Numerical abilities in Williams syndrome

Attila Krajcsi1, Mihály Racsmány2, János Igács1, Csaba Pléh2

1University of Szeged2Budapest University of Technology and Economics

Mail: krajcsi@pszichologia.huWeb: http://www.staff.u-szeged.hu/~krajcsi

Outline

• Numerical abilities

• Numerical problems and possible causes

• Study with WS and DC children

• Conclusion about WS and broader considerations

Numerical abilities

Executive functions (Middle frontal gyrus)

Organizing tasks, order of operations

Arabic numerical representation (Occipitotemporal areas) Arabic numerical symbols

Visual attention (Dorsal stream)

Counting objects, maybe subitizing

Magnitude representation (Intraparietal sulcus)

Estimation, approximation, comparison

Verbal systems (Left inferior frontal and left gyrus

angularis, temporal regions) Exact calculation, multiplication table, storing temporary results

Numerical problems and possible causes

Developmental dyscalculia (DC)

• Mathematical ability, as measured by individually administered standardized tests, is substantially below that expected given the person's chronological age, measured intelligence, and age-appropriate education.

• Normal intelligence• Impaired mathematical performance

Numerical problems in genetical disorders

• Williams syndrome

• Turner syndrome

• Developmental Gerstmann syndrome

• Fragile X syndrome

• Down syndrome

• Etc.

• Adolescents with bad performance on simple arithmetical test

• Increasement in gray matter

Isaacs et al., 2001

Possible causes

Several causes

• A huge amount of ideas explaining numerical problems• Working memory problem (verbal, spatial,

executive)• LTM problem• Anxiety• Etc.

• Different types of numerical disabilities• Different types of DC• Different problems in genetic disorders

Study with WS and DC children

1. Methods2. Presence of effects3. Mean RTs4. Selective load method – alternative RT

Tasks

• Simple addition6 + 3 = 8

• Simple multiplication5 * 4 = 20

• Number comparison7 2

• Dot counting• Multiple object tracking

Verbal retrieval

Verbal retrieval

Number line

Visual functions

Visual functions

Subjects

• 7 WS subject

• 14 DC subject11 years

• 11 control subject10 years

Charles vs. controll: number comparison

540

560

580

600

620

640

660

680

700

720

1 2 3 4 5 6 7 8

Távolság

RI m

s

Kontroll

2000

2200

2400

2600

2800

3000

3200

3400

1 2 3 4 5 6 7 8

Távolság

RI m

s

Charles

Butterworth, 2003

1 2 3 4 5

Távolság

0

1 000

2 000

3 000

RI (

ms)

Williams szindróma

Diszkalkulia

Kontroll

Williams syndrome and DC

Krajcsi, Racsmány, Igács, Pléh, 2005

0

1000

2000

3000

4000

5000

6000

Comparison Addition

WS DK Controll

Krajcsi, Racsmány, Igács, Pléh, 2005

Tasks

• Simple addition• Simple multiplication• Number comparison• Dot counting• Multiple object tracking

Verbal retrieval

Verbal retrieval

Number line

Visual functions

Visual functions

Visual attention (Dorsal stream)

Magnitude representation (Intraparietal sulcus)

Verbal systems (Left inferior frontal and left gyrus

angularis, temporal regions)

Number comparison

(4) Executive functionsDecision

(2) Arabic numerical representation

(3) Magnitude representation Comparison

(1) Visual input

(5) Motor regionResponse

Distance

Tim

e o

f pro

cess

ing

Input

Comparison

Decision

Response

Arabic

Input

Comparison

Decision

Response

Arabic

Selective load

Krajcsi, 2005

(4) Executive functions Decision

(2) Arabic numerical representation

(3) Mental number line Comparison

(1) Visual input

(5) Motor region Response

0,5

0,55

0,6

0,65

0,7

0,75

0,8

0,85

0,9

0,95

1

Comparison distanceeffect

Addition problem sizeeffect

Williams syndromeDevelopmental dyscalculiaControl

Conclusions

• Williams syndrome• Usual effects are present• Relatively bad parietal functions (comparison

and dot counting)• Relatively good verbal functions (simple

addition and multiplication – rote learning)

• Broader considerations• DC is not caused by the deficit of magnitude

representation• Selective load method validation

Thank you for your attention!

Attila Krajcsi1, Mihály Racsmány2, János Igács1, Csaba Pléh2

1University of Szeged2Budapest University of Technology and Economics

Mail: krajcsi@pszichologia.huWeb: http://www.staff.u-szeged.hu/~krajcsi