Symbolic and non-symbolic number processing: behavioural and brain imaging studies
Research has shown that very young infants can discriminate between non-symbolic representations of numerical magnitude (such as arrays of dots). What role do these early representations play in the acquisition of cultural representation of number, such as Arabic numerals and number words. In a series of behavioral and brain-imaging studies we are explore the mapping between symbolic and non-symbolic representations of numerical magnitude. In addition we are asking the development of basic magnitude processing impacts the development of arithmetic skills.
Why does counting count?
Imagine the following: a two-year old is playing with a set of 5 toy animals. During the play the caregiver ask the child to count the toys. The child readily proceeds sequentially touching the toys and labeling them: “1,2,3,4 etc.) after the child has arrived at 5, the caregiver asks the child:”so how many toys do you have” and the child proceeds to recount them or just stares at the caregiver blankly. What is going on here is that the child can count, but has not understood the purpose of this activity: to enumerate or, put differently, to determine the total number of items in a set (the set’s cardinality). This understanding of cardinality develops gradually and is found to be present in most children by around the age of 3 ½ . Understanding the meaning of counting is a crucial milestone in children’s development of number. Children use counting in the early stages of their arithmetic development. It is therefore crucial to understand how children come to understand the meaning of counting and what cognitive processes are associated with this important developmental change in children’s understanding of number.
The calculating brain: development and individual differences
What brain regions are involved in our ability to calculate? How is brain activation during calculation affected by the particular arithmetic operation being performed (e.g do different brain regions subserve subtraction and multiplication)? Does the type of problem-solving strategy result in the use of different brain networks? How does the calculating brain changes as a function of development and education? Together with Dr. Roland Grabner from the ETH in Zurich, Switzerland we are looking for answers to these questions in search for a better understanding of how the brain enables us to become mathematically fluent.
White matter integrity and mathematical skills
A growing number of studies have revealed the functional correlates of mathematical processing (which brain areas are activated during specific numerical and mathematical tasks etc.). However, comparatively less is known about the structural correlates of mathematical abilites in children and adults. How does the structural development of the brain relate to the development of numerical and mathematical skills? Are individual differences in brain structure related to differences between individual in their mathematical competence? In a series of studies we are using Diffusion Tensor Imaging to visualize white matter tracts in the brain. Interestingly, integrity of these white matter structures differs between individuals, we can related individual differences in white matter integrity (using a measure called Fractional Anisotropy) to individual differences in performance on tests of cognitive functioning.
It is a little known fact that about as many children present with specific and severe difficulties with even the most basic aspects of arithmetic as children who suffer from specific reading difficulties (Developmental Dyslexia). Children who exhibit relatively normal verbal and non-verbal IQ but have severe difficulties with arithmetic can be said to have Developmental Dyscalculia. In our research we are using behavioral as well as functional neuroimaging methods to better understand the characteristics, causes and neural correlates of developmental dycalculia. Here we are asking questions such as: is the ability to process and represent numerical magnitude impaired in Developmental Dyscalculia? Are the brain circuits underlying number processing and calculation functionally and structurally atypical in Developmental Dyscalculia? What are the differences and similarities between Developmental Dyscalculia and Developmental Dyslexia?