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A head for figures (and what to do when you lose it!)
Ian AbbottLead Professional – Cognition and LearningSEND Service, Wiltshire Council
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
Dyscalculia is...
• A natural sense of number?
• Our sense of quantity?
Simple Number Concepts?
Birds count!
Corvus corax – common raven
Goldfinches can distinguish a difference of 2 or 3
Nightingales, magpies and crows have been known to count to 3 or 4!
Introduction to Dyscalculia
Animals cannot ‘count’ in the way that we understand counting
They have a natural ‘sense’ of number
Introduction to Dyscalculia
Introduction to Dyscalculia
They have a natural ‘sense’ ofthreeness, 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.
Corvus corax – common raven
So, if birds can count to 3 or 4 ‘naturally’ -
What’s the limit of our ‘numerosity’?
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)
•Constant finding in research literature
•People with good attentional control are typically good at maths...
Attention and Maths
•Another constant finding in research literature
•Positive relationship between maths complexity and working memory demands.
Working Memory and Maths
• 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!!!”
Maths is a memory game?
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
“I ate, I ate, I was sick on the floor”
8 X 8 = 64
Times Tables Mnemonics
• 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.
Times Tables Problems
Understanding Times Tables
Is this based on understanding and meaning?
2
3
2 X 3 = 3 X 2
2 X 3=? Groups of
Lots of
• Use hands on resources numicon or cuisenaire!
Understanding Times Tables
• Would counting money be more meaningful...and useful?
1p, 2p, 5p, 10p
• A good starting point, at least!
Understanding Times Tables
Times Tables Square
• 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 Scenario
• 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
Number Bonds: A Suggestion
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
• 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
Number Bonds by Patterns
10 9 8 7 6 5 4 3 2 1 0
If all else fails, write them down as you begin work...
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!
Retrieving information from Memory
•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!”
And Finally: Remember...
