dyscalculium a first-line screening devise for dyscalculia in higher education

DyscalculiUM a first-line Screening Devise

for dyscalculia in Higher Education

Clare Trott and Nigel Beacham

DDIG conference

Wednesday 13th April 2005

Kerry

• Sent to MLSC by her tutor who suggested she might be dyscalculic

• Kerry interviewed in detail and looked at her work folder

• Very basic difficulties with understanding simple %

• LHS of the formula did not co-exist with the RHS

• Kerry was sent for dyslexia screening which produced a negative result

• However, fundamental problems still remained

• Much discussion

• Kerry sent to Educational Psychologist who confirmed dyscalculia (no dyslexia)

Statistics

According to current estimates (Butterworth (1999))

• about 10% of the population are dyslexic (4% severe, 6% mild/moderate)

• of these 40% have some degree of difficulty with maths

• additionally 4 to 6% is dyscalculic only.

• There is currently no accepted definition of dyscalculia

• A number of different definitions exist

• Numerically based• Cognitive based• Neuroscience based

• The DSM-IV document, used by educational psychologists, defines Mathematics disorder in term of test scores:

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

Two Important Features 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 (1999)

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".

The National Center for Learning Disabilities, http://www.ld.org/LDInfoZone/InfoZone_FactSheet_Dyscacluia.cfm, Access: 22/10/03

More precise specification (Mahesh Sharma)  “Dyscalculia is an inability to conceptualise numbers, number relationships (arithmetical facts) and the outcomes of numerical operations (estimating the answer to numerical problems before actually calculating).”  

The emphasis here being on conceptualisation rather than on the numerical operations

The National Numeracy Strategy The DfES (2001)

 " 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."  

• Currently used by the BDA.

• Perhaps more applicable to education in the early years

• In H.E. emphasis is less on basic computation and more on the application and understanding of skills and techniques

Newman (1997) offers several subdivisons of dyscalculia, including:

• Primary - dyscalculia being the main LD

• Secondary - dyscalculia occurring with other LDs

Butterworth (2002)

Effective problem solving:

"One of the things that distinguishes people who are good at maths, have effective 'mathematical brains', is an ability to see a problem in different ways. This is because they understand it. This, in turn, allows the use of a range of different procedures to solve it and to select the one that will be most effective in this particular task".

Key Points

• Mathematical ability substantially less than expectation

• “Impedes academic achievement or daily living”

• Inability to conceptualise

• Failure to understanding number concepts and relationships

Our Working Definition

“Dyscalculic students have a low level of numerical or mathematical competence compared to expectation. This expectation being based on unimpaired cognitive and language abilities and occurring within the normal range. The deficit will severely impede their academic progress or daily living.

Dyscalculia is therefore an inability to effectively connect with number and mathematics. It may include difficulties recognising, reading, writing or conceptualising numbers, understanding numerical or mathematical concepts and their inter-relationships.

It follows that dyscalculics may have difficulty with numerical operations, both in terms of understanding the process of the operation and in carrying out the procedure. Further difficulties may arise in understanding the systems that rely on this fundamental understanding, such as time, money, direction and more abstract mathematical, symbolic and graphical representations.”

Neuroscience Research

• “An elementary number system is present very early in life in both humans and animals, and constitutes the start-up-tool for the development of symbolic numerical thinking that permeates our western technological societies“ (Dehaene 1997)

• Different mathematical and arithmetical processes are associated with different areas of the brain.

Triple Code Theory (Dehaene (1997))

Numbers need to be

Read as words Recognised in Arabic digital form The corresponding concept of its

quantity formed.

The existence of three related neural regions.

1. A domain where numerical quantity is represented and in which quantities are manipulated

2. A region associated with the verbal processing of numbers

3. A region associated with visual-spatial processing

Dehaene et al. (2002)

Mathematics Support for students with

dyslexia and dyscalculia

Dyslexia and no dyscalculia

Dyslexia and dyscalculia

No dyslexia and

dyscalculia

Mathematically able

Mathematical difficulties

Language based•Working memory•Reading•Understanding text•Presentation

Moving from concrete to

abstract

MathsPhysics

Engineering

EconomicsHuman Sciences

Business

Language based•Working memory•Reading•Understanding text•Presentation

Number related•Number relations•Number concepts•Number operations

Human Sciences

Social ScienceBusiness

Number related•Number relations•Number concepts•Number operations

Human SciencesSocial Science

Business

Framework for Dyslexic and Dyscalculic students

Development of the screener

TIME

understanding

reading

ordering duration

timeline

organising

non- decimal

clocks

Time- tables

analog

digital equivalence

is time decimal?

split up day

medication

historical journey time

test length

lunch break

Developing a dyscalculia screening tool

• Available in both paper and electronic versions

• Electronic version produced on CD-ROM

• Electronic version developed in Perception

Developing a dyscalculia screening tool

• Background colour

• Previous button

• Time taken

• Scrolling and layout

• Submit button

Issues in developing a dyscalculia screening tool

Loughborough Initial Trials

Paper v Electronic version• Three student groups defined

by their primary SpLD– Dyscalculia– Dyslexia– No SpLD

• No significant difference in completion time or in performance scores

• Showed that paper and electronic versions perform the same

0

10

20

30

40

50

60

70

80

90

100

Time (minutes) Performance(%)

Paper

Electronic

Further Analysis

• Sensitivity– The probability that a dyscalculic student

performed below the acceptable threshold– How good is the screener at correctly including

individuals who are dyscalculic

• Specificity– The probability that a non-dyscalculic student

performed above the acceptable threshold– How good is the screener at correctly excluding

individuals who are non-dyscalculic

Dyscalculics v Non-dyscalculics

• Distinguishes between dyscalculic and non-dyscalculic individuals in terms of score

Score Percent

Sensitivity 83.3%

Specificity 92.3%

Dyscalculics v Non-dyscalculics

• Distinguishes between dyscalculic and non-dyscalculic individuals in terms of time

Time Percent

Sensitivity 83.3%

Specificity 69.2%

Dyscalculic v Dyslexic

• Threshold score 87%

• Threshold time 31 minutes

Score Time

Sensitivity 83.3% 66.6%

Specificity 85.7% 57.1%

Dyslexic v Non-dyslexic

• Threshold score 87%

• Threshold time 29 minutes

Score Time

Sensitivity 50.0% 72.7%

Specificity 87.5% 87.5%

Summary of Results• Distinguishes between dyscalculic and non-

dyscalculic in terms of both score, but less well in terms of time

• Distinguishes between dyscalculic and dyslexic individuals in terms of scores but less well in terms of time

• Distinguishes between dyslexic and non-dyslexic individuals in terms of time but less well in terms of score

• No student took longer than 48 minutes• That the score is the key factor

Beacham, N. and Trott, C. (2005) Screening for Dyscalculia within Higher Education, MSOR Connections: Quarterly Newsletter, Vol. 5, No. 1.

New trial

• Involved 30 participants• Organised into three groups

– Dyscalculic– Dyslexic– Control

• Covered a range of academic subjects• Observation carried out• Covering 4 HEIs

Dyscalculics v Control

The first trials used a threshold of 87%. After the trials the test was modified and it is now appropriate to change the threshold to 89%.

Current trial Initial trial

sensitivity 100% 83.3%

specificity 100% 92.3%

Dyscalculics v Control graph

101

102

103

104

105

106

107

108

109

110

301

302

303

304

305

306

307

308

309

310

number

40.00

50.00

60.00

70.00

80.00

90.00

100.00

per

cen

t

group

dyscalculic

control

101102

103104

105106

107108

109110

301302

303304

305306

307308

309310

participant

40.00

50.00

60.00

70.00

80.00

90.00

100.00

percent

O dyscalculic

O control

Dyscalculics v Dyslexics

  Current trial   Initial trial

Sensitivity 100% 83.3%

Specificity 70% 85.7%

Dyslexics v Control

Current trial Initial trial

Sensitivity 30% 50%

Specificity 100% 87.5%

Percentage Scores for 3 Groups

percent

101102

103104

105106

107108

109110

201202

203204

205206

207208

209210

301302

303304

305306

307308

309310

participant

40.00

50.00

60.00

70.00

80.00

90.00

100.00

O dyscalculic

O dyslexic

O control

• The statistics are affected by 3 dyslexics who appear to be in the dyscalculic range. Their scores are 75.8%, 82.5% and 85.8%.

• It is believed that around half dyslexic students have difficulties with Maths

• A one-way Anova was performed on the scores of the 3 groups. (F(3,27) = 20.430, p < 0.0005).

• Post Hoc analysis showed sig. differences between groups 1/2, 1/3 but not groups 2/3 .

Examples from DyscalculiUM

• Decimals

• Direction

• Bar graph

• Interval bisection

• Towards abstraction

DecimalsCompare 3.59 with 3.509

0

20

40

60

80

100

dyscalculic dyslexic control

% correct

DecimalsCompare 0.71 with 0.17

0

20

40

60

80

100

dyscalculic dyslexic control

%correct

Nonverbal Learning Disability*

• High correlation between NLD and dyscalculia

• Good language skills and verbal reasoning

• Poor visual-spatial orientation E.G. reading maps, graphs and charts

*Rourke B.P.(1989) Nonverbal Learning Disabilities: The Syndrome and the Model, New York, Guilford Press

“It makes for interesting travel as I've missed countless trains and buses or got on the wrong train on the wrong platform at the wrong time. Travel directions have to be written in minute detail as I have no understanding of the motorway network and anything more than 'take the next left' goes in one ear and out the other. I can get lost in a box."

J. Blackburn “Damn the Three Times Table”http://ddig.lboro.ac.uk/pages/ideas_exchange.html

Direction

DirectionFollowing a set of directions involving left and right turns.

0

20

40

60

80

100

dyscalculic dyslexic control

% correct

Direction

DirectionUsing clockwise and

anti-clockwise

0

20

40

60

80

100

dyscalculic dyslexic control

% correct

Bar Graph

GraphsReading off the vertical axis on a

bar chart.

0

20

40

60

80

100

dyscalculic dyslexic control

% correct

GraphsBetween which years the

“smallest increase” occurred

0

20

40

60

80

100

dyscalculic dyslexic control

% correct

Towards Abstraction

Towards Abstraction

0

20

40

60

80

100

dyscalculic dyslexic control

% correct

Interval Bisection

• Research has shown that poor visual-spatial skills result in difficulties with number bisection tasks*

* Dehaene, S.,& Cohen, L. (1997). Cerebral pathways forcalculation: Double dissociation between rote verbaland quantitative knowledge of arithmetic. Cortex, 33,219–250.

Which number is half way between 2.8 and 3.2?

0

20

40

60

80

100

dyscalculic dyslexic control

% correct

Subtest

• Takes ≤ 48 minutes• Use for screening process with other

tools• Eliminate items with poor discrimination• Eliminate items that impede students

with dyslexia• Subtest consists of 55 items and takes

approx. 20-25 mins

Graph: percentage scores on the subtest

percent

101102

103104

105106

107108

109110

201202

203204

205206

207208

209210

301302

303304

305306

307308

309310

number

20.00

40.00

60.00

80.00

100.00

O dyscalculic

O dyslexic

O control

Maths Anxiety Dyscalculic group

020406080

100

low medium high

Anxiety Level

%

Maths Anxiety Dyslexic group

020406080

100

low medium high

Anxiety Level

%

Maths Anxiety Control group

020406080

100

low medium high

Anxiety Level

%

Future• More trials in Autumn• 2 versions – long and short• Development of suitable teaching

methods and materials for dyscalculic students

“A thousand words is worth a lot more than two bar charts and a line graph” *

*Zieman, G. (2000) Nonverbal Learning Disability: The Math and Handwriting Problem. Parenting New Mexico. Feb 2000 accessed on http://www.ziemang.com/pnm_articles/00021d.htm

Acknowledgements

• Tony Croft (Loughborough University)

• Sarah Parsons (Harper Adams University College)

• Fiona White (Leicester University)

• Jane Jolliffe (Bournemouth University)

• Jan Robertson (De Montfort University)

• Higher Education Academy MSOR

ReferencesBeacham, N. and Trott, C. (2005) Screening for Dyscalculia within Higher Education, MSOR Connections: Quarterly Newsletter, Vol. 5, No. 1.Butterworth, B. (1999) The Mathematical Brain. London: Macmillan.Butterworth, B (2002) Ch. 10. From fear of fractions to the joy of maths http://www.mathematicalbrain.com/test.htmlDehaene, S.,& Cohen, L. (1997). Cerebral pathways for calculation: Double dissociation between rote verbal and quantitative knowledge of arithmetic. Cortex, 33, 219–250.Dehaene, S. (1997) The number sense, New York Oxford University press.Dehaene, S., Piazza, M., Pinel, P. and Cohen, L. (2002) Three parietal circuits for number processing. Cognitive Neuropsychology, 2003, 20, pp.487-506DfES (2001) The National Numeracy Strategy, Guidance to support pupils with dyslexia and dyscalculia DfES 0512/2001Henderson, A. (2004) Working with Dyscalculia: Recognising Dyscalclulia overcoming barriers to learning in maths, Learning Works International Ltd.The National Center for Learning Disabilities, http://www.ld.org/LDInfoZone/InfoZone_FactSheet_Dyscacluia.cfm, Access: 22/10/03Newman, R.M. (1997) Dyscalculia Symptoms: dyscalculia.org (online), Available from http://www.dyscalculia.org/calc.html, Accessed on 29/10/01.Rourke, B.P. (1998) Significance of Verbal-Performance Discrepancies for Subtypes of Children with Learning Disabilities. WISC-III Clinical Uses and Interpretation. Eds. Prifitera, A, and Saklofske, D. Academic Press.Sharma, M. (1997) Dyscalculia. http://www.dyscalculia.org/BerkshireMath.html, Accessed on 24/11/04.Trott, C. (2003), Mathematics Support for Dyslexic Students. In Lawson, D, Croft, T. and Halpin, M. Good Practice in the Provision of Mathematics Support Centres, pp 22-28 LTSN MSOR, ISSN 1476-1378. Reprinted in MSOR Connections Vol. 3 (3) November 2003 Pp 17-20 ISSN 1473-4869.Zieman, G. (2000) Nonverbal Learning Disability: The Math and Handwriting Problem. Parenting New Mexico. Feb 2000 accessed on http://www.ziemang.com/pnm_articles/00021d.htm

Contact details

• Clare Trott– Email: C.Trott@lboro.ac.uk

• Nigel Beacham– Email: N.Beacham@lboro.ac.uk

• Also see Dyscalculia and Dyslexia Interest Group (DDIG) website– http://ddig.lboro.ac.uk