Dyscalculia in Further and Higher Education

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• Definitions and Prevalence

• Screening

• Supporting Students

Presentation

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Towards a Definition

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Mathematics Disorder: "as measured by a standardised test that is given individually, the person's mathematical ability is substantially less than would be expected from the person’s age, intelligence and education. This deficiency materially impedes academic achievement or daily living"

DSM-IV (2000)

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1. Mathematical level compared to expectation

“Most dyscalculic learners will have cognitive and

language abilities in the normal range, and may excel in non-mathematical subjects“ Butterworth (2001)

Key Features (1)

2. Impedance of academic achievement and daily living

"Dyscalculia is a term referring to a wide range of life long learning disabilities involving math… the difficulties vary from person to person and affect people differently in school and throughout life".

NCLD (2009)

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• What is “mathematical ability” ?

• “Mathematics Disorder” implies a stable cognitive root, not achievement or mastery which is subject to education and environment.

Key Features (2)

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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

The National Numeracy Strategy DfES (2001)

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• “acquire ” emphasises acquisition rather than carrying out arithmetic procedures.

• “difficulty understanding simple number concepts, lack an intuitive grasp of numbers” placing understanding at the core of dyscalculia

Key Features (1)

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“A lack of a true comprehension or understanding of maths will be a key characteristic of dyscalculic people”

Chinn S. (2006)

Key Features (2)

“Learning number facts and procedures” : more dyslexia related?

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According to current estimates

Butterworth (2002)

• About 40% of dyslexic children have some degree of difficulty with learning mathematics

• Additionally 5 to 6% of children of average to superior intelligence having a specific learning deficit in mathematics.

Prevalence

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Geary (2004) 5 - 8%

Desoete et al (2004) 3 - 8%

Butterworth (2002) 5 - 6%

Kosc (1974) 6.4%

Gross-Tsur et al (1996) 6.5%

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12

A first-line screening tool for dyscalculia focusing on

Understanding Mathematics

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Developed by Trott and Beacham, Loughborough University

K erry

d iscuss ion

in-depthd iscuss ion

re ferredby tu tor

w orkfo lder

percentages

E P

form ulae

D A S T

13

Kerry

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Model for Dyscalculia

num berconceptual

inferential

tabular

w ord

visual-spatial

direction

graphical

operational

num bercom parative

spatialtem poral

graphical

sym bolicabstraction

sym bolic

conceptual

tim e

Num ber Applications

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InitialTrials

dys lexic

gooddisc rim ination

e lec tron ic

paper

contro l

paper/e lec tron icno d iffe rence

19s tudents

dysca lcu lic

tim e

2 vers ions

score

Initial Trials

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• Involved 30 participants• Organised into three equal groups

– Dyscalculic– Dyslexic– Control

• Covered a range of academic subjects

Further Trials

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Percentage Scores for 3 Groups

%

101

102

103

104

105

106

107

108

109

110

201

202

203

204

205

206

207

208

209

210

301

302

303

304

305

306

307

308

309

310

participant40.00

50.00

60.00

70.00

80.00

90.00

100.00

O dyscalculic

O dyslexic

O control

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0

20

40

60

80

100

dyscalculic dyslexic control

0

20

40

60

80

100

dyscalculic dyslexic control

Compare 0.71 with 0.17

% c

orre

ct

Compare 3.59 with 3.509

% c

orre

ct

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0

20

40

60

80

100

dyscalculic dyslexic control

0

20

40

60

80

100

dyscalculic dyslexic controlNADP 2010

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Graph: percentage scores (revised)

%

101

102

103

104

105

106

107

108

109

110

201

202

203

204

205

206

207

208

209

210

301

302

303

304

305

306

307

308

309

310

participant20.00

40.00

60.00

80.00

100.00

O dyscalculic

O dyslexic

O control

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Further Trials

sm all sca legenera lpopu la tion dysca lcu lic

ind ividua l

data

large sca le

paper basedw hole c lass e lec tron ic

504s tudents

2nd and 8 thpercentile ranks

low

severe lyat riskvery low

at risk

Further Trials

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19dys lexicw ith M D

5 at risk

3 severe lya t risk

11not a t risk

51dysca lcu lic

on ly

15 severe lyat risk

37 identified byovera ll score

32 a t risk10 identified

by pro file

4not a t risk

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“Small-Scale” Trials, n = 70

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• Overall: “severely at risk ”

• Risk:– No. concepts– No. comparisons– Operations

Key concepts

• Not at risk– Graphical – Tabular – Time – Spatial

More visual applications

OVERALL SCORE

No Conceptual

No Comparative: Word

No Comparative: Symbol

No Comparative: VisSpat

Graphical

Tabular

Symbolic Abstraction

Spatial Direction

Time

Operational: Conceptual

Operational: Inferential

Profiler (Thomas)

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• Online large-scale screener for dyscalculia• On-line delivery of screening tool to identify

students at risk with minimal staff input• Profiler identifies students requiring further

investigation that can be:– In depth interview– Referral for further testing

Learner accesses DysCalculiUM

portal

• Completes screener

• Results automatically analysed

Tutor access DysCalculiU

M portal

• Reviews students results & profiles

• Identify students who are at risk

Further investigation of difficulties

DysCalculiUM process

One-to-one Support for the Dyscalculic Student

A Case Study: Liam

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Weaknesses• Dyscalculic• Sequencing

numbers• Problems with

calculation– Unsure of basic

operations– Use of

inappropriate strategies

Liam: Transport Management

Strengths• Verbal reasoning• Expressive

writing• Reading

comprehension

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Birmingham to

Minutes late (to nearest minute)

On time 1 to 5 6 to 10 Over 10

Paris 8 3 1 0

Brussels 6 3 1 2

Munich 4 1 0 0

Dublin 7 1 1 1

Tables of Information

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Rows and Columns

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Birmingham to

Minutes late (to nearest minute) TOTAL

On time 1 to 5 6 to 10 Over 10

Paris 8 3 1 0 12

Brussels 6 3 1 2 12

Munich 4 1 0 0 5

Dublin 7 1 1 1 10

% of flights to Brussels more than 5 mins late:

%254

1

12

3

321

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12 flights

3 late

312

1003

12

1001

%10012

flights

flight

flights

Alternative Approaches

10012

3

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6635 46 55 706945 7246 72

55 56 57 58 59 60 61 62 63 64 65 66

60.5

Median of delivery route distances (km)

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http://incompetech.com/beta/plainGraphPaper/

Resources

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• Number line

• Extend to 2-D• Moving axes

• Apply to –Correlation–Sales forecasting (interpolation)

Number Lines and Graphs

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A small airline, based at LHR, serves two cities: Oslo and Helsinki. The flying time to Oslo is 21/4 hours and to Helsinki is 3 hours. There should be 3 return flights a day to each city and the turn-round time must be at least 40 minutes, but not more than 1 hour. Construct a schedule.

Time and Scheduling

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Helsinki 1

Start 07.00

Fly time 03.00

Land GMT 10.00

Time Difference 02.00 +

Land local 12.00

Turn round 00.45

Start local 12.45

Fly time 03.00

Land local 15.45

Time difference 02.00 -

Land GMT 13.45

22:45

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L

O H

07.0010.0016.00 12.00

15.0021.00

12.4515.4521.45

13.4516.4522.45

07.0014.0018.0010.15

17.1521.15

11.0018.0022.00

12.4519.4523.45

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There is an urgent need for:• Effective screening and assessment• An understanding of student support

needs

With appropriate support the dyscalculic student can move forward and succeed.

Dyscalculia: The Way Forward

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