Transcript Direction - Richard Hemmings

DyscalculiUM: A First-Line
Screener for Dyscalculia
in Higher Education
Clare Trott and Nigel Beacham
Mathematics Education Centre,
Loughborough University
September 2006
Neurodiversity Conference
DeMontfort University
Definition
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 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.”
Statistics
Geary (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
Cognitive Model for Dyscalculia
inferential
operational
abstract
symbolic
conceptual
number
conceptual
number
comparative
symbolic
verbal
tables
graphical
graphs
visual-spatial
Direction
Time
SpatialTemporal
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
Phase One
Developing the Dyscalculia
Screening Test
Development of the screener
equivalence
digital
is time decimal?
analog
clocks
nondecimal
split up day
reading
organising
Timetables
understanding
medication
TIME
historical
timeline
journey time
ordering
duration
test length
lunch break
• Available in both paper and electronic
versions
• Electronic version produced on CD-ROM
• Electronic version developed in
Perception
Electronic version
Phase Two
Initial Trials
• 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
Dyslexic
Dyscalculic
v control
Percent
Sensitivity
83.3%
Specificity
92.3%
Percent
Sensitivity
83.3%
Specificity
85.7%
Percent
Dyslexic
v Non-dyslexic
Sensitivity
50.0%
Specificity
87.5%
Modifications
• Background colour
• Removed timer
• Scrolling and layout
• Submit button
Phase Three
Further Trials
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
100.00
90.00
group
100.00
dyscalculic
control
80.00
90.00
80.00
70.00
percent
percent
70.00
60.00
60.00
50.00
O dyscalculic
50.00
40.00
40.00
310
309
308
307
306
305
304
303
302
301
110
109
108
107
106
105
104
103
102
101
number
1 1 1 1 1 1 1 1 1 1
3 3
0 3
0 3
0 3
0 3
0 3
0 3
0 3
0 3
1
0 0 0 0 0 0 0 0 0 1 0
1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0
participant
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
100.00
90.00
O dyscalculic
O dyslexic
80.00
percent
O control
70.00
60.00
50.00
40.00
22 2 2 22 2 223 33 3 33 3 3 33
1 1 11 1 11 1 11 2
00 0 0 00 0 010 00 0 00 0 0 01
0 0 00 0 00 0 01 0
1 2 34 5 67 8 90 1 23 4 5 67 8 901 23 4 56 7 8 90
participant
Examples from DyscalculiUM
• Decimals
• Direction
• Bar graph
• Interval bisection
• Towards abstraction
Decimals
Compare 3.59 with 3.509
100
80
%
correct
60
40
20
0
dyscalculic
dyslexic
control
Decimals
Compare 0.71 with 0.17
100
%
correct
80
60
40
20
0
dyscalculic
dyslexic
control
Direction
“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
Direction
Following a set of directions
involving left and right turns.
100
%
correct
80
60
40
20
0
dyscalculic
dyslexic
control
Direction
Direction
Using clockwise and
anti-clockwise
100
80
%
correct
60
40
20
0
dyscalculic
dyslexic
control
Bar Graph
Reading off the vertical axis on a
bar chart.
100
80
%
60
correct
40
20
0
dyscalculic
dyslexic
control
Between which years the
“smallest increase” occurred
100
%
correct
80
60
40
20
0
dyscalculic
dyslexic
control
Interval Bisection
Which number is half way
between 2.8 and 3.2?
100
80
%
60
correct 40
20
0
dyscalculic
dyslexic
control
Towards Abstraction
Towards Abstraction
100
80
%
correct
60
40
20
0
dyscalculic
dyslexic
control
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
100.00
O dyscalculic
O dyslexic
80.00
O control
percent
60.00
40.00
20.00
2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3
1 1 1 1 1 1 1 1 1 1 2
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 1 0
1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0
number
Phase Four
More Trials
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
Threshold
Total Score
Comparative Symbolic
Comparative Verbal
Comparative Visual-Spatial
Conceptual
Graphical
Operational Conceptual
Operational Relational
Spatial Directional
Spatial Temporal
Symbolic Abstraction
Tabular
Time Taken: 25 Minutes
References
Beacham, 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 0512/2001
Geary, D.C. (2004) Mathematics and Learning Disabilities. Journal of
Learning Disabilities, 37, 4-15
Gross-Tsur, V., Manor,O. and Shalev R.S. (1996) Developmental
Dyscalculia: prevalence and demographic features. Developmental
Medicine and Child Neurology. 38, 25-33
Kosc, L. (1974) Developmental Dyscalculia. Journal of Learning
Disabilities, 7, 46-59
Sharma, M. (1997) Dyscalculia.
http://www.dyscalculia.org/BerkshireMath.html