From the experience of teachers teaching children with a specific deficit in dealing with numbers (dyscalculia) it was suggested, that these children suffer from an instable sense of number. They know the digits (the visual signs of numbers) and they know the words for numbers (the auditory sign for numbers) but they did not associate the number of items represented by the visual and auditory signs. The idea was that may be they could not develop this sense of number, because of a visual deficit in their brains.
The corresponding visual capacity is called subitizing (from lat. Subito = immediately). Subitizing is a basic capacity of the visual system to "see immediately" the number of items without counting them. A standardized test task for subitizing item numbers from 1-9 was developed and applied to a large number of control subjects and to children with dyscalculia.
Later the task was also applied to children with dyslexia and other learning problems.
Age Development and Diagnosis
Perfect subitizing is possible for adult subjects up to item numbers of 4 or 5. With increasing numbers additional time is needed to tell the numbers correctly. For 8 items the rate of correct responses drops to 80%and is still reasonably high.
Children with dyscalculia exhibit considerable deficits increasing with age. Even with 1 or 2 items (randomly selected out of 1-9 itms) they need more time as compared with the controls.
Deficits of subitizing were found also in children with dyslexia. They are about as fast in the basic reponses but the recognition speed is significantly lower as compared with the controls.
A training of subitizing helps to overcome this deficit. A training device CountTrain was developed and given to those children, where deficits were encountered. At the beginning the task was made very easy by selecting only 1 to 3 items and presenting them for lnger times. Only when the child improved the performance the task was made more difficult by increasing the maximal number of items and by decreasing the presentation time.
Transfer to Arithmetic
Finally, it was shown, that the training of subitizing transfers to basic mathematical skills as tested by using the DEMAT+2 (a German test battery commercially available) before and after the training. The trained group I gained points, while the waiting group II had no profit from the school lessons. Only after the waiting group was also allowed to do the training an increase of points was obtained.
Fischer B, Gebhardt C, Hartnegg K (2008)
Fischer B, Köngeter A, Hartnegg K (2008)
Sidney Groffman OD, MA, FCOVD (2009)
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