Maths - Assessment and Differentiation (Module

University of Worcester
Tuesday 14th January 2014
Headteacher not Headmaster
I teach Maths most
days either in
groups or whole
“The school is led
from the classroom”
Emergent Maths
In Somerset
the NWP
What is Emergent Maths?
Key Features of Emergent Writing
The writing “emerges” from the child
 The child is treated as a “writer” not an
empty vessel that needs filling
 The principle of the child taking “The Mantle
of The Expert” rather than the teacher
 At its heart lies the confidence and selfesteem of the child
Pedagogical Homogeneity
“Pedagogy trumps
curriculum every
(Dylan Wiliam)
You cannot teach
with pedagogical
What is Emergent Maths?
The Maths springs from the child
 4 Smarties shared between 3
toddlers in 1.33 recurring
but they all
understand the
concept of
What is Emergent Maths?
It is built on the principle that:
All children come to school
with a knowledge of
 They come to the class as
a fledgling Mathematician
 Therefore… Maths can
What is Emergent Maths?
“Mantle of the Expert”
The subliminal message of:
 I am the teacher and I am
cleverer than you
 You are the pupil you
know nothing.
 Therefore I must teach
you through transmission
What is Emergent Maths?
The starting point for me
was always the issue of
Confidence and Self
The child who sees himself
as a learner will learn –
intrinsic motivation
What is Emergent Maths?
Research is now starting to
show that success in
learning is down to “how”
we learn as well as “what”
we learn – Brain plasticity
If we learn in one context or
one style then it will impact
on our ability to transfer
What is Emergent Maths?
What is Emergent Maths?
What is Emergent Maths?
What is Emergent Maths?
Exploring the Concept of Pi
moment of
a theorem
Low Threshold, High Ceiling
“Low Threshold, High
ceiling tasks have easy
access but lots of
Quote from
Nrich website
The Ultimate Open Ended Task
Scaffolding a Task
The 100 Square
provides a
slightly more
Scaffolding a Task
“All the numbers
in the first
column end in 4”
The teacher
remains in
control of the
Scaffolding a Task
“The opposite
corners of the
small square add
up to the same
Where do we
go next?
Scaffolding a Task
What about the
top and bottom
What do you
notice about the
middle number?
Scaffolding a Task
Will it work on
any 9 grid
anywhere on the
100 square?
What do you
think will happen
on a 16 grid
Scaffolding a Task
But the best
question is…
So… What could
we explore from
Scaffolding a Task
Often a mixture
of modelling
ways forward for
exploration and
allowing children
to follow the
Maths for
Scaffolding a Task
Also a mixture
between class led
and class directed
e.g. “Let’s all test
Tom’s theory and
choose our own 9
square and see if
it works” and then
further individual
Mathematical Enjoyment
The problem with
how Maths is usually
taught is that it is
taught in Black and
White and it should
be a subject of
glorious techni-colour
Maths is Right or Wrong
Too often Maths is
taught in the
sphere of right or
 Especially if used
in a didactic
approach where
the emphasis is…
“I will show you…
now do you get it?”
Maths is Right or Wrong
The truth is 2+3=6
is wrong
 But so is; “Wun day
I whent too miy
 Emergent Writing focused on treating the child
as a “real” fledgling writer.
Why can’t we do the same in Maths?
Enjoyment of Maths
According to Jo Boaler
children’s enjoyment of
the subject (especially
girls) plummets when
they focus on dry, taught
procedures only and
aren’t allowed to explore
numbers for greater
Enjoyment of Maths
Instructional Maths
“Rules without
Enjoyment of Maths
A few years ago I
asked our Year 6
children which
subject they enjoyed
most Maths or
“Maths because it is
more creative”
What is Emergent Maths?
The title of a
book by Sue
Teacher Skills
To teach emergently the skill set changes
No Longer…
“The Sage on
the Stage but
the Guide on
the Side”
Classroom Keys
Culture of Learning
Is it better to get work
right or wrong?
The story of Zoe
HayMcBer study: Culture
Secure Subject
Williams Report
Maths and Understanding
Maths is about understanding
 What is 13.5% of 3,245?
 What is a percentage?
Maths and Understanding
No-one could see the practical use as to why
schools SAT scores were compared by
percentages rather than raw numerical data
“Maths is a tool to
solve problems
not an end it itself”
Jo Boaler
Dialogue is the Key
Reasoning and Dialogue
All Maths should be
“constructed” by
the children themselves
 Constructed through dialogue
Built in Assessment
provides built in,
up to the minute
assessment of
where children
are up to
Learning Built on that
There cannot
be an angle
at the bottom
of the Kite
angles look
like this…
Learning Built on that
Learning Built on that
The context had
come from a
discussion about
the internal
angles of a shape
Learning Built on that
Is this an
An Upside Down Triangle!
What is the Fraction?
What is the Fraction?
The power of Schema
All done
with no
“Any individual
task can be
correctly without
Hiebert and Carpenter
Draw 2 lines to complete a square
Follow the Children
The art of the
teacher in this
style of teaching
is to follow the
children and
avoid the cul-desacs
Teacher Questioning
Assessment and the
Learning Objective
Assessment is there to assess
In which case
we need to
ensure that
the learning
is watertight
Assessment and the
Learning Objective
Learning about
The learning should
drive the
What is the Learning?
Ratio and Proportion?
What is the Learning?
So what will the
assessment be?
Using Similes
This does not teach
how to write good
 “What makes a
good simile?”
 Why is this a good
Richard Skemp
Instrumental Understanding – Skemp
describes this as “rules without reasons”
Relational Understanding - Skemp
describes this as “knowing both what to
do and why” and the process of learning
relational mathematics is “building up a
conceptual structure”
What is Emergent Maths?
What is Emergent Maths?
I thought I understood this?!!
Emergent Maths
Emergent Maths tackles
“Relational Understanding”
and on the whole can be undertaken
mainly through Mixed Ability, Whole Class
Whilst not as important
“Instrumental Understanding”
needs clear Differentiation
Differentiated Options
Aye There’s the rub
(Hamlet Act 3 Scene 1)
The majority of research shows clearly that
formal Setting and Streaming has minimal
impact on attainment
Where progress is made it is usually with the
more able but nearly always at the expense of
all other groups of children
Jo Boaler
Jo Boaler
“88% of children
placed in ability
groups at age 4
remain in the same
groupings until they
leave school.
The Influence of Ability Grouping
Dylan Wiliam
It’s not which
school but which
set you’re in that
Progress across schools was similar
if not the same but within schools
remained markedly different
Hattie – Visible Learning
Ability Grouping/Streaming
Comparing attainment and equity effects
Within class Grouping
Children put in formal ability groups
So should we ever group children?
Just a Question…
What is ⅔ of ¾ of 11?
Just a Question…
The Challenge and the learning is
in the level of the question
Differentiated Options
Fluid Grouping
The principles and
understanding can
be the same but
the differentiation
can be in the task
as an outcome
Fluid Grouping
So we might teach the mechanical
principles from this example
But allow the children to explore any
of the following:
Differentiated Options
The Key to Fluid Groups
The children need to understand that…
Learning is about challenge and therefore
the possibility of getting things wrong
The “Zone of Proximal Development”
The Box of Tissues and the yawn
Permission to take control of their own
learning e.g. More able design decimal examples?
Where do
worksheets fit in?
Look, I have spent all last
evening designing this
worksheet so it is just at
your level because you
are too thick to work out
what you need and also I
want to rip every ounce of
empowerment for your
own learning out of you
They don’t!!
You numpty! This
morning it all
clicked for me
and if you let me
loose I could
make staggering
progress which
would impress
inspector sitting
at the back
Moving Groups
The issue of the 88% is
that in “formal” setting it is
hard to structurally move
groups – hence the
stagnation of progress
Fluid groups allow children
to pitch in at their own
level of ability and
And Finally… Assessment returns
Instrumental Maths
 A sum in a book
 How many of them?
Relational Maths
 A sentence written in a book?
 Emphasis on Mathematical vocabulary
Discussion Time
Thank Goodness
he’s shut up now
we might get a
chance to get a
word in edgeways!!
Any thoughts or comments on
the Presentation, The article
“Implementing Curriculum
2014” or on The Wyche
Calculation Document

similar documents