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The Dyslexia Guild 201016th Annual Symposium

How can you assess for dyscalculia in dyslexics and low numeracy students?

What works in intervention?

Jane Emerson: DirectorEmerson House

Hammersmith, London W6.www.emersonhouse.co.uk

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What is dyscalculia?

‘…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.’

Guidance to support pupils with dyslexia and dyscalculia.

Ref. DfES 2001

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What is understood by dyscalculia?

• An umbrella term used to refer to various conditions that cause specific difficulties with numeracy, in particular, developmental dyscalculia.

• Used to refer to different levels of difficulty with numeracy and becomes apparent at different developmental stages.

• The absence of Number Sense or low Number Sense is a sign of dyscalculia.

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Components of a Numerical Idea

• Concept of numbers:

• Linguistic:Two threes

• Procedural: 2 x 3 = 6

• Concepts are the mental representations of the world and how information is organised and generalised.

• The language used to describe what has been conceptualised. The language used affects how the concrete objects are perceived.

• The conventional symbols used to represent a taught procedure as an algorithm.

The two-ness of two

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Assessing for Dyscalculia

• The Dyscalculia Screener by Emeritus Professor Brian Butterworth

• Designed to distinguish the dyscalculic learner from other low attaining learners

• An online assessment which looks for evidence of dyscalculia.

The Dyscalculia Assessment

by Emerson and Babtie

• Shows you how to find out why a child is struggling with basic numeracy

• Explains what you can do to help pupils to learn essential number facts and concepts

• Gives information for teaching plan

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The Dyscalculia Screener can be used in conjunction with The Dyscalculia Assessment

The Dyscalculia Screener by Brian Butterworth pub. by nferNelson• Computerised for use in schools (30 mins)Subtests: Subitizing/counting Number size comparisons Mental arithmetic

• Precise measures including reaction time, standardised and quick to administer

• Assumes dyscalculia is caused by a core deficit in parietal lobe affecting number sense, as opposed to other causes such as co-morbid conditions such as dyslexia or dyspraxia.

See www.mathematicalbrain.com

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What to look for? Surface symptoms that you may see in the classroom.• Delay in flexible counting development• Immature strategies such as counting ‘all’

instead of counting ‘on’, plus finger counting• Poor memorization of facts and procedures (e.g.

doubles, number bonds, tables)• Lack of reasoning from known fact to unknown

fact: 2+2=4 so 2+3=one more than 4.• Poor understanding of place value• Difficulties with application to solve word

problems and multi step calculations

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The Dyscalculia Assessment

• A practical investigation of a pupil’s sense of number, knowledge and skills

• Can be used to assess anyone’s low levels of numeracy

• Does not compare an individual to others, except for planning group teaching

• Considers the child’s style of thinking: visual or auditory

• Information is recorded on a summary sheet

• Practical suggestions for games and activities

The Dyscalculia Assessment looks for evidence of mathematical thinking, that is, the ability to reason about number. If present this suggests a positive prognosis for the effect of tried and tested interventions developed at Emerson House.

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Areas Assessed

• Number Sense and Counting

• Calculation

• Place Value

• Multiplication and Division

• Word problems

• Formal Written Numeracy

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Assessing Number Sense

• An ability to estimate the size of a quantity of objects

• Early knowledge of the way the number system is structured in groups of tens

• Subitizing

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Can you subitize this many?

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What is Subitizing?

• The ability to enumerate a random array of objects at a glance without counting

• Most people can subitize up to 5 objects

• An innate ability which may be lacking in dyscalculics

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How many ladybirds?How many spots on the ladybirds?

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The DyscalculiaAssessment

has

RecordingSheets

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Summary Maths Profile

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What information is gained from the Dyscalculia Assessment and what can be done

with it?• The information can be analysed using the

Interpretation Section. • The information can be recorded on the Summary

Maths Profile form for ease of analysis.• It can be entered onto a Group Grid using an excel

spread sheet given in the appendices.• Children can then be grouped for teaching purposes

depending on the findings.• Activities and games can be selected to match the

needs of the groups from the games chapter.

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What works in intervention?

• Multi-sensory teaching: concrete materials, talking, listening

• Discussion between teacher and pupil

• Do it, see it, say it : understand

• Guided teaching to explore concepts

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Concrete Materials

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Rods for components

Cuisenaire Rods • Rods can be used as continuous materials when children are ready to move from discrete dice patterns

• They can be used to demonstrate both whole numbers and parts of wholes.

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Emerson House Mathematics.

• A systematic, multi-sensory way of teaching numeracy based on the doubles patterns and extending those patterns eg. 2+2 and 2+3

• The universal principle is: teach all bonds, expect internalisation of the minimum, and then teach strategies to derive the others.

• Teach pupils to be flexible thinkers who can recognise, generate and use numbers to solve problems.

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Teaching Number Sense and Counting

• Estimating: developing awareness of quantity

• Counting: counting of items into lines of tens to help pupils develop sense of the tens based system

• Getting pupils to stop counting in ones (The Counting Trap) by seeing the structure of tens and ‘some more’

• Studying dice patterns: 1 to 6 then 7 to 10.

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Building over 100

• Numicon boxes with Base Ten Materials

• Once children are calculating comfortably up to 100, they can study the numbers over 100

• Base 10 can be used to build 100s in tens to emphasise the repeating 10s

• Revise adding 1 or 10 for 100,101,110, 120,121, etc.

• A 100 metre stick can be exchanged for 100s.

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Teaching Calculation• Dice patterns 1-6• Dot patterns 7-10 : made

of doubles and near doubles, visually distinct images, key facts

• Bonds of 10: 5+5, 9+1 etc.• Bonds of the counting

numbers under ten: 3=2+1etc.

• Reasoning from key facts to calculate: to think mathematically; 5+5=10 so 5+6=11

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Semi Abstract Representationsfor Doubles and near Doubles

• Use counters initially: concrete to semi abstract

• Reason for near doubles:• If 2+2=4 then 2+3=‘just

one more’ so must be 5.• This is highly diagnostic

when a young child with possible dyscalculia is first seen.

• Can they reason at all about number?

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Dot pattern games

• To develop quantitative awareness : 6 > 5

• To build pattern recognition skills

• To develop children’s

ability to talk about numbers and relative sizes

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The Tables as repeated addition.

Key facts 1x the table, 10x the table and 5x the table being studied.

So if 5x4=20 then 6x4=20+4 and if 10x4=40 then 9x4=40-4

• Step-count in fours

• Step-count from different starting points

4,8,12 or 20,24,28

• Ask one-step questions:

• What is one more 4 than 20?

• Ask two-steps questions: What are two more 4s than 24? (28+4 revises bridging)

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Teaching Multiplication and Division as closely associated

• Multiplication as repeated addition• Division as grouping and, later, sharing• False separation: teach inverse

relationship of the concepts at the same time to stress the connections:

• 2 x 3 = 6 and 3 x 2 = 6• Two threes in 6 and three twos in 6• 6 divided by 3 is 2 and 6 divided by 2 is 3.

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Teaching Multiplication and Division

• Multiplication as repeated addition

• Multiplication as Area Model

• Division as grouping and, later, sharing:

• Avoid false separation: teach inverse relationship of these concepts

5 x 3 = + + + + = 15

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Teaching Place Value

• Principle of exchange: several items can be represented by another single item

• Place Value: structure of the number system:

HTU:HTU:HTU Teach repeated

pattern of threes

H T UH T U

Thousands

H T U

Millions

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Partitioning with concrete materials on a place value mat

• 57 is partitioned • 50 and 7• 5 tens and 7 units• Base ten Dienes

materials could be used • Stern rods could be used• Flexible partitioning can

be used with older children

• 57 is made of 40 and 17 for example, can be shown to make a column arithmetic sum

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Teaching Bridging as a Universal Strategy

• Bridging is a technique based on linear understanding of the number system where 10 or multiples of ten are used as a stepping stone to the next decade.

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Concrete materials to teach Bridging.

• Bridging forward

9+3= (9+1)+2= 12

• Bridging back for numbers close on a number line

12-3 =(12-2)-1 = 9

‘ I KNOW THAT 12 TAKE AWAY 2 IS 10. THEN TAKE ONE MORE AWAY TO GET BACK TO 9 BECAUSE 9 IS ONE LESS THAN 10.’

‘I KNOW THAT 12 IS MADE OF 3+9 SO 12 TAKE AWAY 3 LEAVES 9.’

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Teaching Word Problems• Pupils explaining their

thinking from the start• Leads to conceptual

foundations for word problems

• Use concrete objects to model the problems

• Draw images or diagrams • Write algorithms• Beware of teaching

trigger words• Check the answer is

possible or sensible

• There are three ducks on four ponds• What is the total number

of ducks?

NOTE IF THE PUPIL CAN DRAW THE IMAGES OR RECORD THEIR THINKING AS 3+3+3+3 OR 3X4

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Teaching Formal Written Methods

• Train the pupil to do a rough estimation to establish the approximate size of the answer to all calculations before doing formal written work.

• Teach the child how to set out and use standard written forms correctly.

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Concluding Remarks

• The information can be analysed using the Interpretation Section.

• The information can be recorded on the Summary Maths Profile form.

• It can be entered onto a Group Grid using an excel spread sheet given in appendices.

• Children can be grouped for teaching purposes depending on the findings.

• Activities and games can be selected to match the needs of the groups from chapter 6.

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Summing up• Why has The Dyscalculia Assessment been carried out?

To find out why a pupil is struggling with basic numeracy, and how they think about numeracy. Is it a memory problem or a reasoning problem?

• What is to be done with the information gained?

A multi sensory teaching plan can be devised to help the pupil to learn essential facts and concepts.

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Today is all about having different points of view.

Open?Enquiring?Fascinated?

Safe?Limited?Confident?

Not Amused?Frustrated?Resigned?