Universität Freiburg, AG Optomotorik

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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.

Development of Subitizing and Number Counting
Subitizing improves with age until adulthood. Both the basic response time (for item numbers of 1 and 2) and the effective rate of correct responses (item numbers of 4 and more) improve. Beyond the age of about 35 years the curves decline.


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.

Basic Response Time in Subitizing by CountTrain
The graph shows the basic response time versus age for two groups. Considering 4 items and more one can calculate the effective recognition speed as the the percent number of correct response divided by the response time.
Effective Recognition Rate in Subitizing by CountTrain
The percent number of subjects failing the range of the age matched controls increases from about 40% to about 70% with age.

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.

Training Effects of Subitizing by CountTrain
The effect of the training shows a significant improvement of the performance at all ages.

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.

Effects of Training in Subitizing by CountTrain on Basic Arithmetic Skills


Fischer B, Gebhardt C, Hartnegg K (2008)
Subitizing and Visual Counting in Children with Problems in Acquiring Basic Arithmetic Skills
Optometry & Vision Development 39: 1 (2008) (abstract)

Fischer B, Köngeter A, Hartnegg K (2008)
Effects of Daily Practice on Subitizing, Visual Counting, and Basic Arithmetic Skills
Optometry & Vision Development 39: 1 (2008) (abstract)

Sidney Groffman OD, MA, FCOVD (2009)
Subitizing: Vision therapy for math deficits
Optometry Vison Development 40(4): 229-238 (2009) (abstract)

A complete list of publications is available.

© AG Optomotorik, Email burkhart.fischer @ blicklabor.de