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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 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

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.

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 r 2

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? 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 =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

Number Bonds by Patterns 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...