## What are the symptoms of dyscalculia?

Because there has been so little work on dyscalculia, there is no definite list of symptoms. But there is still a lot that we do know. I have listed symptoms below according to how we know about them, and the level of certainty we have. Of course not all children may show all symptoms, and we know little about what symptoms remain in adolescence and adulthood (apart from the obvious of difficulty with mathematics).

## Symptoms established by research

The following are seen in primary school, and well established by educational researchers:

1. Delay in counting. Five to seven year-old dyscalculic children show less understanding of basic counting principles than their peers (e.g. that it doesn't matter which order objects are counted in). [1-3]

2. Delay in using counting strategies for addition. Dyscalculic children tend to keep using inefficient strategies for calculating addition facts much longer than their peers. [2, 4, 5]

3. Difficulties in memorizing arithmetic facts. Dyscalculic children have great difficulty in memorizing simple addition, subtraction and multiplication facts (eg. 5 + 4 = 9), and this difficulty persists up to at least the age of thirteen. [6-10]

These symptoms may be caused by two more fundamental difficulties, although more research is needed to be sure:

1. Lack of “number sense”. Dyscalculic children may have a fundamental difficulty in understanding quantity. [11, 12] They are slower at even very simple quantity tasks such as comparing two numbers (which is bigger, 7 or 9?), and saying how many there are for groups of 1-3 objects. The brain areas which appear to be affected in dyscalculia are areas which are specialised to represent quantity.

2. Less automatic processing of written numbers. In most of us, reading the symbol "7" immediately causes our sense of quantity to be accessed. In dyscalculic individuals this access appears to be slower and more effortful. [13-15]. Thus dyscalculic children may have difficulty in linking written or spoken numbers to the idea of quantity.

## Other symptoms

If you have read other websites on dyscalculia you may have seen quite a few other symptoms listed. Many of these are not yet proved to be symptoms (although this does not mean they might not be later on). This is because they have been reported by teachers or special education workers, but haven't yet been studied in detail by researchers. Based on my knowledge of dyscalculia and cognition I have listed likely and unlikely symptoms below.

The following are likely to be symptoms of dyscalculia:

1. Difficulty imagining a mental number line

2. Particular difficulty with subtraction

3. Difficulty using finger counting (slow, inaccurate, unable to immediately recognise finger configurations)

4. Difficulty decomposing numbers (e.g. recognizing that 10 is made up of 4 and 6)

5. Difficulty understanding place value

6. Trouble learning and understanding reasoning methods and multi-step calculation procedures

7. Anxiety about or negative attitude towards maths (caused by the dyscalculia!)

All these symptoms (bar the last) are related to quantity.

The following may sometimes be ASSOCIATED with dyscalculia, but not in all cases:

1. Dyslexia, or difficulty reading

2. Attentional difficulties

3. Spatial difficulties (not good at drawing, visualisation, remembering arrangements of objects, understanding time/direction)

4. Short term memory difficulties (the literature on the relation between these and dyscalculia is very controversial)

5. Poor coordination of movement (dyspraxia)

The following are NOT likely to be symptoms of dyscalculia:

1. Reversals of numbers - this is a normal developmental stage which all children go through and is no cause for alarm in itself

2. Difficulty remembering names - no evidence to suggest that long term verbal memory has anything to do with dyscalculia

## References

[1] D. C. Geary, C. C. Bow-Thomas, and Y. Yao, "Counting knowledge and skill in cognitive addition: A comparison of normal and mathematically disabled children," Journal of Experimental Child Psychology, vol. 54, pp. 372-391, 1992.

[2] D. C. Geary, C. O. Hamson, and M. K. Hoard, "Numerical and arithmetical cognition: A longitudinal study of process and concept deficits in children with learning disability," Journal of Experimental Child Psychology, vol. 77, pp. 236-263, 2000.

[3] D. C. Geary, M. K. Hoard, and C. O. Hamson, "Numerical and arithmetical cognition: Patterns of functions and deficits in children at risk for a mathematical disability," Journal of Experimental Child Psychology, vol. 74, pp. 213-239, 1999.

[4] D. C. Geary, "A componential analysis of an early learning deficit in mathematics," Journal of Experimental Child Psychology, vol. 49, pp. 363-383, 1990.

[5] D. C. Geary, S. C. Brown, and V. A. Samaranayake, "Cognitive addition: A short longitudinal study of strategy choice and speed-of-processing differences in normal and mathematically disabled children," Developmental Psychology, vol. 27, pp. 787-797, 1991.

[6] H. P. Ginsburg, "Mathematics Learning Disabilities: A View from Developmental Psychology," Journal of Learning Disabilities, vol. 30, pp. 20-33, 1997.

[7] N. C. Jordan and T. O. Montani, "Cognitive arithmetic and problem solving: A comparison and children with specific and general mathematics difficulties," Journal of Learning Disabilities, vol. 30, pp. 624-634, 1997.

[8] J. R. Kirby and L. D. Becker, "Cognitive Components of Learning Problems in Arithmetic," Remedial and Special Education, vol. 9, pp. 7-16, 1988.

[9] S. A. Ostad, "Developmental differences in addition strategies: A comparison of mathematically disabled and mathematically normal children.," British Journal of Educational Psychology, vol. 67, pp. 345-357, 1997.

[10] S. A. Ostad, "Developmental progression of subtraction strategies: A comparison of mathematically normal and mathematically disabled children," European Journal of Special Needs Education, vol. 14, pp. 21-36, 1999.

[11] A. J. Wilson and S. Dehaene, "Number sense and developmental dyscalculia," in Human behavior, learning and the developing brain: Atypical development, D. Coch, G. Dawson, and K. Fischer, Eds. New York: Guilford Press, 2007.

[12] B. Butterworth, "Developmental dyscalculia," in Handbook of Mathematical Cognition, J. Campbell, Ed. New York: Psychology Press, 2005.

[13] O. Rubinsten and A. Henik, "Automatic Activation of Internal Magnitudes: A Study of Developmental Dyscalculia," Neuropsychology, vol. 19, pp. 641, 2005.

[14] O. Rubinsten and A. Henik, "Double Dissociation of Functions in Developmental Dyslexia and Dyscalculia," Journal of Educational Psychology, vol. 98, pp. 854, 2006.

[15] L. Rousselle and M.-P. Noel, "Basic numerical skills in children with mathematics learning disabilities: A comparison of symbolic vs non-symbolic number magnitude processing," Cognition, vol. 102, pp. 361-395, 2007.