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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!” [email protected]