Transcript My Presentation

Dyscalculia in Further and
Higher Education
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Presentation
• Definitions and Prevalence
• Screening
• Supporting Students
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Towards a Definition
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DSM-IV (2000)
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"
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Key Features (1)
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)
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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Key Features (2)
• What is “mathematical ability” ?
• “Mathematics Disorder”
– implies a stable cognitive root
– not achievement or mastery which is
subject to education and environment
– Not assessed by achievement test
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The National Numeracy
Strategy 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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Key Features (1)
• “ability to 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
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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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Prevalence
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.
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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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A first-line screening tool for dyscalculia
focusing on
Understanding Mathematics
Developed by Trott and Beacham,
Loughborough University
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Kerry
Kerry
referred
by tutor
in-depth
discussion
percentages
work
folder
formulae
DAST
discussion
EP
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Model for Dyscalculia
Number
Applications
conceptual
tabular
operational
graphical
inferential
graphical
visualspatial
number
comparative
direction
word
symbolic
number
conceptual
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spatial
temporal
time
symbolic
abstraction
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Initial Trials
Initial
Trials
dyscalculic
electronic
paper
2 versions
19
students
dyslexic
control
score
paper/electronic
no difference
good
discrimination
time
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Further Trials
• Involved 30 participants
• Organised into three equal groups
– Dyscalculic
– Dyslexic
– Control
• Covered a range of academic subjects
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Percentage Scores for 3 Groups
100.00
90.00
O dyscalculic
O dyslexic
80.00
%
O control
70.00
60.00
50.00
participant
40.00
22 2 2 22 2 22 3 33 3 33 3 3 33
1 1 11 1 11 1 11 2
00 0 0 00 0 01 0 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 90 1 23 4 56 7 8 90
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Compare
0.71 with 0.17
100
100
80
80
60
60
% correct
% correct
Compare
3.59 with 3.509
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20
40
20
0
0
dyscalculic
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dyslexic
control
dyscalculic
dyslexic
control
18
100
100
80
80
60
60
40
40
20
20
0
0
dyscalculic
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dyslexic
control
dyscalculic
dyslexic
control
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Graph: percentage scores (revised)
100.00
O dyscalculic
O dyslexic
80.00
O control
%
60.00
40.00
participant
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
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Further Trials
Further Trials
data
large scale
whole class
504
students
general
population
dyscalculic
electronic
paper based
2nd and 8th
percentile ranks
very low
low
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small scale
individual
severely
at risk
at risk
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“Small-Scale” Trials, n = 70
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dyscalculic
only
19
dyslexic
with MD
37 identified by
overall score
10 identified
by profile
15 severely
at risk
4
not at risk
32 at risk
3 severely
at risk
11
not at risk
5 at risk
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Profiler (Thomas)
OVERALL SCORE
No Conceptual
No Comparative: Word
No Comparative: Symbol
No Comparative: VisSpat
Graphical
Tabular
Symbolic Abstraction
Spatial Direction
Time
Operational: Conceptual
• Overall: “severely at
risk ”
• Risk:
– No. concepts
– No. comparisons
– Operations
Key concepts
• Not at risk
– Graphical
– Tabular
– Time
– Spatial
More visual applications
Operational: Inferential
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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
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DysCalculiUM process
Learner
accesses
DysCalculiUM
portal
• Completes screener
• Results automatically
analysed
Tutor access
DysCalculiUM
portal
• Reviews students results &
profiles
• Identify students who are at risk
Further
investigation
of difficulties
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• Tutor-led
interview
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One-to-one Support for the
Dyscalculic Student
A Case Study: Liam
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Liam: Transport Management
Strengths
• Verbal reasoning
• Expressive
writing
• Reading
comprehension
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Weaknesses
• Dyscalculic
• Sequencing
numbers
• Problems with
calculation
– Unsure of basic
operations
– Use of
inappropriate
strategies
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Tables of Information
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
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Rows and Columns
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% of flights to Brussels
more than 5 mins late:
Birmingham
to
Paris
Brussels
Munich
Dublin
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Minutes late (to nearest minute)
1  2 1 3to 5
8
3
3 1
 3
6
12 4
4
1
 25 %
On time
7
1
TOTAL
6 to 10
Over 10
1
0
12
1
2
12
0
0
5
1
1
10
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Alternative Approaches
12 flights  100%
100
1 flight 
12
100
3
3 flights 
12
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12 flights
3 late
3
 100
12
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Median of delivery route distances (km)
35
45
46
46
55
66 69
70
72 72
55 56 57 58 59 60 61 62 63 64 65 66
60.5
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Resources
http://incompetech.com/beta/plainGraphPaper/
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Number Lines and Graphs
• Number line
• Extend to 2-D
• Moving axes
• Apply to
–Correlation
–Sales forecasting (interpolation)
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Time and Scheduling
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.
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Start
Fly time
Land GMT
Time Difference
Land local
Turn round
Start local
Fly time
Land local
Time difference
Land GMT
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Helsinki 1
07.00
03.00
10.00
02.00 +
12.00
00.45
12.45
03.00
15.45
02.00 13.45
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10.15
17.15
21.15
O
11.00
18.00
22.00
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07.00
14.00
18.00
12.45
19.45
23.45
L
07.00
10.00
16.00
13.45
16.45
22.45
12.00
15.00
21.00
H
12.45
15.45
21.45
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Dyscalculia: The Way Forward
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.
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References
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Beacham N. and Trott C. (2005) Development of a first-line screener for dyscalculia in Higher
Education, The Skill Journal, 81, pp 13-19
Beacham N. and Trott C. (2006) Project Report: Wider use of DyscalculiUM, an electronic tool for
dyscalculia in H.E. MSOR Connections Vol. 6(2) pp 12-19
Butterworth B (2002) Mathematics and the Brain, Opening address to The Mathematical
Association, Reading 2002, http://www.mathematical brain.com/pdf (accessed 26/11/07)
Butterworth B. (2001) Educational Leadership Interview
http://www.mathematicalbrain.com/int06.html (accessed 26/11/07)
Butterworth B. (1999) The Mathematical Brain. London: Macmillan
Chinn S. (2006) What Dyslexia can tell us about Dyscalculia, Dyslexia Review Vol. 18 (1), pp 15-17
Desoete A., Roeyers H. and De Clercq A. (2004) Children with Mathematics Learning Disabilities in
Belgium Journal of Learning Disabilities, Volume 37 (1) pp 50-61
DfES (2001) The National Numeracy Strategy, Guidance to support pupils with dyslexia and
dyscalculia, DfES 0512/2001 http://publications.teachernet.gov.uk/eOrderingDownload/DfES-05122001.pdf (accessed 26/11/07)
DSM-IV (2000) Diagnostic and Statistical Manual of Mental Disorders, Fourth Edition, Text Revision
(DSM-IV-TR), American Psychiatric Association
Geary D.C. (2004) Mathematics and Learning Disabilities, Journal of Learning Disabilities vol 37 (1)
pp4-15
Gross-Tsur, V., Manor,O. and Shalev R.S. (1996) Developmental Dyscalculia: prevalence and
demographic feature, Developmental Medicine and Child Neurology. 38, pp 25-33
Kosc, L. (1974) Developmental Dyscalculia Journal of Learning Disabilities, 7(3), pp 164-177
The National Center for Learning Disabilities (2009) Dyscalculia
http://www.ncld.org/content/view/463/456174 (accessed 26/11/09)
Trott C. (2007) Identifying Dyscalculia in HE, Dyslexia Review, 18 (2), pp 9-14
Trott C and Beacham N (2010), DysCalculiUM: a first-line screening tool, Iansyst, Cambridge (in
press)
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