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The origins of numerical abilities: the future

Scientific meeting

Event downloads

Starts:

February
222017

09:30

Ends:

February
232017

17:00

Location

Kavli Royal Society Centre, Chicheley Hall, Newport Pagnell, Buckinghamshire, MK16 9JJ

Overview

Satellite meeting organised by Professor Brian Butterworth FBA, Professor Charles Gallistel and Professor Giorgio Vallortigara

Ayumu chimpanzee touching from 1-9. Credit: Tetsuro Matsuzawa

The satellite meeting focused on those questions about the origins of numerical abilities that can only be answered by further research. These include the numerical limits of animal enumeration, the nature of the neural enumeration mechanism, identification of genes that contribute to the development of numerical abilities, and the role of symbolisation (words and tallies) in the prehistory of numerical abilities.

Speaker abstracts and biographies are available below. Recorded audio of the presentations are also available below.

Prior to this meeting there was a related discussion meeting 'The origins of numerical abilities' held at the Royal Society, London on 20 - 21 February 2017.

Enquiries: Contact the Scientific Programmes team

Schedule of talks

22 February

Session 1 09:30-12:30

Genetics of numerical abilities

4 talks Show detail Hide detail

Chairs

Professor Stanislas Dehaene, Collège de France, France

09:45-10:15 How can zebrafish be used to explore the evolution and genetics of numerosity?

Dr Caroline Brennan, Queen Mary University of London, UK

Abstract

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.

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10:15-10:45 The genetics of mathematical abilities: lessons learnt from genetic studies of literacy and language

Dr Silvia Paracchini, University of St Andrews, UK

Abstract

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.

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10:45-11:00 Coffee

11:00-11:30 Reassessing lateralisation in calculation

Professor Carlo Semenza, University of Padova, Italy

Abstract

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.

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11:30-12:00 Discussion

12:00-13:00 Selected short talks

13:00-14:00 Lunch

Session 2 14:00-17:00

Neural implementation of numerical abilities

4 talks Show detail Hide detail

Chairs

Dr Andreas Nieder, Tübingen University, Germany

14:00-14:30 The power of brain plasticity: insights from the number brain

Dr Marinella Cappelletti, Goldsmith's, University of London, UK

Abstract

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.  

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14:30-15:00 New tools from neuroimaging for measuring brain microstructure and connectivity: relevance to learning and mathematical cognition

Professor Christopher Clark, UCL, UK

Abstract

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.

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15:00-15:30 Tea

15:30-16:00 Neural correlates of numerical learning in the typical and atypical developing brain

Dr Teresa Iuculano, Stanford University School of Medicine, USA

Abstract

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.

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16:00-16:30 Learning and numerical competence after brain damage

Professor Margarete Delazer, Medical University Innsbruck, Austria

Abstract

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.

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16:30-17:00 Discussion

17:00-18:00

Poster session

23 February

Session 3 09:30-12:30

Limits of numerical abilities

4 talks Show detail Hide detail

Chairs

Dr Rosa Rugani, University of Padova, Italy

09:30-10:00 Numerical abilities of teleost fishes: future research directions

Professor Angelo Bisazza, University of Padova, Italy

Abstract

Fish are the most distant relatives of primates and are therefore an ideal group for testing whether the numerical systems of all vertebrates have a common ancestry. Fish offer unique opportunities for investigating some other topics. In higher vertebrates it is difficult, if not impossible, to compare young and adults with the same paradigms and to devise experiments that dissociate the role of genes, maturation and experience on the development of numerical abilities. In contrast, fish offspring are completely independent at birth and show the same behavioural repertoire of adults (e.g., evading predators, catching prey, interacting with conspecifics). This allows researchers to employ associative learning in newborns or exploit a number of spontaneous behaviours such as the preferences for the largest number of companions or food items, the same preferences studied in adults. Most studies to date have investigated if fish spontaneously discriminate between two observable quantities or if they can be trained to do so, and research has shown that they excel in these abilities. In these tasks, fish show the typical signatures of the number system of humans and their close relatives. It is unknown whether fish share other features that are shown by mammals and birds. In particular, future experiments should determine 1) whether a learned discrimination can be generalised to new stimulus formats, 2) whether fish show spontaneous cross-modal transfer of numerical information, 3) whether fish can perform simple arithmetic operations such as addition or subtraction and 4) whether they can be trained to associate a given quantity to an abstract stimulus.

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10:00-10:30 TBC

10:30-11:00 Coffee

11:00-11:30 Counting and numerical decision-making in mice: new data and future directions

Professor Fuat Balci, Koç University, Turkey

Abstract

Animals time and count with similar psychophysical properties suggesting their reliance on common information processing dynamics. Importantly, formal analyses reveal that the resultant representational uncertainty is one of the determinants of the reward-rate maximising temporal and numerical decisions. To this end, animals have been shown to optimise their time-based decisions based on their endogenous timing uncertainty. This talk will extend the same decision-theoretic approach to the numerosity domain based on two recent mouse studies. The first study investigated if mice can count their responses and optimise their numerical decisions solely based on endogenous counting uncertainty. Results confirmed that mice can count in accordance with scalar property and they can maximise reward rate by incorporating their endogenous counting uncertainty into their numerical decisions. The second study investigated whether mice can modulate their numerical choice behaviour adaptively also by incorporating exogenous probabilistic information (i.e., relative frequency of ‘few’ vs. ‘more’ trial types) into their numerical decisions. Results showed that mice can categorise numerosities and adaptively modulate their numerical decisions based on the experienced probabilistic contingencies again in directions predicted by optimality. Overall, these results point at informationally-rich counting and numerical decision-making abilities of mice. Future directions will be discussed in relation to two critical questions arising from these results.

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11:30-12:00 The perception of numerosity, and texture density, and their relationship to mathematical abilities

Professor David Burr, University of Florence, Italy

Abstract

Humans and other animals can estimate rapidly and reasonably accurately the number of items in the scene. Professor Burr will present psychophysical evidence showing that at moderate densities, humans discriminate number spontaneously and directly, rather than indirectly from estimates of density and area. At high densities, as the elements become too crowded to be segregated, different mechanisms come into play to encode ‘texture-density’. The group uses adaptation techniques to provide further evidence for the existence of specialised numerosity mechanisms, or numbersense. They go on to show that this sense of number is truly general, encoding the numerosity of both simultaneous and sequential sets of elements, in all modalities, as well as interacting with the generation of motor acts. Finally they show that the capacity to discriminate numerosity (but not density) correlates with mathematical ability in school-age children, reinforcing the idea that discrimination of numerosity may serve as a ‘startup tool’ for acquisition of maths.

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12:00-12:30 Discussion

12:30-14:00 Lunch

Session 4 14:00-17:00

The perception, symbolisation and education

4 talks Show detail Hide detail

Chairs

Professor Tetsuro Matsuzawa, Kyoto University, Japan

14:00-14:30 Talk title TBC

Professor Marco Zorzi, University of Padova, Italy

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14:30-15:00 Perceptions of number in Anindilyakwa-speaking Australian Aboriginal children: evidence of a universal cognitive prerequisite for early arithmetic

Professor Robert Reeve, The University of Melbourne, Australia

Abstract

The importance of visuo-spatial abilities for early numerical cognition in North American and European cultures raises the issue whether these abilities are similarly important for children in cultures that lack counting words. If the same visuo-spatial factors predict culturally-appropriate arithmetic, it would support the hypothesis that the same cognitive representations are deployed by individuals with and without counting words. In numerate societies, early arithmetic development is associated with visuo-spatial working memory, executive functions, nonverbal intelligence, and magnitude comparison abilities. Here we ask to what extent are these associations due to cultural practices or to general cognitive prerequisites? To answer this question, Anindilyakwa-speaking Aboriginal children living on a remote island in northern Australia, whose culture contains few counting words or counting practices, and non-indigenous children from an Australian city were administered standardised tests of cognitive abilities (Corsi Blocks, Raven’s Coloured Progressive Matrices, Porteus Maze). The indigenous children completed a non-verbal addition task, and the non-indigenous children completed a single-digit addition task. Consistent with previous observations, indigenous children exhibited superior spatial abilities. Nevertheless, correlation matrices among variables show similar patterns of relationships, and parallel regression analyses showed visuo-spatial working memory was the main predictor of addition performance, in both groups. The findings contribute to the growing body of evidence supporting the hypothesis that the same cognitive abilities are deployed by individuals with and without counting words. The implications of this hypothesis and of these findings for a more complete account of numerical cognition will be discussed.

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15:00-15:30 Tea

15:30-16:00 The real preschoolers of Orange County, and their numerical abilities

Professor Barbara Sarnecka, University of California, Irvine, USA

Abstract

In recent years, researchers have become interested in the question of how children's innate, approximate numerical abilities are related to their mastery of symbolic (spoken and written) numbers, counting and mathematics. Some have even expressed optimism that interventions targeting the approximate number system may improve children's mathematics learning and achievement. In this talk, Professor Sarnecka will argue that while the connection between approximate and exact number representations is theoretically interesting, most children's struggles with maths do not stem from deficits in the approximate number system. And the most problematic gaps in maths achievement - those related to children's socio-economic status - have little or nothing to do with the approximate number system. Finally, Professor Sarnecka will argue that researchers' standard ways of measuring approximate-number-system acuity are invalid for use with children who have not yet grasped the cardinality principle of counting. All of these arguments support the conclusion that in the real world, variations in maths performance are much more likely to stem from differences in mastery of the symbolic number system than from differences in individuals' nonsymbolic numerical abilities.

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16:00-16:30 Learning number sense from adaptive digital games

Professor Diana Laurillard, University College London, UK

Abstract

Neuroimaging studies show that for dyscalculic learners there is a local structural abnormality, with less activation in the parietal cortex for numerical tasks. These studies suggest that dyscalculics fail to understand basic number concepts, and this needs to be remediated before moving on to formal arithmetic. There is already some evidence that remedial interventions can improve performance, and can also modify brain structure and function. 

However, although the findings from cognitive science and neuroscience have identified targets for intervention, they have not, so far, informed pedagogy. Typically interventions have used answer selection to rehearse facts and concepts already encountered. By contrast, an effective pedagogic design would recruit the way the brain learns about the world without a teacher, using prediction-error learning with informational feedback. For learning about numbers, this would mean learners engaging with a world in which numbers become objects whose properties the learner can predict, observe, and manipulate to achieve a goal. 

Professor Laurillard will present examples of adaptive, constructionist, digital games that create such a world. They enable the learner not only to rehearse known facts and concepts, but also to develop new concepts. 

A research programme for interventions for dyscalculia – and other types of low attainment in numeracy – should test their effectiveness against improved numerical competence, and also against predictable changes in neural structures and functioning. 

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16:30-17:00 Discussion

Related events

The origins of numerical abilities: the future Kavli Royal Society Centre, Chicheley Hall Newport Pagnell Buckinghamshire MK16 9JJ