Symptoms established by researchI wonder what she means by "inefficient strategies for calculating addition facts."
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.
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
update: I think she means that children with dyscalculia continue to use counting-all to perform simple addition after their peers have switched to counting-on.