Ep 142: The Ultimate Guide To Primary Maths: Fluency, Reasoning, Problem Solving & How To Teach It Well!

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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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00:10:05,640 --> 00:10:06,720
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

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

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

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

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That's down to you as a teacher.
I think good schemes give lots

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of opportunities for fluency
like this.

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But you as a teacher need to
understand what fluency is and

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

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

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

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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.

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

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

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00:11:02,640 --> 00:11:05,600
a pothole model, I'm adding,
even though this is maybe a bar

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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?

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

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

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

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

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

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

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

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

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

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

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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

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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

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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

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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

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

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

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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

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

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

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

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

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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

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

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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

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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.