Individual Needs-What works? Cuisenaire Rods

Dyscalculia or Low numeracy?:
Jane Emerson
Individual Needs – What works?
Saturday Workshop 3
Individual Needs-What works?
A maths programme for children
with DYSCALCULIA
or Low Numeracy: age 5-11.
Is this a bad day
at the
hairdressers?
Jane Emerson: Director
Emerson House
Hammersmith, London.
www.emersonhouse.co.uk
Is this the state
of the research
into
Dyscalculia?
12
13
What tests for Dyscalculia are
available?
What sort of profile might you see?
• Dyscalculia Screener by Brian Butterworth pub by
nferNelson 2003.
• Suitable for ages 6-14
• Compares simple reaction time to
• Dot Enumeration: (How many random dots?
Counting or Recognising without counting?
• Number Comparison( 7>8?)
• Arithmetic Achievements (Add.and Mult.)
• Does not give guidance what to do.
• Gives result in terms of ‘Evidence of Dyscalculia’ or
not. Useful to alert to possible cases.
• Other tests look at aspects of maths to determine
topic gaps. At present, this is still a very new field….
• Child ‘M’. Age 7.5 years on the WISC IV where 100 is
average. On Screener, was found to be DYSCALCULIC.
• Wechsler Intelligence Scale for Children.
• Verbal Comprehension:
(Similarities, Vocab., Comp.) VERBAL IQ 108
• Working
W ki Memory:
M
(Digit
(Di it S
Span, L
Letter/Number
tt /N b
Sequence.) AUDITORY MEMORY 83
• Perceptual Reasoning: (Block Design, Picture Concepts,
Matrix Reasoning)
NON VERBAL IQ 98
• Processing Speed: (Coding, Symbol Search) SPEED 70
• ‘M’ has responded to multi-sensory Emerson House
maths programme and is learning her tables……….
14
15
16
17
Cuisenaire Rods
• A box of rods
• The staircase model
• Easier laid flat.
©Jane Emerson
Learning Works® [email protected]
Dyscalculia or Low numeracy?:
Jane Emerson
Individual Needs – What works?
Saturday Workshop 3
First : Oral counting+ tools
Bead strings, glass nuggets, caterpillar tracks, metre ruler, Stern equip.
•
•
•
•
•
•
•
•
Caterpillar Tracks for Counting to
make Tens System explicit.
Counting from 1-10
Estimating/sorting into repeated 10s
Number location 1-10: cat tracks/beads
+1/-1 using Tins Game for ‘counting on’
C
Counting
ti on/back
/b k ffrom a number
b <10
10 tto100
100
Counting on/back from a number >10
Counting in 10s to 100, forwards/backwards
THE SAVAGE IRONY OF ‘MUST BE ABLE TO
COUNT BUT :DON’T COUNT: CALCULATE’
18
The Stern Counting Board
• To introduce size comparisons
and early maths language
19
Odds and Evens,
doubles and near doubles
• The counting board can be
used from the start to introduce
an idea of relative size of the
numbers in relation to each
other.
• Language of one more, one
l
less,
bi
bigger th
than //smaller
ll th
than
• Young children can use it as a
puzzle to discover how each
number is one block bigger
than the last: number sense of
3<4 etc.
• www.mathsextra.com
• Stern pattern boards: • Similar to Numicon
• A different model of
models
the same thing as the • Adding 1 to a number
dot patterns.
always
y results in the
• Individual
I di id l cubes
b can
next number.
be used to show
subtraction with whole • Shows doubles by
splitting evens with a
template remaining.
pencil.
20
21
Counting Track or Beads
A. Counting forms the basis of maths
• Many young children learn to rote count from an
early age without understanding the system.
• It is useful to introduce the idea as early as
possible, that our number system is organized
into sections of tens.
• Why? In this way, children can lay down an idea
or a visual model in their brain, which can form
the basis for number sense.
• How to develop this? Work with tracks,
organised into tens, such as red/white bead
strings and other counting materials and tools.
• Counting and Subitizing
• To subitize: to recognise
without counting.
• Beads can be moved,
counted, and located.
• Number of beads can be
subitized or recognized
without counting
counting.
• Up to 3 or 4 can be
subitized by most people.
• 10 to 14 can be subitized
using colour change as a
clue.
22
©Jane Emerson
Learning Works® [email protected]
23
Dyscalculia or Low numeracy?:
Jane Emerson
Individual Needs – What works?
Saturday Workshop 3
Counting in Fives with Cuisenaire Rods
on Numicon Track.
Counting in Tens on Track.
• Track to 100 but several tracks can be
used to count several hundreds.
• Many children who can rote count have a
hazy idea beyond 100
100.
24
25
The Stern Number Track
• Transferring a basic
• Any number bonds
fact to higher decades
which are being
studied can be
• 3+5=8
applied through the
13+5=18
5 18
• 13
following decades.
• 23+5=28
• Many children treat
• 93+5=28
each calculation as a
new one without
applying previous
knowledge.
26
27
Numicon Component Boxes
for Number Bonds.
• Read the components
•
•
•
•
The story of 6
Six is made of 1+5
Six is made of 2+4
Six is made of 3+3
key fact/doubles fact
• Six is made of 4+2
• Six is made of 5+1
28
©Jane Emerson
Learning Works® [email protected]
29
Dyscalculia or Low numeracy?:
Jane Emerson
Individual Needs – What works?
Saturday Workshop 3
Component Boxes as a different
model to study number bonds.
• What makes 9? Etc.
Discouraging Counting in Ones.
• Select a box to study
the component facts
• Eg. 9=4+5 or 5+4
• 9=1+8,2+7,3+6,etc.
• Here the quantity can
be clearly estimated
as 3 lots of tens,
making 30 and ‘some
more’ units: 3 visible.
• The colour change
removes the need to
count in ones.
• Cuisenaire rods: the
same could be built in
the lid of a rod box if
you are working with
rods.
30
Concrete materials to teach Bridging.
31
Extending Bridging though the
Decades
• 9+3=(9+1)+2=12
• 19+3=(19+1)+2=22
• 59+3=(59+1)+2=62
8+5=(8+2)+3=13
18+5=18+2=3=23 etc.
• Children with poor number sense can fail to see the
pattern. Give plenty of practise with extending number
facts through the decades onto bigger numbers.
• Demonstrate on the track with 2 colours of nuggets.
• Young Children really like the idea that just as children
always want to be older than they are, then numbers
always want to be bigger than they are! 9 really want to
be 10,19 wants to be 20…
32
33
Bridging for addition, to the next 10
• Bridging forward means
applying number bonds of
10 to the first number
• Example here
• 9+3 = (9+1)+2 =10+2=12
• Why?
• 9 needs 1 to make 10
• 2 left because 3 is made
of 1 and 2.
• Encourage child to do
the talking NOT the
teacher.
34
©Jane Emerson
Learning Works® [email protected]
35
Dyscalculia or Low numeracy?:
Jane Emerson
Individual Needs – What works?
Saturday Workshop 3
Demonstrating Column Addition Concretely.
The Dual Board
• Here can be seen 4
tens and 9 units
• 3 more are to be
added to make one
more ten and 2 units
remaining:
• 49+3=50+2=52
36
The Stern 10 box for counting
• What makes ten?
37
The meaning of the ‘teens’.
• First the staircase can
be built from 1-10
• Then the gaps can be
filled in to show the
repeating pattern.
• This also
demonstrates very
neatly the number
bonds of ten: 1+9 etc.
• Counting and building
into the ‘teens’
• This demonstrates the
repeating nature
• The ‘teens’ are ten plus
the counting numbers
again
again.
• For a mental image talk
about teenagers with
ages in the teens.
• Older people drinking
‘tea’ when they are
twen’ty’,thir’ty’ etc.
38
39
Counting above 100
• Numicon Trays
• Step counting in 10s
• Establish the ‘flat’ as
the hundred square,
known or built.
• Move
M
beyond
b
d 100
counting in 10s
• Record the numbers
built on the mats in
digits or on squared
paper.
Place ‘flats’:
Hundreds
here.
Place ‘longs’:
Tens
here.
40
©Jane Emerson
Learning Works® [email protected]
Pl
Place
‘‘ones’’
Units
here.
41
Dyscalculia or Low numeracy?:
Jane Emerson
Individual Needs – What works?
Saturday Workshop 3
Place Value : :: :::
::::
Base Ten Materials with Cubes
Place Value Mats
See Dyscalculia Guidance book.
•
• At the end of Level One children are
introduced to the Place Value Mats
• At first the Tens and Units mat is used
• Build unit dot patterns on the mat to show
that 4+3 becomes the pattern of 7
• Keep all addition totals to under 10
• Ready for level 2 to introduce exchanging
10 units for a ten ‘long’
Use mats in groups of 3:
HTU of millions: use digit cards
HTU of thousands: use digit cards
HTU of ones: demonstrate with base 10.
•
Build numbers on the first mat showing HTU, building the ones in
th dot
the
d t patterns
tt
up to
t 9.
9
•
Explain that ten is not allowed in the units column so 10 ones or
units must be exchanged for a ten and moved into the tens
column.
•
Record one ten in the tens column and no units in the units
column.
•
Many children, even with number sense, do not understand that
10 means one ten and no units: make it explicit.
42
43
Universal Strategies
to escape the Counting Trap.
What Works? Universal Strategies: can be
demonstrated on Empty Number Lines
• So, Universal Strategies are big value methods
that can be relied on to work.
• Bridging forwards for simple additions
For example, 27+5=(27+3)+2=32
• Bridging back for numbers close to each other
on the number line. 23-4=(23-3)-1=19
• Compensatory Addition (Shopkeeper’s Method)
for difference work for numbers far apart on the
number line: thinking forwards.
• 95-27=27 to 30,30 to 90,90 to 95
= 3
+60
+5= Total of 68.
• Key Component facts of all the counting
numbers to ten from dice patterns 1-10
• 10 =5+5, 9=5+4, 8=4+4, 7=4+3, 6=3+3
etc.
• Key facts must be known by heart
• Other facts of each number derived from
the keys 10=5+5, 6+4, 7+3, 8+2,9+1,etc.
• Bridging: Forwards and backwards.
• Partitioning: Using place value knowledge.
44
45
Dot Patterns = a) Key Facts 1-5
b) Commutativity principle
The Dot Pattern Model
• The usual canonical (standard practice)
dice patterns are used and extended.
• They encourage pattern recognition and
therefore subitizing
subitizing.
• They discourage counting in ones so help
children get out of the counting trap.
• Embedded in them are the doubles and
the near doubles: 2+2 and 2+3.
a)
1
1
b)
2
0
1
1
0
3
1
2
2
1
1
4
1
2
3
1
1
5
2
3
4
2
46
©Jane Emerson
Learning Works® [email protected]
2
2
5
2
2
3
47
Dyscalculia or Low numeracy?:
Jane Emerson
Individual Needs – What works?
Saturday Workshop 3
Early Dot Pattern Work
to develop Numerosity
What are the Key Components?
• The Keys are chosen as the doubles and
near doubles facts for each of the counting
numbers 1-10
y open
p the door to leaving
g the counting
g
• They
trap behind
• Children move on at an early stage to
early calculations: 4 is made of 2 and 2 so
2+2=4
• The dot patterns from familiar dice
patterns are studied
• Play dice games like snakes and ladders
• Encourage
E
children
hild
tto subitize,
biti
nott countt
• Copy the patterns by drawing and sticking
• Talk about the pattern differences
• Move on to study the key components
48
49
Dot Patterns =Key Facts of 6-10
Higher Dot Patterns 6-10
6=3+3
7=4+3
6
a)
3
b)
3
8=4+4
7
3
4
6
8
3
4
7
?
4
9=5+4
9
4
5
4
10
4
5
9
8
?
10=5+5
?
5
5
• Study the higher dot patterns: make them,
copy them, remember them, talk about
them
y games
g
with them such as Snap,
p, Card
• Play
Wars (higher pattern wins)
• Crocodile Comparisons 3>4 with dots
• Looking for smaller patterns in higher ones
10
?
?
5
50
Components of 4, 6, 8
Nuggets, Stern Blocks, Spinner Games
Low Doubles
Dot pattern cards, 1-5 dice, squared paper, mirror
•
•
•
•
•
•
•
51
• 4=2+2, 3+1, 1+3, 4+0, 0+4
• 6=3+3, 5+1, 1+5, 4+2,2+5, 5+2, 5+0
• 8=4+4, 7+1,1+7, 6+2,2+6, 5+3, 3+5, 8+0
• Missing addends for all additions facts
• Use ‘mystery’ triads first, then :
Eg. 4=2+? 4= 3+? 6=3+? 8=5+? etc
From the lower dot patterns:
1+1, 2+2, 3+3, 4+4, 5+5
Draw the patterns of 2,4, 6, 8, 10
Split them into two equal groups
Draw the doubles triads
Games with doubles: throw dice, score is double
Find the line of symmetry, talk about even patterns
52
©Jane Emerson
Learning Works® [email protected]
53
Dyscalculia or Low numeracy?:
Jane Emerson
Individual Needs – What works?
Saturday Workshop 3
Dot Patterns = Component facts of 4, 6 and 8
The story of 10: Crucial facts
4
2
4
2
3
4
4
6
1
3
4
0
1
6
3
2
1
4
4
8
6
?
8
5
7
4
8
1
6
• The facts of 10 underpin all calculations
throughout the number system
• Spend more time on these facts
• Revise
R i th
them more often
ft
• Derive other facts from them
• Extend through the decades as a
Universal Strategy
2
54
55
Dot Patterns = Facts of 10 and ‘Mystery Triad examples.
Study all the component facts
?+5=10
5+?=10
10
5
10
5
9
10
3
10
1
8
10
?
4
10
2
7
2
3
6
10
10
?
10
?
5
4
10
?
6
• By the end of level one children will have
learnt:
• All the dot patterns 1-10
• All the key facts off by heart
• How to derive the rest of the component
facts
• Missing addends, +and - ,for all the
counting numbers
?
56
57
Dot Patterns = Facts of 5, 7, 9 (+and - ) Study all the facts of each number.
The Language of Missing Addends.
5
3
5
2
4
5
3
7
1
4
5
?
5
9
4
5
4
4
8
9
7
?
9
?
5
1
9
?
1
• 4 is made of 2 and 2
• 4=2+? ‘4 is made of 2 and what?’
• 4-2=? If you have 4 and take away 2
what is left? 2 is left because 4 is made of
2 and 2.
• 7=4+? 7 is made from 4 and what?
• 7-3=? If 7 is made of 4 and 3 if you take
away 3 you are left with 4.
?
58
©Jane Emerson
Learning Works® [email protected]
59
Dyscalculia or Low numeracy?:
Jane Emerson
Individual Needs – What works?
Saturday Workshop 3
7
The Language of Multiplication
7-3=?
3
8
• Important to demonstrate and talk about the
language of groups concretely with objects that
can be touched and moved.
• Plastic animals can be used but the same
animal must be used for each group.
• For example there could be groups of killer
whales, or fish, or teddies for younger children.
• Nuggets or counters are the least patronising.
8 - 4 =?
?
4
9
5
9 - 5 =?
60
61
62
63
64
65
©Jane Emerson
Learning Works® [email protected]
Dyscalculia or Low numeracy?:
Jane Emerson
Individual Needs – What works?
Saturday Workshop 3
Times tables: a universal strategy:
Build equal size groups with nuggets.
Introduction to Times Tables.
The 4 times for example.
• For every table the key tables facts must
be known: 1x the table,10x the table and
5x the table.
• If 10 x 2 are 20 then 5 x 2 are half of 20
• Practise halving even, then odd numbers
• Show with Cuisenaire Rods( 10s and 5s)
• Pupils calculate up and down table from
key facts
• If 5x2=10 then 6x2=12 (one group more)
• Step-count in 4s
• Step-count from different starting points
• Ask one-step questions: what is one more
group of 4 after 8?
66
b) From multiplication to division without the sign.
• Ask two-steps questions: what are two groups
of 4 after 20?
67
b) Division to 40
5 x 4 = 20
5 x 4 = 20
10 x 4 = 40
i.
How many 4s in 16?
How many 4s in 24? Yes, there are 6 fours
in 24.
How many groups of 4s in 8?
How many 4s in 36? Yes there are 9 fours in
36.
How many 4s to build 20?
68
69
Abstract Work: the language of division.
Key facts:
5 x 4=20
1 x 4=4
Beyond Tables Facts?
10 x 4=40
• It is essential to check the rote learning
style learners understand what they are
doing.
questions to check:
• Ask them q
• If 12 twos are 24 then what are 13 twos?
• What do you have to add to calculate from
24, to find what 13 twos make?
• The story of H. age 10, who added 13
more.
So ten 4s in 40 and five 4s in 20 (Half of 40)
How many 4s in 20?
How many
y 4s to build 24?
40 ÷ 4 =
So 36 ÷ 4=
So…..
20 ÷ 4 =
28 ÷ 4 =
Use the language: If there are 10 fours in 40, there must
be 9 fours in 36, because 36 has one group of 4 less.
40 ÷ 4 =
32 ÷ 4 =
20 ÷ 4 =
24 ÷ 4 =
70
©Jane Emerson
Learning Works® [email protected]
71
Dyscalculia or Low numeracy?:
Jane Emerson
Individual Needs – What works?
Saturday Workshop 3
Advanced methods for beyond the
tables.
13x10: Can be built with rods:
orange to total = 130
• The box method seems to be the easiest
for children who find maths difficult.
10x10=100
10 ten rods or
Base Ten 100 square
3x10=30
(3 ten
rods)
72
Grid method:15x125:rods /base10
100
20
Grid method:15x125:rods /base10
5
100
10
Total 1000
Total 200
Total 50
Total 1000
5
Total 200
Total 50
Total 100
Total 25
5
Total 100
Total 25
74
Total 500
75
Each number can be found from 8 and 4
Summary
•
•
•
•
•
•
•
20
10
5
Total 500
73
Oral Counting and onto counting tracks
Strategies to get out of the Counting trap
Place Value Mats
Dice patterns for subitizing not counting
Bridging for addition and subtraction
Partitioning for addition and subtraction
Multiplication and division strategies.
76
©Jane Emerson
Learning Works® [email protected]
77
Every school is different and
we work very hard to tailor our
events to suit the context,
pupils and particular needs of
staff.
To discuss your ideas and/or
book your professional
training or pupil challenge
event please ring Dominique
on:
+44 (0)1672 512914
or email Fil directly:
[email protected]
12h Annual Residential SEN Conference 2009
Individual Needs - What works?
CAP It All!
Fil Came and Gavin Reid
Described as 'a practical manual for assessing individual needs' Baroness Mary
Warnock goes further in her foreword and suggests that 'CAP It All' is a tool kit 'that all
teachers can use'. It is certainly all of these things and much more besides!
The introduction recognises that busy teachers need to identify problems before they
begin to interfere with a student's learning. Not all teachers have specialist training in SEN,
but they are required to cater for all students in their classes. This book will enable
ANY teacher to work through a process of assessment efficiently and professionally.
Those who are familiar with Gavin Reid's work will recognise the sound research on
which it is based, and those who have worked with Fil Came will rejoice to see so much
that is practical and instantly usable!
Clearly organised into 10 separate areas, any teacher can go straight to the section
they require by consulting the detailed table of contents.
Specialist teachers will find much within these pages to interest them and support
them in their quest to develop excellent specialist practice. There is a superb glossary of
assessment terms which is a helpful reminder to us all and a really useful tool when
delivering INSET to colleagues. The, resources section also holds a wealth of information
particularly for those involved in outreach to parents and carers. The pupil self‐assessment
section is interesting – exploring ways of encouraging students to take responsibility for
their own learning.
CAP It All is excellent. Clear, accessible and so useful. It may perhaps appeal more to
those in the primary sector where initial concerns and accurate assessments as early as
possible are so vital. However, it will also prove invaluable to those of us who work with
older students, enabling us all to keep clear, concise records of student development and
progress.
Edwina Cole
SENCo and Head of ALC Stanbridge
Earls School
Romsey.
Peer
Review 1
2009 Learning Works® +44 (0) 1672 512914 email [email protected]
12h Annual Residential SEN Conference 2009
Individual Needs - What works?
CAP It All!
Fil Came & Gavin Reid
Fil Came is leading consultant for Learning Works®, having previously been a teacher,
Research Fellow at Bristol University and later an SEN adviser. Dr. Gavin Reid is an
experienced teacher, author and international speaker. This book aims to be a practical
manual for assessing individual needs and can be used as a resource bank for busy
teachers, learning support staff and SEN co‐ordinators who work with pupils who have
learning difficulties. Its purpose is to assist the process of identification and assessment of
pupils who are beginning to cause concern, due to their lack of progress in learning so
that remediatory strategies can be applied to help reduce the problems.
Ten sections in the book explore the following:
• Initial Concern, outlines initial assessment and where to find information and evidence.
Useful proforma are included.
• Formal Assessment examines standardised tests and advises which ones to use.
• Informal Assessment helps to gather information about/from the pupil. Helpful tick
sheets and checklists are included.
• Assessing Literacy Skills advises on checks to make such as, pre‐reading skill, phonological
awareness, vocabulary, reading strategies used, spelling and writing.
• Assessing Maths Skills helps to identify concepts where difficulties are common, such as
the counting system, vocabulary, syntax and the four rules.
• M o n i t o r i n g Be h a vi o u r h a s c he c kl is t s a n d assessment sheets to help record
behaviour patterns over time.
• Pupil Self‐assessment sheets help pupils to realise what type of learner they are and how
they feel about their own learning.
• Planning to make a Difference advises on targets and Individual Educational Plans
• The book concludes with useful websites, lists of resources and support groups.
All resource material is written in accessible language, ensuring qualifications in SEN are
not required to fully access this solution‐focused manual. Those working with pupils with
SEN in all phases will find this a brilliant resource.
£35.00 from Learning‐Works
Tel: 01672 512914
For more information and sample pages visit:
www.learning‐works.org.uk
Peer
Review 2
2009 Learning Works® +44 (0) 1672 512914 email [email protected]
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