Dyscalculia in Further and Higher Education NADP 2010 1
Jan 14, 2016
Dyscalculia in Further and Higher Education
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• Definitions and Prevalence
• Screening
• Supporting Students
Presentation
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Towards a Definition
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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"
DSM-IV (2000)
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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)
Key Features (1)
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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• What is “mathematical ability” ?
• “Mathematics Disorder” implies a stable cognitive root, not achievement or mastery which is subject to education and environment.
Key Features (2)
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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
The National Numeracy Strategy DfES (2001)
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• “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
Key Features (1)
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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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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.
Prevalence
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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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12
A first-line screening tool for dyscalculia focusing on
Understanding Mathematics
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Developed by Trott and Beacham, Loughborough University
K erry
d iscuss ion
in-depthd iscuss ion
re ferredby tu tor
w orkfo lder
percentages
E P
form ulae
D A S T
13
Kerry
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Model for Dyscalculia
num berconceptual
inferential
tabular
w ord
visual-spatial
direction
graphical
operational
num bercom parative
spatialtem poral
graphical
sym bolicabstraction
sym bolic
conceptual
tim e
Num ber Applications
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InitialTrials
dys lexic
gooddisc rim ination
e lec tron ic
paper
contro l
paper/e lec tron icno d iffe rence
19s tudents
dysca lcu lic
tim e
2 vers ions
score
Initial Trials
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• Involved 30 participants• Organised into three equal groups
– Dyscalculic– Dyslexic– Control
• Covered a range of academic subjects
Further Trials
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Percentage Scores for 3 Groups
%
101
102
103
104
105
106
107
108
109
110
201
202
203
204
205
206
207
208
209
210
301
302
303
304
305
306
307
308
309
310
participant40.00
50.00
60.00
70.00
80.00
90.00
100.00
O dyscalculic
O dyslexic
O control
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18
0
20
40
60
80
100
dyscalculic dyslexic control
0
20
40
60
80
100
dyscalculic dyslexic control
Compare 0.71 with 0.17
% c
orre
ct
Compare 3.59 with 3.509
% c
orre
ct
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0
20
40
60
80
100
dyscalculic dyslexic control
0
20
40
60
80
100
dyscalculic dyslexic controlNADP 2010
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Graph: percentage scores (revised)
%
101
102
103
104
105
106
107
108
109
110
201
202
203
204
205
206
207
208
209
210
301
302
303
304
305
306
307
308
309
310
participant20.00
40.00
60.00
80.00
100.00
O dyscalculic
O dyslexic
O control
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Further Trials
sm all sca legenera lpopu la tion dysca lcu lic
ind ividua l
data
large sca le
paper basedw hole c lass e lec tron ic
504s tudents
2nd and 8 thpercentile ranks
low
severe lyat riskvery low
at risk
Further Trials
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19dys lexicw ith M D
5 at risk
3 severe lya t risk
11not a t risk
51dysca lcu lic
on ly
15 severe lyat risk
37 identified byovera ll score
32 a t risk10 identified
by pro file
4not a t risk
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“Small-Scale” Trials, n = 70
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• Overall: “severely at risk ”
• Risk:– No. concepts– No. comparisons– Operations
Key concepts
• Not at risk– Graphical – Tabular – Time – Spatial
More visual applications
OVERALL SCORE
No Conceptual
No Comparative: Word
No Comparative: Symbol
No Comparative: VisSpat
Graphical
Tabular
Symbolic Abstraction
Spatial Direction
Time
Operational: Conceptual
Operational: Inferential
Profiler (Thomas)
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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
Learner accesses DysCalculiUM
portal
• Completes screener
• Results automatically analysed
Tutor access DysCalculiU
M portal
• Reviews students results & profiles
• Identify students who are at risk
Further investigation of difficulties
DysCalculiUM process
One-to-one Support for the Dyscalculic Student
A Case Study: Liam
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Weaknesses• Dyscalculic• Sequencing
numbers• Problems with
calculation– Unsure of basic
operations– Use of
inappropriate strategies
Liam: Transport Management
Strengths• Verbal reasoning• Expressive
writing• Reading
comprehension
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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
Tables of Information
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Rows and Columns
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Birmingham to
Minutes late (to nearest minute) TOTAL
On time 1 to 5 6 to 10 Over 10
Paris 8 3 1 0 12
Brussels 6 3 1 2 12
Munich 4 1 0 0 5
Dublin 7 1 1 1 10
% of flights to Brussels more than 5 mins late:
%254
1
12
3
321
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12 flights
3 late
312
1003
12
1001
%10012
flights
flight
flights
Alternative Approaches
10012
3
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6635 46 55 706945 7246 72
55 56 57 58 59 60 61 62 63 64 65 66
60.5
Median of delivery route distances (km)
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http://incompetech.com/beta/plainGraphPaper/
Resources
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• Number line
• Extend to 2-D• Moving axes
• Apply to –Correlation–Sales forecasting (interpolation)
Number Lines and Graphs
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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.
Time and Scheduling
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Helsinki 1
Start 07.00
Fly time 03.00
Land GMT 10.00
Time Difference 02.00 +
Land local 12.00
Turn round 00.45
Start local 12.45
Fly time 03.00
Land local 15.45
Time difference 02.00 -
Land GMT 13.45
22:45
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L
O H
07.0010.0016.00 12.00
15.0021.00
12.4515.4521.45
13.4516.4522.45
07.0014.0018.0010.15
17.1521.15
11.0018.0022.00
12.4519.4523.45
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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.
Dyscalculia: The Way Forward
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