Good and bad at numbers: typical and atypical development of number processing and arithmetic

This thesis elucidates the heterogeneous nature of mathematical skills by examining numerical and arithmetical abilities in typical, atypical and exceptional populations. Moreover, it looks at the benefits of intervention for remediating and improving mathematical skills. First, we establish the nature of the ‘number sense’ and assess its contribution to typical and atypical arithmetical development. We confirmed that representing and manipulating numerosities approximately is fundamentally different from the ability to manipulate them exactly. Yet only the exact manipulation of numbers seems to be crucial for the development of arithmetic. These results lead to a better characterization of mathematical disabilities such as Developmental Dyscalculia and Low Numeracy. In the latter population we also investigated more general cognitive functions demonstrating how inhibition processes of working memory and stimulusmaterial interacted with arithmetical attainment. Furthermore, we examined areas of mathematics that are often difficult to grasp: the representation and processing of rational numbers. Using explicit mapping tasks we demonstrated that well-educated adults, but also typically developing 10 year olds and children with low numeracy have a comprehensive understanding of these types of numbers. We also investigated exceptional maths abilities in a population of children with Autism Spectrum Disorder (ASD) demonstrating that this condition is characterized by outstanding arithmetical skills and sophisticated calculation strategies, which are reflected in a fundamentally different pattern of brain activation. Ultimately we looked at remediation and learning. Targeted behavioural intervention was beneficial for children with low numeracy but not in Developmental Dyscalculia. Finally, we demonstrated that adults’ numerical performance can be enhanced by neural stimulation (tDCS) to dedicated areas of the brain. This work sheds light on the entire spectrum of mathematical skills from atypical to exceptional development and it is extremely relevant for the advancing of the field of mathematical cognition and the prospects of diagnosis, education and intervention

Recommendations for neonatologists and pediatricians working in first level birthing centers on the first communication of genetic disease and malformation syndrome diagnosis: consensus issued by 6 Italian scientific societies and 4 parents’ associations

Background: Genetic diseases are chronic conditions with relevant impact on the lives of patients and their families. In USA and Europe it is estimated a prevalence of 60 million affected subjects, 75% of whom are in developmental age. A significant number of newborns are admitted in the Neonatal Intensive Care Units (NICU) for reasons different from prematurity, although the prevalence of those with genetic diseases is unknown. It is, then, common for the neonatologist to start a diagnostic process on suspicion of a genetic disease or malformation syndrome, or to make and communicate these diagnoses. Many surveys showed that the degree of parental satisfaction with the methods of communication of diagnosis is low. Poor communication may have short and long-term negative effects on health and psychological and social development of the child and his family. We draw up recommendations on this issue, shared by 6 Italian Scientific Societies and 4 Parents’ Associations, aimed at making the neonatologist’s task easier at the difficult time of communication to parents of a genetic disease/malformation syndrome diagnosis for their child. Methods: We used the method of the consensus paper. A multidisciplinary panel of experts was first established, based on the clinical and scientific sharing of the thematic area of present recommendations. They were suggested by the Boards of the six Scientific Societies that joined the initiative: Italian Societies of Pediatrics, Neonatology, Human Genetics, Perinatal Medicine, Obstetric and Gynecological Ultrasound and Biophysical Methodologies, and Pediatric Genetic Diseases and Congenital Disabilities. To obtain a deeper and global vision of the communication process, and to reach a better clinical management of patients and their families, representatives of four Parents’ Associations were also recruited: Italian Association of Down People, Cornelia de Lange National Volunteer Association, Italian Federation of Rare Diseases, and Williams Syndrome People Association. They worked from September 2019 to November 2020 to achieve a consensus on the recommendations for the communication of a new diagnosis of genetic disease. Results: The consensus of experts drafted a final document defining the recommendations, for the neonatologist and/or the pediatrician working in a fist level birthing center, on the first communication of genetic disease or malformation syndrome diagnosis. Although there is no universal communication technique to make the informative process effective, we tried to identify a few relevant strategic principles that the neonatologist/pediatrician may use in the relationship with the family. We also summarized basic principles and significant aspects relating to the modalities of interaction with families in a table, in order to create an easy tool for the neonatologist to be applied in the daily care practice. We finally obtained an intersociety document, now published on the websites of the Scientific Societies involved. Conclusions: The neonatologist/pediatrician is often the first to observe complex syndromic pictures, not always identified before birth, although today more frequently prenatally diagnosed. It is necessary for him to know the aspects of genetic diseases related to communication and bioethics, as well as the biological and clinical ones, which together outline the cornerstones of the multidisciplinary care of these patients. This consensus provide practical recommendations on how to make the first communication of a genetic disease /malformation syndrome diagnosis. The proposed goal is to make easier the informative process, and to implement the best practices in the relationship with the family. A better doctor-patient/family interaction may improve health outcomes of the child and his family, as well as reduce legal disputes with parents and the phenomenon of defensive medicine

Preschoolers' Precision of the Approximate Number System Predicts Later School Mathematics Performance

The Approximate Number System (ANS) is a primitive mental system of nonverbal representations that supports an intuitive sense of number in human adults, children, infants, and other animal species. The numerical approximations produced by the ANS are characteristically imprecise and, in humans, this precision gradually improves from infancy to adulthood. Throughout development, wide ranging individual differences in ANS precision are evident within age groups. These individual differences have been linked to formal mathematics outcomes, based on concurrent, retrospective, or short-term longitudinal correlations observed during the school age years. However, it remains unknown whether this approximate number sense actually serves as a foundation for these school mathematics abilities. Here we show that ANS precision measured at preschool, prior to formal instruction in mathematics, selectively predicts performance on school mathematics at 6 years of age. In contrast, ANS precision does not predict non-numerical cognitive abilities. To our knowledge, these results provide the first evidence for early ANS precision, measured before the onset of formal education, predicting later mathematical abilities

Impact of High Mathematics Education on the Number Sense

In adult number processing two mechanisms are commonly used: approximate estimation of quantity and exact calculation. While the former relies on the approximate number sense (ANS) which we share with animals and preverbal infants, the latter has been proposed to rely on an exact number system (ENS) which develops later in life following the acquisition of symbolic number knowledge. The current study investigated the influence of high level math education on the ANS and the ENS. Our results showed that the precision of non-symbolic quantity representation was not significantly altered by high level math education. However, performance in a symbolic number comparison task as well as the ability to map accurately between symbolic and non-symbolic quantities was significantly better the higher mathematics achievement. Our findings suggest that high level math education in adults shows little influence on their ANS, but it seems to be associated with a better anchored ENS and better mapping abilities between ENS and ANS

Preliminary evidence for performance enhancement following parietal lobe stimulation in Developmental Dyscalculia.

Nearly 7% of the population exhibit difficulties in dealing with numbers and performing arithmetic, a condition named Developmental Dyscalculia (DD), which significantly affects the educational and professional outcomes of these individuals, as it often persists into adulthood. Research has mainly focused on behavioral rehabilitation, while little is known about performance changes and neuroplasticity induced by the concurrent application of brain-behavioral approaches. It has been shown that numerical proficiency can be enhanced by applying a small-yet constant-current through the brain, a non-invasive technique named transcranial electrical stimulation (tES). Here we combined a numerical learning paradigm with transcranial direct current stimulation (tDCS) in two adults with DD to assess the potential benefits of this methodology to remediate their numerical difficulties. Subjects learned to associate artificial symbols to numerical quantities within the context of a trial and error paradigm, while tDCS was applied to the posterior parietal cortex (PPC). The first subject (DD1) received anodal stimulation to the right PPC and cathodal stimulation to the left PPC, which has been associated with numerical performance's improvements in healthy subjects. The second subject (DD2) received anodal stimulation to the left PPC and cathodal stimulation to the right PPC, which has been shown to impair numerical performance in healthy subjects. We examined two indices of numerical proficiency: (i) automaticity of number processing; and (ii) mapping of numbers onto space. Our results are opposite to previous findings with non-dyscalculic subjects. Only anodal stimulation to the left PPC improved both indices of numerical proficiency. These initial results represent an important step to inform the rehabilitation of developmental learning disabilities, and have relevant applications for basic and applied research in cognitive neuroscience, rehabilitation, and education

The mental cost of cognitive enhancement.

Noninvasive brain stimulation provides a potential tool for affecting brain functions in the typical and atypical brain and offers in several cases an alternative to pharmaceutical intervention. Some studies have suggested that transcranial electrical stimulation (TES), a form of noninvasive brain stimulation, can also be used to enhance cognitive performance. Critically, research so far has primarily focused on optimizing protocols for effective stimulation, or assessing potential physical side effects of TES while neglecting the possibility of cognitive side effects. We assessed this possibility by targeting the high-level cognitive abilities of learning and automaticity in the mathematical domain. Notably, learning and automaticity represent critical abilities for potential cognitive enhancement in typical and atypical populations. Over 6 d, healthy human adults underwent cognitive training on a new numerical notation while receiving TES to the posterior parietal cortex or the dorsolateral prefrontal cortex. Stimulation to the the posterior parietal cortex facilitated numerical learning, whereas automaticity for the learned material was impaired. In contrast, stimulation to the dorsolateral prefrontal cortex impaired the learning process, whereas automaticity for the learned material was enhanced. The observed double dissociation indicates that cognitive enhancement through TES can occur at the expense of other cognitive functions. These findings have important implications for the future use of enhancement technologies for neurointervention and performance improvement in healthy populations

Core information processing deficits in developmental dyscalculia and low numeracy

There are two different conceptions of the innate basis for numerical abilities. On the one hand, it is claimed that infants possess a 'number module' that enables them to construct concepts of the exact numerosities of sets upon which arithmetic develops (e.g. Butterworth, 1999; Gelman & Gallistel, 1978). On the other hand, it has been proposed that infants are equipped only with a sense of approximate numerosities (e.g. Feigenson, Dehaene & Spelke, 2004), upon which the concepts of exact numerosities are constructed with the aid of language (Carey, 2004) and which forms the basis of arithmetic (Lemer, Dehaene, Spelke & Cohen, 2003). These competing proposals were tested by assessing whether performance on approximate numerosity tasks is related to performance on exact numerosity tasks. Moreover, performance on an analogue magnitude task was tested, since it has been claimed that approximate numerosities are represented as analogue magnitudes. In 8-9-year-olds, no relationship was found between exact tasks and either approximate or analogue tasks in normally achieving children, in children with low numeracy or in children with developmental dyscalculia. Low numeracy was related not to a poor grasp of exact numerosities, but to a poor understanding of symbolic numerals. © 2008 The Authors.link_to_subscribed_fulltex

Short-term cognitive training recapitulates hippocampal functional changes associated with one year of longitudinal skill development

Development Psychopathology in context: schoo

Genetics and Mathematics: FMR1 premutation female carriers

Neuropsychological investigations of FMR1 premutation carriers without FXTAS present one domain resulting in contradictory findings, namely that of mathematical skills. One reason for this might be that standard clinical batteries used so far may be inadequate to uncover precise deficits within specific mathematical skills. In fact, these batteries do not clearly distinguish between specific mathematical abilities and are therefore likely to provide only a generic indication of a deficit. Mathematical skills in a group of females with FMR1 premutation were investigated through the use of an extensive, theoretically grounded battery of mathematical tasks, encompassing counting, number comprehension, numerical transcoding, calculation skills and arithmetic principles. Moreover, the mental representation of numbers was assessed by studying the Spatial Numerical Association of Response Codes (SNARC) effect and mental number line (MNL) bisection. The FMR1 premutation group (N=18) comprised 29-50 years old women of normal intelligence, who were individually matched on age, sex and education to a group of healthy participants (N=18). Specific yet subtle weaknesses were detected on processes of basic number understanding such as dealing with analogue scales and certain aspects of number transcoding, in the presence of otherwise spared calculation abilities