The Dyscalculia Toolkit

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The Dyscalculia Toolkit

• Ronit Bird

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Dyscalculia

• Dyscalculia poor at arithmetic skills, number
  concepts, no intuitive grasp of numbers, problems
  number facts procedures
• Otherwise normal but uses finger counting in all
  numeric operations beyond normal, no feel for
  numbers, ability to estimate small quantities or
  idea if answers is reasonable
• Forgets if a procedure has 2 or 3 steps, counting
  forward is a problem backwards much worse.

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Dyscalculia Indicators

• Inability to see without counting, to estimate or
  if answer is reasonable
• Weak long short-term memory
• Count forward backwards reliably visual
  spatial orientation
• Direction, left right, processing speeds
• Sequencing, patterns, all aspects of money
• Marked delay in reading the clock or to tell
  time
• To manage time in their daily lives.

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D,D,ADHD ADD

• Dyslexics 50 have difficulty in Maths but more
  ability in speaking
• Dyspraxia clumsy, problems equipment hard to
  decipher
• ADHD ADD problems but not always, must learn to
  manage their impulsivity and concentration
  problems.

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Dyscalculia Toolkit

• CD Rom or PDF
• 200 Activities
• 40 Games
• Age range 7 - 14

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Progression

• Starting with concrete activities
• Gradually progresses to intermediate
  diagrammatic
• Works towards the abstract stage of calculation.

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Role of the teacher

• Activities are teacher led rather than for the
  children to work through on their own
• Important to ask lots of questions
• Direct discussion to point out any connections
  with previous work in class.

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Four Sections

• Early number work numbers up to 10 basic
  calculation with numbers above 10 place value
  times tables, multiplication division
• Overview what are the main problems how to help
  activities.

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Time to reflect

• We forget why we need to use concrete materials
  especially in KS2
• Concrete manipulative materials and Cuisenaire
  rods are for all classes
• The Dyscalculia focussed teacher helps all the
  children in the class.

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Manipulative Materials

• Manipulative materials are any materials that
  allow pupils to physically touch, move and
  rearrange them.
• In mathematics, they can model operations on
  numbers as well as the numbers themselves, and so
  allow learners to explore ideas, patterns and
  relationships in a concrete, rather than an
  abstract, way.

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Concrete Materials

• Concrete materials are multi-sensory learning by
  visual, spatial, kinaesthetic routes through talk
  discussion.
• Too much variety can create problems, new models
  to illustrate new procedures can leave pupils
  with an incoherent view of maths as a series of
  isolated topics.

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Coherent Model

• Using a spike abacus for demonstrations of place
  value but for nothing else results in
  compartmentalise place value thinking separately
  from thinking about mental calculations
• Teaching division as repeated subtraction then
  explaining fractions by shading pictures of pizza
  slices does not help pupils with the
  interconnection between two concepts.
• Fragmentation is detrimental for those with
  little number sense or natural feel for numbers
  they benefit from having a coherent model that
  highlights the patterns connections within
  maths.

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Cuisenaire Dienes

• Best and most versatile apparatus to use with
  pupils are continuous base-10 materials such as
  Cuisenaire Rods and Dienes Blocks.
• Robust materials, in the sense of being capable
  of modelling many different situations and
  procedures at many different levels.

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Young Children

• Naturally, for very young children discrete
  materials, such as counters, nuggets or cubes,
  will precede work with rods or blocks
• Overuse of discrete materials tends to encourage
  pupils to cling to inefficient counting-in-ones
  strategies.

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Inter-related Interdependent

• Working with the right concrete materials and
  explicitly building connections between topics
  helps to foster a cohesive view of mathematics as
  a rational subject whose components are
  interrelated and interdependent.

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Counters

• Changing the size and shape of counters from one
  activity to the next can be both valuable and fun
  for children
• Larger items suitable for younger children
  those with dyspraxia.

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Counters

• Best to avoid too much variety of size or colour,
  counters with solid colours are easier to
  distinguish and count than rainbow-coloured or
  patterned ones
• Regular shapes like discs and cubes are easier to
  distinguish than irregular shapes like handprints
  or alphabet letters
• It is easier to see the pattern of five if each
  of the five counters are the same size and shape
  as each other
• Counters are not suitable for numbers much above
  20.

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Cuisenaire Rods

• CR Dienes for larger denominations
• Colour identify, no measuring or counting
• Quantities seen as a whole rather than a
  collection of single units
• Encourages efficient calculation methods that do
  not depend on counting in ones.
• Professor Sharma sees them to help construct
  sound robust cognitive models.

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How to use concrete materials

• Introduce carefully teacher demo
• Explain rods used to make principles visible,
  develop insight intuition
• Materials allow learners to make meaning to
  create a model to understanding internalise.

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How to use concrete materials

• Supports progression to abstract high-level
  thinking not a primitive alternative to
  calculating machines should not be used in a
  mechanical way to simply to find an answer
• Not used only for demonstration purposes or used
  only for very basic work.

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How to use concrete materials

• They are to handle explore, most useful when
  the same materials are used at different stages,
  for different topics and at different levels of
  difficulty

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How to use concrete materials

• Teachers must remind pupils that the actual maths
  is not what happens to numerals on paper but what
  happens to numbers subjected to maths operations
• Paper pencil records what happens or to support
  our memory as we engage in mental calculation
  abstract thinking.

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Progression

• In this book are 100 ideas for activities that
  propose the use of concrete materials as a route
  to learning and understanding maths.
• A further 100 activities are designed to help
  pupils progress by leading them to make the
  transition from concrete to abstract mathematical
  thinking.

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• The Dyscalculia Toolkit