dyscalculium: a first-line screener for dyscalculia in higher education clare trott and nigel...
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DyscalculiUM: A First-Line Screener for Dyscalculia
in Higher Education
Clare Trott and Nigel Beacham
Mathematics Education Centre, Loughborough University
September 2006Neurodiversity Conference
DeMontfort University
There is currently no accepted definition of dyscalculia
A number of different definitions exist
• Numerically based• Cognitive based• Neuroscience based
Definition
• 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 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"
Two Important Features 1. Mathematical level compared to expectation
2. Impedance of academic achievement and daily living
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
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.”
StatisticsGeary (2004) 5 - 8%
Desoete et al (2004) 3 - 8%
Butterworth (1999) 4 - 6%
Kosc (1974) 6.4%
Gross-Tsur (1996) 6.5%
Kerry • Sent to MLSC by her tutor, suggesting dyscalculia
• Detailed interview and look at work folder
• Very basic difficulties with understanding simple %
• LHS of the formula did not co-exist with the RHS
• Dyslexia screening - negative result
• However, fundamental problems still remained
• Much discussion
• Kerry sent to Educational Psychologist who confirmed dyscalculia (no dyslexia)
• Highlighted urgent need for screener
numberconceptual
operational
numbercomparative
conceptual
inferential
verbal
visual-spatial
graphical
symbolic
abstract symbolic
graphs
tables
Spatial-Temporal
Direction
Time
Cognitive Model for Dyscalculia
Cognitive Model
• Conceptual – understanding of number, place value
• Comparative – relative size
• Verbal• Symbolic• Visual-Spatial
Operational
• Conceptual – conception of correct operation to
• achieve required outcome• reverse a process
• Inferential – given an operational definition
• make comparative inferences about an outcome, without realising the outcome
• Infer an operational relationship
• Abstract Symbolic
• Spatial-Temporal– Understanding
• Visual-Spatial diagrams• Time
• Graphical – Reading and Interpreting
• Graphs• Tables
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
• Available in both paper and electronic versions
• Electronic version produced on CD-ROM
• Electronic version developed in Perception
• 19 students
• Dyscalculic only, dyslexic only,
no SpLD
• Showed no difference between paper and electronic versions
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
Dyscalculic v control
Percent
Sensitivity 83.3%
Specificity 92.3%
Percent
Sensitivity 83.3%
Specificity 85.7%
Dyslexic
v Non-dyslexic
Dyscalculic v Dyslexic
Percent
Sensitivity 50.0%
Specificity 87.5%
• Background colour
• Removed timer
• Scrolling and layout
• Submit button
Modifications
Phase Three Trials
• Involved 30 participants• Organised into three equal groups
– Dyscalculic– Dyslexic– Control
• Covered a range of academic subjects• Observation carried out• Covering 4 HEIs
Dyscalculics v Control
Threshold = 87% (changed from 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
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
“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
DirectionUsing clockwise and
anti-clockwise
0
20
40
60
80
100
dyscalculic dyslexic control
% correct
Reading off the vertical axis on a bar chart.
0
20
40
60
80
100
dyscalculic dyslexic control
% correct
Between which years the “smallest increase” occurred
0
20
40
60
80
100
dyscalculic dyslexic control
% correct
Interval BisectionWhich number is half way
between 2.8 and 3.2?
0
20
40
60
80
100
dyscalculic dyslexic control
% correct
Towards Abstraction
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 61 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
Phase 4 Trials
• 137 students
• 4 HE institutions
• 3 FE colleges
• Large groups/small groups/individuals
Trials: Screening
• 16 out of 137 identified “at risk” – 8% prevalence
• Geary (2004) 5 - 8%
• Desoete et al (2004) 3 - 8%
• Butterworth (1999) 4 - 6%
• Not post-16
Further Issues
• English not first language– 2 out of 5 “at risk”– Mathematical or language difficulties?
• Neurodiversity– Dyslexia, Asperger’s Syndrome, ADHD, Dyspraxia
• More research needed
Summary• Provides an effective screening tool for HE• Discriminates dyscalculia from dyslexia• Easily accommodated into screening process• Large or small groups or individuals
Future• Extensive trials in Autumn 2006• Profile reporting, based on cognitive model
Profiler
Conceptual
Operational Conceptual
Graphical
Tabular
Symbolic Abstraction
Comparative Visual-Spatial
Spatial Directional
Total Score
Comparative Symbolic
Comparative Verbal
Operational Relational
Spatial Temporal
Time Taken: 25 Minutes
Threshold
ReferencesBeacham, N. and Trott, C. (2006) Project Update, Widening the use of DyscalculiUM: A first-line screening test for dyscalculia in Higher Education, MSOR Connections, Vol 6 No 1.Beacham, N. and Trott, C. (2005) Screening for Dyscalculia within Higher Education, MSOR Connections Vol 5 No 1.Butterworth, B. (1999) The Mathematical Brain. London: Macmillan.Desoete, A., Roeyers, H. & De Clercq, A. (2004) Children with Mathematics Learning Disabilities in Belgium, Journal of Learning Disabilities, 37, 50-61.DfES (2001) The National Numeracy Strategy, Guidance to support pupils with dyslexia and dyscalculia DfES 0512/2001Geary, D.C. (2004) Mathematics and Learning Disabilities. Journal of Learning Disabilities, 37, 4-15Gross-Tsur, V., Manor,O. and Shalev R.S. (1996) Developmental Dyscalculia: prevalence and demographic features. Developmental Medicine and Child Neurology. 38, 25-33Kosc, L. (1974) Developmental Dyscalculia. Journal of Learning Disabilities, 7, 46-59Sharma, M. (1997) Dyscalculia. http://www.dyscalculia.org/BerkshireMath.html