Transcript Dyslexia: - St John's Marlborough

Work out...
A head for figures (and what
to do when you lose it!)
Ian Abbott
Lead Professional – Cognition and Learning
SEND Service, Wiltshire Council
Dyscalculia is...
Dyscalculia is a condition that affects the ability to
acquire arithmetical skills. Dyscalculic learners may
have difficulty understanding simple number concepts,
lack an intuitive grasp of numbers, and have problems
learning number facts and procedures. Even if they
produce a correct answer or use a correct method, they
may do so mechanically and without confidence.
What works for children with mathematical
difficulties, DCSF, 2009
Simple Number Concepts?
• A natural sense of number?
• Our sense of quantity?
Introduction to Dyscalculia
Birds count!
Goldfinches can distinguish a
difference of 2 or 3
Nightingales, magpies and
crows have been known to
count to 3 or 4!
Corvus corax –
common raven
Introduction to Dyscalculia
Animals cannot ‘count’ in the way
that we understand counting
They have a natural ‘sense’ of
number
Introduction to Dyscalculia
They have a natural ‘sense’ of
threeness, fourness
Introduction to Dyscalculia
This is termed
What is Numerosity?
‘The perception of
numerical quantities that
allow you to compute
their exact number’
(Dehaene, ‘97)
SUBITISING
A limited ‘sense of number’
Introduction to Dyscalculia
If birds can count to 3 or 4
‘naturally’, what about humans?
What’s the limit of our
‘numerosity’?
One concept of dyscalculia
Get ready to count the dots!
How many dots are there?
Did you have to count them or did you know?
Did you use a strategy?
Some individuals would have to count the dots one
by one.
They have no concept of numerosity.
Get ready to count the dots
again!
How many dots are there this
time?
Did you have to count them all over again or did
you know?
Did you use a strategy this time?
Some individuals would have to count the dots
from scratch.
Some would not understand that 7 was one more
than 6, for example.
So, if birds can count to 3 or 4
‘naturally’ -
What’s the limit of our
‘numerosity’?
Corvus corax –
common raven
One concept of dyscalculia
3 or 4 is the limit of our numerosity
Don’t believe me?
Think about tallying
Count the sticks quickly…
One concept of dyscalculia
3 or 4 is the limit of our numerosity
We build on this to make larger
numbers
Individuals with pure dyscalculia
cannot build on this fundamental
knowledge – this impacts on
arithmetic (but not all maths)
Attention and Maths
•Constant finding in research literature
•People with good attentional control are
typically good at maths...
Working Memory and Maths
•Another constant finding in research
literature
•Positive relationship between maths
complexity and working memory demands.
Maths is a memory game?
• Sometimes we actively encourage use of
memory rather than understanding!
Maths is a memory game?
• E.g. For dividing one fraction by another.
½÷¼=?
Maths is a memory game?
• E.g. For dividing one fraction by another.
½÷¼=
“ours is not to reason
why: invert the last and multiply!!!”
General Mnemonics
The hole in my sock has just been repaired...
The area mended is...
General Mnemonics
The hole in my sock has just been repaired...
The area mended is...pi r2
General Mnemonics
General Mnemonics
General Mnemonics
Times Tables Mnemonics
Times Tables Mnemonics
“I ate, I ate, I was sick on the
floor”
8 X 8 = 64
Times Tables Problems
• What do your pupils do when you ask them,
“tell me the six times table”
•
•
•
•
A number sequence?
A language sequence?
Can they remember it?
Can they use it?
Times Tables Problems
• What do your pupils do when you ask them,
“tell me the six times table”
•
•
•
•
A number sequence? “6, 12, 18, 24, 30...”
A language sequence? “lion, elephant, rhino...”
Can they remember it? “6, 12, 20, 30, 40...”
Can they use it? “Tell me 7 X 6”
Times Tables Problems
• Maths facts are language based!
• Rote learning is useful...
• But base it on understanding.
Understanding Times Tables
Is this based on understanding and meaning?
2 X 3=?
3
Groups of
2
2X3=3X2
Lots of
Understanding Times Tables
• Use hands on resources numicon or cuisenaire!
Understanding Times Tables
• Would counting money be more
meaningful...and useful?
• A good starting point,
at least!
1p, 2p, 5p, 10p
Times Tables Square
Number Bonds: A Scenario
• September 2014 : IEP target
“Ben will know his number bonds to 10”
Number Bonds: A Scenario
• February 2015 : IEP target
“Ben will know his number bonds to 10”
Number Bonds: A Scenario
• May 2015 : IEP target
“Ben will know his number bonds to 10”
Number Bonds: A Scenario
• September 2015 : IEP target
“Ben will know his number bonds to 20”
• Even though Ben still hasn’t mastered them
to 10!
Number Bonds: A Suggestion
• Make the target smaller...
“Ben will know the numbers that ‘make
5’”
1+4=5; 2+3=5; 3+2=5; 4+1=5
Number Bonds: A Suggestion
• Use concrete resources
• (e.g. cuisenaire rods)
• Use number families such as...
• 1+4=5; 2+3=5; 3+2=5; 4+1=5
1+4=5;
2+3=5;
3 +2=5;
4+1=5
1+4=5
2+3=5;
Number Bonds by Patterns
• How many?
Number Practice by Games
Number Bonds by Patterns
• 4+1=
Number Bonds by Patterns
• 4+1=
Number Bonds by Patterns
• 4+1=
Number Bonds by Patterns
• 2+3=
Number Bonds by Patterns
• 2+3=5
Number Bonds by Patterns
0 1 2 3 4 5 6 7 8 9 10
10 9 8 7 6 5 4 3 2 1 0
If all else fails, write them down as you begin work...
Retrieving information from
Memory
Give PROCESSING TIME to retrieve
information
“Liam...(wait for attention). How many edges
are there on the cone? (wait for processing)”
Give them time – count up to nine!
And Finally: Remember...
•To be positive when talking about maths!
•The simple fact –most children get better at maths
with practice.
•Challenge the statement, “I’m rubbish at maths! I’ll
never be able to do it!”
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