Q. I would like to know more about the statistics being used by Daniel Ansari. What correlation coefficient is acceptable in order to make a statement that there is actually a correlation? Also regarding the sample: how are students/type of educational establishments selected and what is considered to be a minimum sample size for a study to be valid
DA. We use standard statistics for our correlations such as Pearson's correlations.We check for extreme outliers which may influence our correlations It is difficult to say what a reasonable correlation coefficient is. According to Cohen (1988) a coefficient that is larger than 0.5 is large, between 0.3-0.5 is moderate and below 0.3 is considered to be low. Our correlations between symbolic number processing and arithmetic are therefore in the range of effect sizes that would be considered 'moderate' according to Cohen's classification. The sample sizes have varied in our studies, but in most of our correlational studies we have tested more than 50 children. It is hard to say what a minimum sample size is. That depends on the method and scientific question. For correlational studies, larger samples are desirable to estimate the size of effects using a representative sample. In our latest study we tested around 1400 children from grades 1-6. It is critical to replicate correlations. Our research shows that the correlation between symbolic magnitude processing and arithmetic achievement replicates well. Thus this relationship seems to be quite reliable, which is critical. As I pointed out in my presentation, we do not mean to say that symbolic number processing explains all of the variance in young children's numerical and mathematical skills but that it seems to be one critical component of the pieces that children need to have in order to build solid foundations for higher-level competencies.
Q. I would like Dr Ansari to give us the 8 constructs that his research associates were working on so that we know which concepts are being studied by researchers at the moment. Also I would like to have the publication details of their research.
DA. This is thus far unpublished research. As soon as it is published I will be very happy to share it.
Q. Please can you recommend some excellent diagnostic assessment tools for mathematics? We have WJ, Key Math and we will purchase Jane Emerson's book to look at children's math misconceptions. What else is out there?
DA. Currently there are no really 'excellent diagnostic tools' in my view. They are being developed. Among the published ones there are many that are useful and you list some of them. I am not sure whether it is available in the UK, but the Test of Early Math Achievement (TEMA) is good, but rather long (in terms of test administration) But I am not convinced that there is yet a measure that captures the latest research on the factors underlying Developmental Dyscalculia. Watch this space!
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Q. I would like to ask Dr Ansari what steps he would suggest schools take to support children identified as 'at risk' of dyscalculia
DA. Great question. I have to admit that I am not an expert on interventions or pedagogical support. However, it is clear from the research in my laboratory and that of others that children with Dyscalculia have a particular problem in understanding numerical symbols, such as number words and Arabic numerals. Therefore I would think that activities that scaffold their understanding of these symbolic representations of quantity and link them with non-symbolic representations (such as sets of objects) would be helpful. In general, I believe that integrating more talk about numbers and numerical relationships can be helpful (in formal and informal contexts). Beyond these cognitive factors, it is important to consider the emotional side of difficulties in learning about numbers. I would suggest that schools ensure that children who are exhibiting difficulties and may therefore be at risk find ways to build children's confidence about numbers and thereby avoid the potentially long-term, adverse effects of mathematics anxiety.
Q. If research is showing that infants have an innate ability to sense numerical properties, does this mean that we cannot do anything about it?
DA. This is an excellent question and a very important one. Just because infants can discriminate between numerical quantities this does not mean that Developmental Dyscalculia is an innate deficit of numerical quantity representations. Indeed, as I showed in my talk, our research and that of others seems to suggest that children with Developmental Dyscalculia have greater problems in dealing with man-made, culture representations of numbers such as Arabic numerals than they have with non-symbolic representations (e.g discriminating which of dot arrays is numerically larger). Therefore, it seems that it is in the connection between the innate and the cultural system of numerical quantity representations that a deficit arises. I therefore am quite confident that Dyscalculia can be remediated through finding more effective ways of helping children make this connection, thereby building a scaffold for the learning of more complex numerical and mathematical operations.
Q. What would Daniel Ansari say the fine line between dyscalculia and general maths learning difficulties is? If research is showing that children with dyscalculia have a biological deficiency, will they ever be able to do the same maths as their peers?
DA. It is important to recognize that a biological predisposition to developing a specific learning disorder does not mean that this disorder immutable. Take the example of Developmental Dyslexia. There is clear evidence that the brains of children with Developmental Dyslexia function differently and genetic studies suggest that it is heritable. Yet there has been much success in remediating Dyslexia and helping children who are affected by this specific learning disorder develop strategies to aid their ability to read. This example shows that a biological predisposition does not mean that there is nothing one can do about a specific learning disorder. One of the major advances in neuro-science has been the discovery of brain plasticity, which is the ability of the brain to change in response to experience. Research in Developmental Dyslexia has shown that structured intervention programs lead to brain plasticity. In other words, children with Developmental Dyslexia can reorganize their brains to improve their reading difficulties. This does not necessarily mean that these children will go onto become completely fluent readers but it may allow them to function normally and succeed at tasks in their lives that require reading abilities. There is nothing to suggest that this should be different in children with Developmental Dyscalculia. While biology places constraints on what we can and cannot learn, it is through the complex interaction of biology and the environment that our eventual strengths and weaknesses emerge over developmental time.
Q. From the research, how do I go about supporting symbolic number understanding? I realise language and exposure is a key issue but more concrete interventions would be helpful.
DA. Again, I am a researchers and therefore unfortunately not an expert on intervention. What I would suggest however, are activities that help children see the links between sets of objects and number symbols (words and Arabic numerals). Furthermore, there is research by Robert Siegler from Carnegie Mellon University showing that playing with number lines and linear arrangements of numbers in board games can enhance children's understanding of number symbols.
Daniels website: http://www.numericalcognition.org/?page_id=6
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