DyscalculiUM a firstline Screening Devise for dyscalculia in Higher Education

1
DyscalculiUM a first-line Screening Devise for
dyscalculia in Higher Education

• Clare Trott and Nigel Beacham
• DDIG conference
• Wednesday 13th April 2005

2
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

3

• 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)

4

• 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.

5

• There is currently no accepted definition of
  dyscalculia

• A number of different definitions exist

• Numerically based
• Cognitive based
• Neuroscience based

6

• 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"

7

• Two Important Features
• 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)

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• 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_Dy
  scacluia.cfm, Access 22/10/03

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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
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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."  
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• 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

12

• Newman (1997) offers several subdivisons of
  dyscalculia, including
• Primary - dyscalculia being the main LD
• Secondary - dyscalculia occurring with other LDs

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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".

Butterworth (2002)
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Key Points

• Mathematical ability substantially less than
  expectation
• Impedes academic achievement or daily living
• Inability to conceptualise
• Failure to understanding number concepts and
  relationships

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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.
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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.
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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.
18
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.
  

19

• Triple Code Theory (Dehaene (1997))
• Numbers need to be
• Read as words
• Recognised in Arabic digital form
• The corresponding concept of its quantity formed.
  

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• The existence of three related neural regions.
• A domain where numerical quantity is represented
  and in which quantities are manipulated
• A region associated with the verbal processing
  of numbers
• A region associated with visual-spatial
  processing
• Dehaene et al. (2002)

21
Framework for Dyslexic and Dyscalculic students
22
Development of the screener
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Developing a dyscalculia screening tool

• Available in both paper and electronic versions
• Electronic version produced on CD-ROM
• Electronic version developed in Perception

24
Developing a dyscalculia screening tool
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Issues in developing a dyscalculia screening tool

• Background colour
• Previous button
• Time taken
• Scrolling and layout
• Submit button

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Loughborough Initial Trials
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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

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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

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Dyscalculics v Non-dyscalculics

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

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Dyscalculics v Non-dyscalculics

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

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Dyscalculic v Dyslexic

• Threshold score 87
• Threshold time 31 minutes

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Dyslexic v Non-dyslexic

• Threshold score 87
• Threshold time 29 minutes

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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.
34
New trial

• Involved 30 participants
• Organised into three groups
• Dyscalculic
• Dyslexic
• Control
• Covered a range of academic subjects
• Observation carried out
• Covering 4 HEIs

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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.

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Dyscalculics v Control graph
100.00
O dyscalculic O control
90.00
80.00

percent
70.00
60.00
50.00
40.00
1
1
1
1
1
1
1
1
1
1
3
3
3
3
3
3
3
3
3
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
participant
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Dyscalculics v Dyslexics
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Dyslexics v Control
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Percentage Scores for 3 Groups
O dyscalculic O dyslexic O control
percent
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• 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 lt 0.0005).
• Post Hoc analysis showed sig. differences
  between groups 1/2, 1/3 but not groups 2/3 .

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Examples from DyscalculiUM

• Decimals
• Direction
• Bar graph
• Interval bisection
• Towards abstraction

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DecimalsCompare 3.59 with 3.509
correct
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DecimalsCompare 0.71 with 0.17
correct
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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

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• 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

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Direction
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DirectionFollowing a set of directions involving
left and right turns.
correct
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Direction
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DirectionUsing clockwise and anti-clockwise
correct
50
Bar Graph
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GraphsReading off the vertical axis on a bar
chart.
correct
52
GraphsBetween which years the smallest
increase occurred
correct
53
Towards Abstraction
54
Towards Abstraction
correct
55
Interval Bisection

• Research has shown that poor visual-spatial
  skills result in difficulties with number
  bisection tasks
• Dehaene, S., Cohen, L. (1997). Cerebral
  pathways for
• calculation Double dissociation between rote
  verbal
• and quantitative knowledge of arithmetic. Cortex,
  33,
• 219250.

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Which number is half way between 2.8 and 3.2?
correct
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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

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Graph percentage scores on the subtest
O dyscalculic O dyslexic O control
percent
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Maths Anxiety Dyscalculic group

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Maths Anxiety Dyslexic group

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Maths Anxiety Control group

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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.co
  m/pnm_articles/00021d.htm

63
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

64
References
Beacham, 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.html Dehaene
, S., Cohen, L. (1997). Cerebral pathways for
calculation Double dissociation between rote
verbal and quantitative knowledge of arithmetic.
Cortex, 33, 219250. 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.487-506 DfES (2001) The National
Numeracy Strategy, Guidance to support pupils
with dyslexia and dyscalculia DfES
0512/2001 Henderson, 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/LDInfoZon
e/InfoZone_FactSheet_Dyscacluia.cfm, Access
22/10/03 Newman, 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
65
Contact details

• Clare Trott
• Email C.Trott_at_lboro.ac.uk
• Nigel Beacham
• Email N.Beacham_at_lboro.ac.uk
• Also see Dyscalculia and Dyslexia Interest Group
  (DDIG) website
• http//ddig.lboro.ac.uk