The origins of numerical abilities: the future

What underlies the ability to count and where did it come from? Current hypotheses propose that our ability to accurately represent the number of objects in a set, and to carry out numerical comparisons and simple arithmetic, developed from an evolutionarily conserved system for approximating numerical magnitude, the ANS (approximate number system). According to this hypothesis the ability to assess numerosities would have an evolutionarily conserved genetic and neural basis, and one might expect at least some aspects of the neurobiology underlying ability to perform approximate numerical tasks and to accurately represent number to be shared. Zebrafish are an ideal model species in which to test this hypothesis and to explore the cell biology of numerosity: Teleost fish have long been used for comparative studies of numerosity using both numerical discrimination and match-to-sample task. These studies have recently been extended to zebrafish and preliminary analysis indicates that automated systems and behavioural assays developed in our lab can be used for assessment of zebrafish numerosity. These behavioural assays coupled with advances in gene editing and in vivo imaging techniques make zebrafish an ideal model species for investigating the neural correlates of numerosity. Identification of the neural circuitry underlying numerosity in distantly related vertebrates such as zebrafish, and analysis of the impact of the disruption of homologues of genes associated with human numerosity could provide a breakthrough in our understanding of the evolution of numerosity and its the basis of disturbances in our own species.

Twin studies indicate that dyscalculia (or mathematical disability) is caused partly by a genetic component. However specific genes have not been identified yet. Only a few candidate genes have been proposed so far but they have not been convincingly replicated. This failure is mainly due to lack of investigations in this area. Dyscalculia can co-occur with other neurodevelopment conditions, such as dyslexia. Genetic studies of dyslexia are far from explaining the biological component of this condition but have led to the identification of few susceptibility genes. These studies highlighted significant challenges for such approaches but equally provide a useful model to study neurodevelopmental conditions like dyscalculia. One of the key elements determining the success of genetic studies is phenotypic assessment. Assessing reading abilities is extremely challenging especially because of high heterogeneity across studies and populations. Maths offers the advantage of potentially being assessed through homogenous tests not dependent on the spoken language. This facilitates the collection of data in independent samples that can be combined for large genetic screenings. Consensus on such tests would provide an important contribution for paving the way towards successful studies of maths abilities.

Clinical studies as well as recent investigations conducted with other methodologies (e.g. neuroimaging, transcranial magnetic stimulation, direct cortical electro-stimulation) leave several unanswered questions about the contribution of the right hemisphere in calculation. All methods, indeed, increasingly show an involvement of the right hemisphere in functions traditionally believed to be in the domain of the left hemisphere. In particular, novel clinical studies show that right hemisphere acalculia encompasses a wide variety of symptoms, affecting even simple calculation, that cannot be entirely attributed to spatial disorders or to a generic impoverishment of processing resources as previously believed. 

Moving from the conclusions of these studies, new data were collected, by means of Direct Cortical Electrostimulation during glioma surgery and Magneto-Encephalography (MEG), concerning simple calculation, i.e., one-digit addition and multiplication. Up to very recent times, these tasks were believed to be carried out by the left hemisphere. The studies reported here show instead how the right hemisphere has its own specific role and that only a bilateral orchestration between the respective functions of each hemisphere guarantees, in fact, precise calculation.

Vis-à-vis these data, the traditional wisdom, that attributes to the right hemisphere a role mostly confined to spatial aspects of calculation, needs to be significantly reshaped. The question for the future is whether it is possible to precisely define the specific contribution of the right hemisphere in several aspects of calculation while highlighting the nature of the cross-talk between the two hemispheres.

Healthy ageing is characterised by changes in brain volume and connectivity corresponding to cognitive changes, especially diminished memory and attention processing. Dr Cappelletti will present evidence to complement this view and demonstrate that, instead, some cognitive abilities and brain structures can be resilient to ageing. She will use numeracy skills as an example of a cognitive ability that is maintained in ageing adults, and she will further demonstrate that elderly can also improve their performance in numeracy and attention following training, or training coupled with brain stimulation. Using data from a large neuroimaging study, Dr Cappelletti will propose that resilience to ageing may be explained in terms of complex alterations in the microstructure of myelin and iron content. 

Based on this evidence, Dr Cappelletti suggests that resilience to ageing is an example of brain plasticity, and that numeracy is maintained in ageing because it is supported by a network of brain regions that age less compared to others.  

Diffusion tensor imaging has provided unique information about brain microstructure. The trajectories of these brain microstructural changes have been mapped from birth to adulthood. In particular sexual dimorphisms have been demonstrated which appear to be related to the differential onset of puberty in males and females. In addition to this several studies have used diffusion tensor imaging to detect changes in the structure of the brain over short time scales i.e. hours, following various learning tasks. This raises the question as to whether these types of experiment can be used to measure brain structural changes as a result of the acquisition of mathematical skills. This talk will explore the latest developments in measuring brain tissue microstructure and connectivity using MRI and will discuss their suitability for future experiments designed to better understand the acquisition of mathematical abilities as well as exploring the neural basis of dyscalculia.

The acquisition of any complex cognitive skill, such as learning to count and perform arithmetic, is the result of regional- and system-level interactions within and between brain areas, that occur over development. This process of neuroplasticity is marked by functional brain specialisation, strengthening of structural and functional brain connections, as well as the maturation of memory circuits through subcortical-cortical interactions. Dr Iuculano will report the results of a series of studies where the group exploits a well-controlled learning design that uses an intensive 8-week numerical training combined with event-related functional resonance imaging (fMRI), to assess brain plasticity during numerical problem solving in different cohorts of primary-school children. First, they show that training elicited dramatic neuroplasticity in a population of 7-9 year olds with mathematical learning disabilities by reducing functional activity in multiple brain systems in the prefrontal, parietal and ventral temporal-occipital cortices, that encompass multiple stages of the information processing hierarchy necessary for successful numerical problem solving. Crucially, in typically developing children, the same training was associated with greater engagement of memory systems anchored in the hippocampus, and concurrent increases in hippocampal-cortical connectivity. Third, they show that in children with high levels of math anxiety, neuroplasticity effects were characterised by reduced activity and connectivity in emotion-related circuits anchored in the amygdala. Together, these findings suggest that the recruitment of brain circuits important for numerical problem solving changes as a function of training and different cognitive and affective profiles. More generally, this work helps to perfect neurodevelopmental models of numerical learning and cognition.

Numerical competence is essential for leading an autonomous and successful life. Numerical deficits have a negative impact on patients’ decisions and negatively influence their health management. Stroke, head trauma or degenerative diseases frequently lead to deficits in specific numerical functions. Research suggests that not only parietal structures, but a complex cortical-subcortical network supports symbolic and non-symbolic number elaboration. Patients’ deficits may concern the processing of quantities, the retrieval of declarative as well as procedural number knowledge, but also the understanding of numerical concepts, such as ratio, risk or probability. Neuropsychological rehabilitation studies show that patients are able to acquire new fact knowledge after brain damage and indicate that different cues may support the learning progress. Importantly, fact knowledge has to be supported by conceptual understanding. Less is known about learning more complex concepts. Recent findings suggest that numerical training may also improve the comprehension of ratios and risks. These findings are important for patients, as ratio processing together with executive functions have a strong impact on real-life decision making. Future research has to evaluate different rehabilitation approaches and to define outcome measures which are relevant for patients’ everyday life.