Speaking, Listening and Learning – mathematics supplement
Introduction
The recent Primary National Strategy pack, ‘Speaking, listening and Learning:
working with children in Key Stage 1 and 2’, highlighted the importance of speaking
and listening in teaching and learning in the primary classroom.
The pack stressed that speaking and listening objectives should be taught not just
through literacy, but also across the curriculum.
However, the examples for links with mathematics are rather limited, and where they
do exist are fairly obvious examples – play ‘guess my shape’ type games, or ask
children to explain their answers.
This supplement is designed to highlight opportunities in mathematics where less
obvious objectives or activities could be used to extend children’s speaking and
listening skills.
How can speaking and listening improve the learning within a mathematics
lesson?
The introduction to the PNS Speaking, Listening and Learning handbook states the
following:
Language is an integral part of most learning and oral language in particular has a
key role in classroom teaching and learning…in their daily lives, children use
speaking and listening to solve problems, speculate, make decisions and reflect
on what is important’.
The outcomes listed above are all characteristics of a good mathematician – along
with thinking flexibly, linking ideas and making connections, predicting, drawing
conclusions and having the confidence to take risks. Being able to fill a book with
pages of ‘sums’ is not a characteristic of a well-rounded mathematician; it is a byproduct of their skills.
Developing speaking and listening skills in mathematics could:
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Enable children to become fluent in their use and understanding of
mathematical vocabulary
Help them to embed their short term learning into long term
Allow children to explore different concepts and make links between them
Allow less able children, or children who are restricted by written elements of
mathematics, to participate more fully in the lesson and increase their level of
learning
Allow children to rehearse their answers or ideas before presenting them in
an open forum – thus building confidence and self-esteem (currently
undermined by the predominant ‘hands-up’ systems still practised in many
mathematics lessons)
Enable children to learn from each other and explore each other’s ideas
Create strong foundations for children to develop their problem solving skills,
particularly those problems that involve high levels of language and
vocabulary
Speaking, Listening and Learning – mathematics supplement
Speaking, Listening and Learning – mathematics supplement
Culture and ethos
The ethos of the ‘speaking and listening’ mathematical classroom is of vital
importance. We constantly need to challenge the traditional views of how
mathematics is most effectively taught, for example:
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Why is independent work usually individual and of a written nature?
Why is completing a textbook page more useful and memorable than the
children discussing the key facts and ideas about what they are learning,
using drawings, diagrams or equations to illustrate their ideas?
What ways can the 3-part lesson be modified to allow for more discussion
opportunities?
What is the role of the teacher today? The role of the learner?
How are we developing children to see learning as something that is ‘risky’
and is not always about the ‘right’ answer?
The table presented on page 22 of the Handbook highlights the possible ‘dos’ and
‘don’ts’ of teacher talk. Unfortunately much of the ‘don’t’ column can still be related to
teacher talk in mathematics lessons – some of the ideas and activities in this
supplement are to help teachers to develop more of the ‘dos’.
Many thanks to the contributors of this supplement:
Christine Lone – Balfour Infant School
Julie Smith – Balfour Infant School
Caroline Hemsley – Balfour Junior School
Julie Wheeler – Bligh Infant School
Tim Muggridge – Cliffe Woods Primary School
Lynda Robbins – Cuxton Infant School
Sue Tombs – Cuxton Junior School
Lesley Shepherd – Delce Junior School
Rebecca Parry – Delce Junior School
Joanna Barber – Elaine Primary School
Vanessa Chambers – Featherby Infant School
Sara McKenna – Greenvale Infant School
Julia Gaughan – High Halstow Primary School
Darran Callaghan – Maundene Primary
Lynn McLaughlin – Maundene Primary
Karen Connolly – Rivermead
Ruth Wells – Spinnens Acre Junior
Zoe Huggett – St Augustine’s RCP
Jackie Blackman – St James’ CEVA Primary School
Deb Gamson – St Margaret’s Infants
Jane Elworthy – St Mary’s Primary
Donna McGartland – St William of Perth
Bev Butler – Twydall Infants
Miriam Noble – Wayfield Primary School
Speaking, Listening and Learning – mathematics supplement
Speaking, Listening and Learning – mathematics supplement
Leaflet: Speaking – making it work in the classroom
Speaking and listening
technique
Talk Partners
Use in mathematics lesson
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Debates
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Use when asking a question that
requires thinking time, or requires
children to recall past
learning/vocabulary
Use in the plenary where the pair could
identify the key learning points from the
session, or prepare a question for the
next lesson etc
Discuss different strategies in the M+O
starter
Peer assessment throughout the
lesson, including marking
Joint presentation of findings/work
Use as a ‘when you are stuck’ strategy
Rehearse vocabulary – putting key
words into a sentence or question, or
creating a definition
Paired activities encourage talk and
enhances vocabulary– e.g. positional
language, measures
Plenary placemat giving starter prompts
to discuss ready to share
Play ‘True or False’. Give pupils
statements and ask them to show T or
F on their whiteboard (or thumbs up,
thumbs down). Combine with talk
partners, which will result in the children
having to justify their ideas to their
partner.
Extend this game to exploring general
statements, as per objectives in the
problem-solving strand:
1. Set up a class courtroom, where
the different ‘lawyers’ have to
give their arguments to the ‘jury’
and the jury has to decide
whose presentation/definition/
answer etc is correct, or most
logical.
2. Play ‘Call my bluff’. Ask the
children to write definitions or
statements – some right and
some wrong – and present
these to the class, who then
have to debate, which is the
correct answer. Could be used
both as an effective whole
lesson, or a teacher prepared
plenary.
Use the ‘Why isn’t?’ question at any
point in the lesson to explore children’s
points of view or misconceptions. This
will lead to richer answers (especially
again if discussed first with talk partner).
Consider the different responses to
holding up a cube and asking:
1. What shape is this? Or
2. Why isn’t this shape a
Speaking, Listening and Learning – mathematics supplement
Health warning?
Advice? Comments?
Think carefully about
the pairing – social
group, mixed ability,
same ability etc. The
Handbook
recommends
keeping the
partnership the same
for half a term to
build confidence and
trust
Seat accordingly
before the lesson –
be aware of absence
Beware of special
needs/children who
find it hard to get
along – vary partners
where necessary
Links with
conscience alley
Difficult to produce
statements which
lead to effective
discussions
Physical opinion poll
– line/placement
Constant reminders
of expectations
Beware of children
who copy – sit these
at the front
Praise
Give instructions
before moving into
place – remind
Give all children a
role or a task,
purpose for watching
to avoid behaviour
problems, lack of
interest
Where children really
want to have a turn –
save children with
behaviour problems
Speaking, Listening and Learning – mathematics supplement
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Predicaments and
problems
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Glove puppets and shadow
theatre
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Photos and paintings
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cylinder?
Collate a number of different strategies
for solving a particular problem or
calculation and ask groups to persuade
their peers which strategy is the best
and why. The same activity could also
be used to debate the most appropriate
resource e.g. trundle wheel v metre
stick, 100 square v number line
Give a question or statement and a
number of answers, children to debate
which answers are right/possible and
which are not
Scenarios / problem solving to act out
different ways of solving or finding an
answer.
Problem of the week, children to explain
how they have solved it or difficulties
that they have encountered.
Give a problem and children to identify
ways of tackling the problem
Historical context e.g. Francis Drake is
sailing round the world. He needs your
help with directions to get home. His
compass is broken! One child takes on
role of Drake; others talk about
directions to move ‘Drake’ from one end
of the room to the other avoiding
obstacles.
Place problem in an historical context ~
e.g. how many blocks will be needed to
build the Pyramid (angles etc), how
many miles of road will the Romans
build
Give children sets of mathematical
equipment with a few ‘red herrings’.
Ask children to discuss which pieces of
equipment would be used solve a
particular problem, which ones would
not work
Present a scenario where a piece of
equipment does not work as expected
e.g. only 3 number keys on a calculator
work, and ask if it can still be used or
whether it can still give a particular
answer/result
Use a puppet that makes ‘mistakes’ that
the children can correct (good plenary
activity)
Ask the children to explain their method,
ideas etc to the puppet
The puppet does not understand a
concept/idea/word or fact. Children
have to explain it and provide a
question to check the puppet has
understood.
Present a calculation as a piece of
shadow theatre. Children to say what it
is.
Use Matisse – discuss the way in which
he uses shape in his paintings.
Use Kandinsky/Mondrian paintings to
discuss shape identification and
Speaking, Listening and Learning – mathematics supplement
to later in order to
keep them
motivated. They
may loose interest
after they have had
their turn.
This may become
very loud
Speaking, Listening and Learning – mathematics supplement
tessellation or measurement of line.
Using paintings for positional language
e.g. identify position of objects within
paintings.
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Using photos, digital images e.g.
buildings, gates, windows etc. Work in
pairs to identify shapes, number
combinations, patterns.
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Give children a camera to take
photographs of examples of shapes
meeting certain criteria – children then
feedback to class explaining reasons for
choosing the picture and reinforcing key
vocabulary.
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Give children a picture of a speed limit
sign. Children have 2 minutes to
discuss what they know about that
number
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Picture of someone who does a
particular job, what maths do they need
to do their job and what would happen if
they couldn’t do it?
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Give headlines – e.g.
Shape has been stolen – what shape is it?
Problem solving (number) – 3 people left on
train, it arrived 3 hours late – what time did it
arrive? Then they can make their own.
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Report findings from explode a
number to others
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Children work in groups to create a
radio jingle to explain a rule for
describing calculations/patterns/shapes
etc. etc e.g. multiplying or dividing by
10/100 – ‘To make it lighty, move it to
the righty!, to make it hefty, shift it to the
lefty!’; describing the properties of a
square; rules for describing a number
sequence
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The world has lost the ability to do
maths. What would the headlines be?
What are the advantages and
disadvantages? (links to debates)
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A new law bans a particular
number/word or operation. What are the
consequences? What will we need to
do instead?
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Put together a broadcast for a given
audience to explain or persuade them
that e.g. all shapes have something in
common.
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Put together a broadcast to give the
findings of a data handling activity.
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Useful assessment activity – ask pupils
to talk for one minute (can be altered for
differentiation) about:
1. The topic you have just covered, or a
topic recently covered
2. A times table they have been learning
3. A historical mathematical figure they
have been researching
4. A shape
5. A graph e.g. tell the story described by
a line graph
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Radio Broadcast
Just a minute
Speaking, Listening and Learning – mathematics supplement
Consider how many
other children the
speaker is talking to
– is it their talk
partner, or a group of
pupils (what size?)
Could a tape
recorder or
Dictaphone be used?
Speaking, Listening and Learning – mathematics supplement
6.
7.
8.
A mathematical resource (bead string,
cubes, protractor)
A mathematical word
Teacher models speaking for 1 min –
pupils spot deliberate mistakes.
Could a follow up
activity be to then
ask the group to
record all their
thoughts onto a large
sheet of paper –
class display?
1 minute may be a
little long for KS1
Role Play
Role play scenarios:
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Shop ~ money and weight
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Kitchen / Cooking ~ weight, time
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Railway ticket / booking office ~ money,
timetables, map reading
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Café ~ money, measures etc (children
could enter as book characters and talk
in role if it was extended into Literacy)
Speaking, Listening and Learning – mathematics supplement
Use prompt card /
give examples first.
Resourcing
Timetabling ~ within
maths lessons or at
other times
How will the maths
learning be
monitored /
assessed?
Speaking, Listening and Learning – mathematics supplement
Leaflet: Drama
Speaking and Listening
Technique
Conscience/Calculation
Alley
Use in Mathematics Lesson
Conscience /Calculation
Alley
Children decide on an individual operation –
create a line. A child is given an initial number
and is asked to walk the length of the line
carrying out the children’s operation (e.g. +2 or
+10) on his/her number. Child explains how they
arrived at their answer.
Groups decide on function(s) as a group – child
walking along line gives random number and
person in line gives the answer after the
function(s) has been carried out. Guesser has to
try to work out function(s) (e.g. +10 or +9).
Final person in each line ask ‘what is the
function? How do you know?’
Child explains how they arrived at their answer.
Function fin/hat/label to be worn on head of child
walking along line. Child holds up start number
and the children in line call out the answer after
function has been carried out. Final person in
each line ask ‘what is the function? How do you
know?’
Child has to identify the function on each side of
fin. Child explains how they arrived at their
answer. (e.g. +9 or +11)
A pair of children chooses to go down
Calculation Alley. Teacher tells rest of class to
think of a specific number e.g. think of a multiple
of 10 or an even number. As the pair walk down
Calculation Alley the rest of the children call out
their number. When pair reach the end they are
given time to try and work out the operation or
rule. Feed back to the class.
Child or adult on hot-seat. Rest of class ask
mathematical questions to try to find out number;
shape; scale; function … e.g. wear a hat with
number, shape, etc, other children to give clues
for wearer to guess
Issues with level of S+L
hence discussion at the end
Conscience /Calculation
Alley
Conscience /Calculation
Alley
Conscience /Calculation
Alley
Hot Seating
Meetings
In groups children decide on a number or a
shape. Groups stand in a line and offer clues as
to their secret number or shape to another child
tries to guess the number based on clues given.
Extend by adding one piece of incorrect
information, informing the ‘guesser’ that there is
a red herring in the clues. Can they identify the
hidden number/shape as well as the ‘red
herring’?
A meeting would be set up concerning, for
instance a tuck shop. The teacher being in the
role of a shopkeeper.
A prepared graph, containing items which are
sold will be shown to the children. As a ‘staff’
children discuss trends and offer opinions of
Speaking, Listening and Learning – mathematics supplement
Health warning?
Advice? Comments?
Some will need to
brainstorm in a group
the different clues
they have – may be
useful to use mixed
ability groups / pairs.
The person guessing
could be from a
different group, who
are also doing the
same activity, rather
than being left
outside, waiting for.
Human function
machine
Encourage speaking
and listening skills by
adding ‘red herrings’
and asking children
to explain how they
know which answers
are the ‘red herrings.’
Encourage speaking
and listening skills by
adding ‘red herrings’
and asking children
to explain how they
know which answers
are the ‘red herrings.’
Need to be given
examples – modelled
to begin with. Will
also need to see
pictures as examples
Could be carried out
in small groups and
with limited number
of questions.
This can be recorded
through
observation/tape
recordings.
Use this technique
for setting
Speaking, Listening and Learning – mathematics supplement
Meetings
Paired improvisation
See practical activities pack
what to reorder and which items to no longer
purchase. Discuss stock levels, calculate profit,
profit margins, raise and lower prices by
percentages etc.
This could also be adopted when going on a
school trip.
A meeting is called to discuss the class’s
timetable. Maybe beginning with a day at a time.
Discussions about time etc will occur.
Children phone the ‘Shape Shop’ (or number)
The caller asks the shopkeeper for a shape by
describing its properties. The shopkeeper works
out the shape.
Shopkeeper may say that they don’t have the
shape, yet they have… and describe a different
shape.
Speaking, Listening and Learning – mathematics supplement
up/developing role
play area, or at a
more basic level for
younger children
This can be recorded
through
observation/tape
recordings.
Focus on using
specific
mathematical
vocabulary – to be
maths detectives.
This can be recorded
through
observation/tape
recordings.
Speaking, Listening and Learning – mathematics supplement
Leaflet: Group discussion and interaction
Speaking and listening
technique
Think-pair-share
Snowballing
Statement Game
Envoys
Use in mathematics lessons
General problem solving – set problem that
children discuss in pairs and feedback to
class/group. E.g.
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Which operations are required?
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What parts of the problem are important
or not. I give problems with important
info missing e.g. numbers / size or give
answer – what was the question.
e.g. 1 person got on the bus… when they
arrived at the bus station there were 11
people – what happened in between.
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Give number story with lots of irrelevant
info – e.g. 3 people on the bus, names
were Fred / Bill and Dave, they were
wearing…… pupils to highlight useful
important?
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Investigating a general statement. E.g.
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A multiple of 6 always divisible by 3.
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All shapes with straight sides will
tessellate.
Children are discussing their theories in a
smaller group, than justifying to a larger group.
Building up to a whole class consensus.
True or false game based on a set of statements
about
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Comparison of units of measure
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Properties of a 2 or 3 D shape
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Properties of a number
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Information from a given table, chart or
graph.
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Calculations – E.g. all the answers are
a given number.
Power Triangle – discussion before playing a
‘What am I?’ game.
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Statements to be produced, by either
teacher or pupils.
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Pupils order the statements from the
most general to the most specific.
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After playing the game – discuss
reasons for choice of order and for
alterations to choices.
Children work on an investigation or calculation
and discuss their method of calculation. Then an
envoy moves around the groups gathering
information on chosen methods of calculation.
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Use of informal methods of calculation
to solve a problem. E.g. 6+7 – possible
responses could be count on, near
double, apparatus, number bonds,
bridging through 10.
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Old SATs questions that require
showing your working box.
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As above using mental strategies.
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Present the same data on different
types of graphs/charts – share with
class and debate best choice (see
conscience alleys and debates)
Speaking, Listening and Learning – mathematics supplement
Health warning?
Advice? Comments?
KS1 + 2
Seems similar to talk
partners
Time limit – all pairs
some pairs – inform
children to avoid
disappointment
KS2
Classroom
organisation needs
to be fluid.
Pupils could make
their own statements
– including false.
Size of groups could
be changed
according to the
children.
A true and false card
could be used –
thumbs up/down
saves calling out
Organisation!?
Consider space in
hall etc.
More KS2 orientated
Speaking, Listening and Learning – mathematics supplement
Leaflet: Listening
Listening techniques
Use in Mathematics lesson
Babble gabble
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Preparation for MA tests
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Barrier games
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Word Tennis
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Written version too
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Teacher presents a problem orally
Children work in pairs – partner A retells the
problem while partner B listens and records
key elements, check together that all the
relevant information is included
Together discuss how they are going to
approach solving the problem
Use of 2 cards for lower ability pupils; 1 card
is beginning of problem, 1 card is end of
problem. On cards are pictures, they have
to orally retell problem & then they both
decide on middle.
Orientation game (paper and acetate
problem)
Encourage listener to ask questions
Draw pictures – e.g. shapes / position /
number (write number 8 next to the number
4 – what number have you written?). See if
both have same pictures.
In pairs take turns to describe a property of
a given shape – 2D or 3D
The aim of the game is to be the last to
name a relevant property – without
repetition.
Could be adapted for describing a particular
number: prime, odd, greater than, multiples,
factors, square numbers…
Health warning?
Advice? Comments?
Modelling of how to
approach problems
by teacher may be
needed prior to
lesson
Children may want to
peep – a physical
barrier such as a
screen or blind fold
may be appropriate!
Recap and display
relevant vocabulary.
Difficult with KS1
(would need to focus
on number)
Certain rules would
need to be made i.e.
greater than 50 and
then greater than
51is not acceptable
Draw a story
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Visualisation is a skill that
needs teaching too
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Draw a story
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Draw a story
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Telephone conversation
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Teacher to read a problem while the children
listen.
At strategic points the teacher stops and
children are asked to pick out the relevant
information needed from that section – and
record it.
At the end of the problem – encourage the
children to work in pairs to retell and solve
the problem using their previous jottings
Teacher to describe a geometrical drawing
while children visualise this in their heads
Children then encouraged to draw what they
see
Children to work in pairs. Partner A to draw
a geometrical drawing from Partner B’s
instructions
Both children sit back to back and have the
same data in front of them (possibly
represented in different ways – graph, table)
Pass on interpreted information from the
data
Children must listen carefully to make sure
they are being given the correct information
Speaking, Listening and Learning – mathematics supplement
Choose appropriate
problems which lend
themselves to
pictorial
representations
Verbal instructions
only, no hand signals
allowed!
Think carefully about
the data given and
how it is represented
and the differing
ways it can be
interpreted.
Speaking, Listening and Learning – mathematics supplement
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Visualisation activities
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Children could also ask their partner
questions to be answered from the data
Give some children a selection of
mathematical vocabulary to plan a phone
conversation where the vocabulary is used
in a non-mathematical context e.g. The
mean lady in the flat next door to the takeaway is going into hospital for an operation
on the side of her face as an odd area has
appeared. She needs to find some products
to co-ordinate so that she can rotate her
outfits, but her son does not see the value in
this or what function it will serve!! Other
children have to listen to the conversation
and identify the mathematical vocabulary
that was included.
Imagine a capital letter ‘T’. If it turns 90°
what does it look like?
Letter/shape detective using feely bags
Kim’s game – visualise the missing thing,
describe the properties
Visualise and act out stories behind the
problems/calculations
Behind the wall, slowly reveal the
number/letter – who can name it first
Net unfolding – what shapes make the
faces? How many faces are **?
Internalising number lines/squares or
counting sticks by using them with blanks to
fill
Visual number strings
Describe movements on a hidden bead
string. Children describe what the string
looks like
Speaking, Listening and Learning – mathematics supplement
Speaking, Listening and Learning – mathematics supplement
Appendices:
Speaking and listening observation sheet
Sentence Starters
Sentence Starters (Y6 more able training)
Question Starters
Group problem solving
Visualisation from 5 day course
Visualisation from Shape & space
Speaking, Listening and Learning – mathematics supplement