetic. 
Hayden, I'm hoping for what 

1313
00:54:13,000 --> 00:54:15,480
we've said today. 
You can really understand that 

1314
00:54:15,480 --> 00:54:18,640
unless you've nailed that, the 
true goal is pointless. 

1315
00:54:18,720 --> 00:54:21,600
Yeah, You can't build on top of 
broken foundations. 

1316
00:54:21,960 --> 00:54:23,400
You need to have the foundations
in place. 

1317
00:54:23,560 --> 00:54:26,480
We are trying to target the 
thing that matters the most, 

1318
00:54:26,640 --> 00:54:29,840
which is the foundation. 
And we know one of the side 

1319
00:54:29,840 --> 00:54:33,080
effects of mass mastery is the 
misconception of having to do. 

1320
00:54:33,120 --> 00:54:35,080
We just need to put in loads 
more reasoning and problem 

1321
00:54:35,080 --> 00:54:36,440
solving. 
And the horrible side effect of 

1322
00:54:36,440 --> 00:54:39,640
that is in some places, in some 
schools, in some classrooms, 

1323
00:54:39,920 --> 00:54:41,880
arithmetic and fluency is 
actually getting a little bit 

1324
00:54:41,880 --> 00:54:44,160
weaker because what they would 
have been doing way more of that

1325
00:54:44,160 --> 00:54:45,800
before, they're now not doing as
much because they think they 

1326
00:54:45,800 --> 00:54:46,720
have to. 
I've got to do reasonable 

1327
00:54:46,720 --> 00:54:49,000
problem solving every lesson. 
And now they're not as fluent. 

1328
00:54:49,000 --> 00:54:50,080
And it's like, oh, man, we need 
it. 

1329
00:54:50,080 --> 00:54:51,480
We. 
Yeah, we're trying to tackle the

1330
00:54:51,480 --> 00:54:52,640
problem from every angle. 
Yeah. 

1331
00:54:53,120 --> 00:54:55,080
Yeah. 
I I had a conversation with 

1332
00:54:55,080 --> 00:54:58,280
someone the other day who said 
they're in year 6. 

1333
00:54:58,280 --> 00:55:00,800
They messaged us and they said 
our school is thinking of 

1334
00:55:00,800 --> 00:55:04,600
starting to do arithmetic every 
week and I was like, sure what? 

1335
00:55:06,040 --> 00:55:08,920
They were doing excuse. 
Me and it's like people go so 

1336
00:55:08,920 --> 00:55:11,680
far down this road of schemes 
and I suppose just wanted to get

1337
00:55:11,680 --> 00:55:14,640
your quick thought on schemes 
because I am not anti scheme. 

1338
00:55:14,640 --> 00:55:19,080
I think schemes are really good.
However, when implemented really

1339
00:55:19,080 --> 00:55:22,720
robustly and strictly and 
stringently and, and badly, they

1340
00:55:22,720 --> 00:55:24,840
can be awful. 
And I think this is a symptom of

1341
00:55:24,840 --> 00:55:28,040
this where schools might buy 
into schemes or say, yeah, we've

1342
00:55:28,040 --> 00:55:29,760
got this. 
It's, it's rooted in evidence, 

1343
00:55:29,760 --> 00:55:33,360
It's a good scheme and it has 
lots of chances, fluency and 

1344
00:55:33,360 --> 00:55:35,040
reasoning and problem solving, 
all that kind of stuff. 

1345
00:55:35,520 --> 00:55:39,560
But maybe it's missing just 
enough to just practise and 

1346
00:55:39,560 --> 00:55:42,120
become really fluent in actually
doing the maths and then a 

1347
00:55:42,120 --> 00:55:45,280
school doesn't do it because 
they're so wedded to the scheme 

1348
00:55:45,280 --> 00:55:47,560
so very quickly. 
If you could just summarise our 

1349
00:55:47,560 --> 00:55:49,120
thoughts on schemes. 
So now we're on the same page 

1350
00:55:49,120 --> 00:55:52,080
here. 
Is that a reason to bin schemes 

1351
00:55:52,080 --> 00:55:53,440
or do you just think, look, come
on. 

1352
00:55:53,920 --> 00:55:56,000
Absolutely not scheme. 
I'm going to say what I said 

1353
00:55:56,000 --> 00:55:57,360
earlier. 
Schemes are really good for 

1354
00:55:57,360 --> 00:55:59,560
mapping coverage of lesson 
objectives that you're teaching 

1355
00:55:59,560 --> 00:56:01,600
the main bit of your lesson. 
Schemes are very good at that. 

1356
00:56:01,600 --> 00:56:03,840
What I feel like schemes lack a 
lot of, and which is another 

1357
00:56:03,840 --> 00:56:06,200
reason we're doing this, is 
because we feel like it's not 

1358
00:56:06,200 --> 00:56:08,040
there. 
What schemes aren't so good at 

1359
00:56:08,040 --> 00:56:11,320
is taking something like just 
arithmetic and providing loads 

1360
00:56:11,320 --> 00:56:14,120
of resources and loads of 
fluency tools and ways for you 

1361
00:56:14,120 --> 00:56:16,880
to just practise that bit and 
saying like, oh hey, in your 20 

1362
00:56:16,880 --> 00:56:18,720
minute segment that you do in 
the afternoon or in your 20 

1363
00:56:18,720 --> 00:56:20,320
minute segment that you do at 
the beginning of your lesson. 

1364
00:56:20,320 --> 00:56:22,760
However, your school allocates 
this bit of extra time that 

1365
00:56:22,760 --> 00:56:24,000
we're talking about. 
Like Dylan said earlier, it 

1366
00:56:24,000 --> 00:56:25,240
doesn't need to be within your 
maths lesson. 

1367
00:56:25,240 --> 00:56:26,440
It could be another part of the 
day. 

1368
00:56:27,120 --> 00:56:28,480
Here's the resources and map for
that. 

1369
00:56:28,480 --> 00:56:29,840
And this is how this is some 
great. 

1370
00:56:29,920 --> 00:56:33,440
It doesn't exist, I don't think 
not not to a not to a level that

1371
00:56:33,440 --> 00:56:36,040
I think is good enough, which is
why we are building this 

1372
00:56:36,040 --> 00:56:38,640
arithmetic tour. 
That is going to be I, I, I'm 

1373
00:56:38,640 --> 00:56:40,680
getting too, I get too excited 
about have to calm myself down. 

1374
00:56:40,680 --> 00:56:42,880
But I genuinely think it's going
to be transformational because I

1375
00:56:42,880 --> 00:56:46,080
think if you get those 
foundations right with a really,

1376
00:56:46,080 --> 00:56:50,440
really good adaptive tool that 
works at the exact nuances of, 

1377
00:56:50,600 --> 00:56:52,920
you gave an example. 
When you've got a tool that 

1378
00:56:52,920 --> 00:56:55,640
knows the difference between a 
four digit number, add a three 

1379
00:56:55,640 --> 00:56:58,520
digit number with exchange with 
exchange or exchange and the 

1380
00:56:58,520 --> 00:57:00,440
different and all of the 
combinations of that and 

1381
00:57:00,440 --> 00:57:03,440
understands those nuances. 
And if I want, if I want more of

1382
00:57:03,440 --> 00:57:04,960
these questions, it's like, 
yeah, you can have more of these

1383
00:57:04,960 --> 00:57:06,400
questions because that's what 
you want to practise. 

1384
00:57:06,400 --> 00:57:08,560
Like you said in your starter, 
you might practise one day. 

1385
00:57:08,840 --> 00:57:10,960
A very specific misconception 
that your kids are making. 

1386
00:57:10,960 --> 00:57:13,960
Give them five more of those A. 
Misconception, which literally 

1387
00:57:13,960 --> 00:57:16,320
couldn't be taught if you just 
did random numbers exactly 

1388
00:57:16,320 --> 00:57:18,120
because if you're doing random 
numbers, you might not get 

1389
00:57:18,120 --> 00:57:20,440
exchanging, you might not get 
the same number of digits, 

1390
00:57:20,440 --> 00:57:21,840
etcetera. 
You're so right. 

1391
00:57:21,840 --> 00:57:23,920
And it has it. 
This is where it's going to be 

1392
00:57:23,920 --> 00:57:26,960
transformative because you can 
create 100 questions 

1393
00:57:27,200 --> 00:57:29,480
regenerating the same thing. 
And do you know why I think it's

1394
00:57:29,480 --> 00:57:32,360
going to be such a good tool? 
Because it it puts together 2 

1395
00:57:32,480 --> 00:57:35,120
things that we're really 
passionate about. 1 is quality 

1396
00:57:35,120 --> 00:57:38,480
maths teaching and whether you 
are adept to it or not. 

1397
00:57:38,480 --> 00:57:40,800
I'm not judging you as an 
individual because some people 

1398
00:57:40,800 --> 00:57:42,480
are much more adept, like we 
know it inside out. 

1399
00:57:42,720 --> 00:57:44,040
Other people won't and that's 
fine. 

1400
00:57:44,040 --> 00:57:45,640
Their passion might be English, 
but they've got to teach maths 

1401
00:57:45,640 --> 00:57:46,760
and they're really good at 
teaching maths. 

1402
00:57:47,320 --> 00:57:50,240
Whether or not you're, you're 
really, really like to clued on 

1403
00:57:50,400 --> 00:57:54,120
this can do it for you. 
And what it does is then allows 

1404
00:57:54,120 --> 00:57:57,360
you to teach, this isn't going 
to be the thing that like 

1405
00:57:57,360 --> 00:58:00,520
suddenly just takes over your 
class and teaches children how 

1406
00:58:00,520 --> 00:58:03,080
to do it more than you know. 
What this is going to do is give

1407
00:58:03,080 --> 00:58:06,720
you the tools to be able to 
teach it so well and save you 

1408
00:58:06,720 --> 00:58:10,440
time and give you exact things 
that the children need and do 

1409
00:58:10,440 --> 00:58:13,320
gap analysis for you and give 
them targeted intervention. 

1410
00:58:13,520 --> 00:58:15,560
It's going to do that. 
And then you as the teacher can 

1411
00:58:15,560 --> 00:58:18,480
go around and say, right, you're
struggling with this 5 minutes 

1412
00:58:18,480 --> 00:58:20,520
with the white board, let's go. 
And you can teach them it. 

1413
00:58:20,520 --> 00:58:22,200
It's so powerful. 
Can I fix because now we're 

1414
00:58:22,200 --> 00:58:24,200
getting super excited. 
Can I finish by telling that 

1415
00:58:24,200 --> 00:58:26,600
there's a, there's a moment that
I can think of where I was like,

1416
00:58:27,160 --> 00:58:29,120
this tool just doesn't exist. 
This doesn't exist and I need 

1417
00:58:29,120 --> 00:58:30,960
it. 
Which was it was it was a SATS 

1418
00:58:30,960 --> 00:58:32,960
question that I was looking at. 
It was I can't the exact one. 

1419
00:58:32,960 --> 00:58:35,480
It was something along the lines
of like 2 1/2, lots of 57. 

1420
00:58:35,560 --> 00:58:37,720
It was a really horrible. 
It was like the last question in

1421
00:58:37,720 --> 00:58:39,680
the SATS paper once. 
And I was like, that's rancid in

1422
00:58:39,680 --> 00:58:42,760
terms of giving the kids that 
and I wanted to have more. 

1423
00:58:42,760 --> 00:58:44,440
I just, I was like, I want to 
practise these questions because

1424
00:58:44,440 --> 00:58:46,280
that's actually really hard. 
I've got a high mass set on a on

1425
00:58:46,280 --> 00:58:48,960
a practise mixed numbers times 
like really horrible numbers 

1426
00:58:48,960 --> 00:58:50,720
where you can't even divide by 
the denomination. 

1427
00:58:50,720 --> 00:58:53,240
Like 50 doesn't divide by two 
without going to decimals. 

1428
00:58:53,400 --> 00:58:55,360
It's horrible. 
And when I used a random number 

1429
00:58:55,360 --> 00:58:58,240
generator to just like generate 
more, they just, they didn't 

1430
00:58:58,240 --> 00:59:01,000
get, they didn't get the nuance.
It gave me stuff like 2 1/2, 

1431
00:59:01,000 --> 00:59:02,560
lots of 20. 
And I was like, no, this isn't 

1432
00:59:02,560 --> 00:59:05,920
what I want. 
I want it to understand so why 

1433
00:59:05,920 --> 00:59:07,880
this is hard. 
So we're building this all that 

1434
00:59:07,880 --> 00:59:10,000
does that and that's it. 
That's it for me. 

1435
00:59:10,000 --> 00:59:12,120
I was like, I need to that needs
to exist and that needs to exist

1436
00:59:12,120 --> 00:59:13,880
and it needs to get every single
level of nuance on every 

1437
00:59:13,880 --> 00:59:16,600
question and be able to just 
give me 10 more like that, you 

1438
00:59:16,600 --> 00:59:18,840
know, anyways, but. 
You're right, you're right. 

1439
00:59:18,840 --> 00:59:20,440
And I think this is it's built 
in. 

1440
00:59:20,680 --> 00:59:23,080
Hopefully again from this whole 
episode, you get how much we 

1441
00:59:23,080 --> 00:59:24,640
love maths. 
We're obsessed with maths. 

1442
00:59:24,920 --> 00:59:27,000
We get good results for our 
children. 

1443
00:59:27,000 --> 00:59:29,680
We literally, it's what our 
passion is. 

1444
00:59:30,160 --> 00:59:35,640
And the ability to have been 
building this makes me so happy 

1445
00:59:35,800 --> 00:59:39,320
because I'm not building this. 
And then, oh, yeah, it's 

1446
00:59:39,320 --> 00:59:40,920
important because I've built 
this thing. 

1447
00:59:41,040 --> 00:59:43,640
No, I, I, I believe everything 
I've said in this whole episode.

1448
00:59:43,720 --> 00:59:44,960
Yeah. 
And that's why I think this is 

1449
00:59:44,960 --> 00:59:47,360
such a thing that I've thought 
for years would be so powerful 

1450
00:59:47,360 --> 00:59:49,680
and good to build. 
It's happening like it's going 

1451
00:59:49,680 --> 00:59:52,280
to be so, so, so useful. 
Watch this space, guys. 

1452
00:59:52,320 --> 00:59:54,200
Yeah, keep asking us, because 
every time you ask us questions 

1453
00:59:54,200 --> 00:59:55,760
about it, we get really giddy 
and excited. 

1454
00:59:56,160 --> 00:59:58,720
So excited we're going to wrap 
it up, but there's just one last

1455
00:59:58,720 --> 01:00:00,680
thing I wanted to mention. 
And I don't think we need to go 

1456
01:00:00,680 --> 01:00:02,480
into detail about it because 
we've gone into so much detail 

1457
01:00:02,480 --> 01:00:04,480
already. 
But I think part of the problem 

1458
01:00:04,920 --> 01:00:07,280
if we're going back full circle 
is obviously preparing for the 

1459
01:00:07,280 --> 01:00:08,240
test, right? 
Yeah. 

1460
01:00:08,240 --> 01:00:10,520
So think about SAT at the end 
and we're thinking, oh, well, 

1461
01:00:10,520 --> 01:00:12,280
yeah, you're just creating a 
thing that helps you prepare for

1462
01:00:12,280 --> 01:00:13,560
the SAT. 
Yeah, it does. 

1463
01:00:13,560 --> 01:00:14,840
It does help you prepare for the
SAT. 

1464
01:00:15,320 --> 01:00:16,640
It also makes kids better at 
maths. 

1465
01:00:16,960 --> 01:00:19,120
But the Venn diagram can 
overlap, right? 

1466
01:00:19,680 --> 01:00:21,640
Just because you're preparing 
for the test doesn't necessarily

1467
01:00:21,640 --> 01:00:23,600
mean everything you're doing is 
bad for the kids. 

1468
01:00:23,880 --> 01:00:26,640
Fundamentally, knowing how to do
maths and practising and getting

1469
01:00:26,640 --> 01:00:29,200
quicker and more accurate makes 
you a better mathematician. 

1470
01:00:29,320 --> 01:00:31,240
Does it also mean you're going 
to boost your arithmetic scores 

1471
01:00:31,240 --> 01:00:32,760
in your Sats? 
Yeah, Yeah, it does. 

1472
01:00:32,880 --> 01:00:35,080
And and that's good as well, 
because you're better at maths. 

1473
01:00:35,080 --> 01:00:37,600
Because you're better at maths, 
not because you're just knowing 

1474
01:00:37,600 --> 01:00:40,280
how to get around a test or 
fudge your way through. 

1475
01:00:40,360 --> 01:00:42,520
No, you can do maths more 
quickly and more accurately. 

1476
01:00:42,920 --> 01:00:46,160
And one thing I was going to put
over to you about the sats, you,

1477
01:00:46,160 --> 01:00:47,360
you're in your 6 for a long 
time. 

1478
01:00:48,000 --> 01:00:49,960
I've never liked the naming of 
the sats. 

1479
01:00:50,280 --> 01:00:52,640
Sounds ridiculous. 
There's arithmetic paper and a 

1480
01:00:52,640 --> 01:00:54,400
reasoning paper. 
And I'm like, oh, what? 

1481
01:00:54,560 --> 01:00:56,680
Like what? 
Like, OK, there are reasoning 

1482
01:00:56,680 --> 01:00:59,520
questions, I suppose. 
Like explain this in the thought

1483
01:00:59,520 --> 01:01:01,280
bubble. 
Of course that's a reasoning 

1484
01:01:01,280 --> 01:01:04,040
question. 
Fine, but the reasoning paper 

1485
01:01:04,160 --> 01:01:05,400
has fluency in it. 
Yep. 

1486
01:01:05,560 --> 01:01:07,680
It's not reasoning. 
It has just straight up fluency 

1487
01:01:07,680 --> 01:01:09,040
questions like order these 
numbers. 

1488
01:01:10,120 --> 01:01:12,160
Like it just has like how you 
know, how many sides does a 

1489
01:01:12,160 --> 01:01:13,760
square have kind of thing. 
Like it has those kind of 

1490
01:01:13,760 --> 01:01:15,560
fluency questions. 
It has some reasoning and it's 

1491
01:01:15,560 --> 01:01:16,880
filled with problem solving, 
yeah as well. 

1492
01:01:17,320 --> 01:01:20,320
It's, it has always annoyed me 
because I feel like it 

1493
01:01:20,320 --> 01:01:22,200
contributes to the problem of 
like people getting confused 

1494
01:01:22,200 --> 01:01:24,680
between the problem. 
Because realistically what's 

1495
01:01:24,680 --> 01:01:27,440
happening is, yeah, you've kind 
of summarised it, the two 

1496
01:01:27,440 --> 01:01:29,280
papers. 
It, it feels like it's supposed 

1497
01:01:29,280 --> 01:01:32,000
to say we have a fluency paper 
and then we have a reasoning 

1498
01:01:32,000 --> 01:01:33,600
problem solving paper. 
I feel like that's how people 

1499
01:01:33,760 --> 01:01:35,760
interpret that when they see 
arithmetic and reasoning. 

1500
01:01:35,760 --> 01:01:37,840
They're like, OK, that's the 
split they make in their mind. 

1501
01:01:37,840 --> 01:01:40,960
But really the split is, yeah, 
we have this really a subset of 

1502
01:01:41,120 --> 01:01:43,200
of fluency, which is arithmetic 
as one paper. 

1503
01:01:43,480 --> 01:01:46,400
And then we have all of the rest
of fluency, all of problem 

1504
01:01:46,400 --> 01:01:48,520
solving, and all of reasoning 
that comes in between that, 

1505
01:01:48,520 --> 01:01:49,720
because reasoning is just 
everything. 

1506
01:01:49,720 --> 01:01:52,120
Because I I think I think 
there's some reasoning in 

1507
01:01:52,120 --> 01:01:53,560
arithmetic. 
Some some people might tell me 

1508
01:01:53,560 --> 01:01:54,920
I'm wrong here. 
What is the example I gave 

1509
01:01:54,920 --> 01:01:56,840
earlier? 
Exactly like the the idea of in 

1510
01:01:56,840 --> 01:02:00,400
arithmetic, the, you know, yeah,
OK, being fluent includes the 

1511
01:02:00,400 --> 01:02:02,680
ability to know which method to 
go for and why etcetera. 

1512
01:02:02,880 --> 01:02:06,080
But but that is reasoning. 
Like it inherently is the 

1513
01:02:06,080 --> 01:02:07,640
thought process of do you know 
what? 

1514
01:02:07,640 --> 01:02:09,800
I'm in this test. 
I've got a method here that'll 

1515
01:02:09,800 --> 01:02:13,120
take me 10 seconds or a method 
that'll take me a minute knowing

1516
01:02:13,120 --> 01:02:14,760
to go for the 10 second one. 
That's reasoning. 

1517
01:02:14,760 --> 01:02:15,520
You're thinking it's. 
True. 

1518
01:02:15,520 --> 01:02:17,200
I've got a really good example 
of that which I'll say really 

1519
01:02:17,200 --> 01:02:18,600
quickly. 
Long division always happens, 

1520
01:02:18,600 --> 01:02:20,640
right? 
If you, if you give a child A4 

1521
01:02:20,640 --> 01:02:23,320
digit number divided by 45 and 
another question, it's a four 

1522
01:02:23,320 --> 01:02:27,040
digit number divided by 47. 
A child that hasn't been taught 

1523
01:02:27,040 --> 01:02:29,480
fluency properly with very 
fluency might just have one 

1524
01:02:29,480 --> 01:02:31,040
method they use that works. 
And do you know what they could 

1525
01:02:31,040 --> 01:02:32,000
get it right? 
And that's fine. 

1526
01:02:32,160 --> 01:02:34,640
But the reason comes into play 
when you go, oh, some children 

1527
01:02:34,720 --> 01:02:37,600
will look at 45 and think, I can
factorise that into two short 

1528
01:02:37,600 --> 01:02:39,080
divisions. 
I can divide by 9, get an 

1529
01:02:39,080 --> 01:02:41,960
answer, divide that by 5, making
it on the whole a lot easier 

1530
01:02:41,960 --> 01:02:43,920
because I don't have to think 
about the 45 times tables and 

1531
01:02:43,920 --> 01:02:46,080
finding huge remainders. 
That's way quicker to me. 

1532
01:02:46,080 --> 01:02:48,360
And another child when you look 
at 47, they'll go, oh, that's a 

1533
01:02:48,360 --> 01:02:50,480
prime. 
I can't, I can't factorise this 

1534
01:02:50,480 --> 01:02:52,120
into into two times tables that 
I know. 

1535
01:02:52,120 --> 01:02:54,160
So I'm going to have to just do 
this, my long division method. 

1536
01:02:54,400 --> 01:02:56,240
And in the first one, they save 
loads of time, and the second 

1537
01:02:56,240 --> 01:02:57,280
one, they're using the proper 
method. 

1538
01:02:57,280 --> 01:02:58,600
And you're telling me they 
haven't done reasoning? 

1539
01:02:59,040 --> 01:03:00,360
Yeah, that's what I mean. 
Like that. 

1540
01:03:00,360 --> 01:03:01,680
Then that's in the arithmetic 
paper. 

1541
01:03:01,680 --> 01:03:03,160
Exactly. 
So reasoning kind of is 

1542
01:03:03,160 --> 01:03:05,200
everywhere, yet we call one of 
the papers reasoning. 

1543
01:03:05,640 --> 01:03:07,560
I get it because it's more 
reasoning. 

1544
01:03:07,560 --> 01:03:11,040
Arithmetic is more stripped. 
But it's not reasoning to just 

1545
01:03:11,040 --> 01:03:14,320
be able to do a number that's 
adding ten. 

1546
01:03:14,560 --> 01:03:16,000
But how often does that come up 
in the reasoning? 

1547
01:03:16,000 --> 01:03:17,880
What's 10 more? 
What they do is to make it look 

1548
01:03:17,880 --> 01:03:19,800
different though, is they'll put
three of them in one question. 

1549
01:03:19,800 --> 01:03:22,720
It'll be like this 1 + 10, this 
1 + 10, this 1 + 10, this one 

1550
01:03:22,720 --> 01:03:24,280
plus what equals this. 
You have to get all three to get

1551
01:03:24,280 --> 01:03:26,760
one mark and it's. 
Like each one of those questions

1552
01:03:26,760 --> 01:03:28,680
could have in the paper. 
Yeah, if it was just one of 

1553
01:03:28,680 --> 01:03:31,400
them. 
So yeah, that's all I would say.

1554
01:03:31,400 --> 01:03:33,160
It's slightly confusing. 
I don't think it's an issue. 

1555
01:03:33,240 --> 01:03:35,040
Like I said, I think reasoning 
permeates everything. 

1556
01:03:35,040 --> 01:03:37,480
I don't think you can say it's 
not reasoning. 

1557
01:03:37,480 --> 01:03:40,440
It's annoying, but I just think 
it just helps to push the 

1558
01:03:40,440 --> 01:03:42,640
narrative of a bit of misunder. 
I mean, on the upside as well, 

1559
01:03:42,640 --> 01:03:44,880
it does also just kind of 
reinforce the idea that 

1560
01:03:45,320 --> 01:03:47,280
arithmetic is unbelievably 
important because they felt the 

1561
01:03:47,280 --> 01:03:49,520
need to put an entire paper to 
that part of fluency. 

1562
01:03:49,520 --> 01:03:50,800
Yes. 
And then call them, you know, 

1563
01:03:50,800 --> 01:03:52,000
the naming we can, we can 
disagree with. 

1564
01:03:52,000 --> 01:03:54,480
But yeah, ultimately arithmetic 
is like, yeah, it's essential. 

1565
01:03:54,640 --> 01:03:56,520
It's an essential underpinning 
part of maths. 

1566
01:03:56,520 --> 01:03:58,920
And we should be looking at can 
the kids do the maths and then 

1567
01:03:58,920 --> 01:04:01,440
also looking at can the kids 
apply in any context, you know? 

1568
01:04:01,640 --> 01:04:05,320
Absolutely got I, that is 
probably my favourite chat I've 

1569
01:04:05,320 --> 01:04:06,280
had in a long time. 
There's. 

1570
01:04:06,280 --> 01:04:08,600
So much more we could. 
Say, I know like somebody don't 

1571
01:04:08,600 --> 01:04:10,160
see it, maybe this this one in 
the future. 

1572
01:04:10,160 --> 01:04:13,360
But guys, if you enjoyed that, 
please do leave us a review 

1573
01:04:13,360 --> 01:04:15,240
wherever you get it. 
And most importantly, honestly, 

1574
01:04:15,320 --> 01:04:18,120
for this one, just share it 
around a little bit, especially,

1575
01:04:18,120 --> 01:04:20,000
you know, if you're a newer 
teacher, if you're training, 

1576
01:04:20,000 --> 01:04:23,000
just send it around to people 
because it is really important 

1577
01:04:23,000 --> 01:04:25,200
information to know. 
And if you're more experienced 

1578
01:04:25,200 --> 01:04:27,920
staff, what I would say to you 
is what we've all said here, 

1579
01:04:27,920 --> 01:04:30,560
it's rooted in, it's rooted in 
fact, it's rooted in research is

1580
01:04:30,560 --> 01:04:33,640
what it's what it is. 
So if you kind of are noticing 

1581
01:04:33,640 --> 01:04:36,720
in your school, maybe the 
balance is a bit often and you 

1582
01:04:36,720 --> 01:04:39,400
as a professional kind of have 
this idea of like it's not been 

1583
01:04:39,400 --> 01:04:41,400
done properly. 
Push back a bit. 

1584
01:04:41,400 --> 01:04:44,360
Like just just ask about it. 
Just say like look OK you might 

1585
01:04:44,360 --> 01:04:46,880
get shot down fine but you might
not and you might be able to 

1586
01:04:46,880 --> 01:04:49,320
change stuff. 
And also talk to us because if 

1587
01:04:49,320 --> 01:04:51,200
there's anything else more you 
want to, you want us to talk 

1588
01:04:51,200 --> 01:04:52,960
about about Mouse, you know, we 
love it. 

1589
01:04:52,960 --> 01:04:54,560
So if there's ever, if there's 
elements you thought, I wonder 

1590
01:04:54,560 --> 01:04:56,080
if they're going to talk about 
this in this episode. 

1591
01:04:56,080 --> 01:04:58,400
And we didn't please write in 
because there's almost 

1592
01:04:58,400 --> 01:05:00,280
definitely another episode we'll
do in the future where we can 

1593
01:05:00,280 --> 01:05:02,560
talk about these other elements.
Of maths, but we're going to be 

1594
01:05:02,560 --> 01:05:04,160
building our maths platform 
every. 

1595
01:05:04,320 --> 01:05:07,920
Episode from next week will 
exclusively be about maths this.

1596
01:05:08,000 --> 01:05:09,800
Is a maths, but it's not that 
we're going to change it. 

1597
01:05:09,920 --> 01:05:12,640
Welcome back to MONEY. 
That toxic school soon fine. 

1598
01:05:12,840 --> 01:05:14,360
Only if they're doing maths 
incorrectly. 

1599
01:05:14,640 --> 01:05:15,480
See you next week. 
See. 

1600
01:05:15,720 --> 01:05:15,960
You guys.