Living at the beginning of the 21st century requires being numerate, because numerical abilities are not only essential for life prospects of individuals but also for economic interests of post-industrial knowledge societies. Thus, numerical development is at the core of both individual as well as societal interests. There is the notion that we are already born with a very basic ability to deal with small numerosities. Yet, this often called “number sense” seems to be very restricted, approximate, and driven by perceptual constraints. During our numerical development in formal (e.g., school) but also informal contexts (e.g., family, street) we acquire culturally developed abstract symbol systems to represent exact numerosities – in particular number words and Arabic digits – refining our numerical capabilities. In recent years, numerical development has gained increasing research interest documented in a growing number of behavioural, neuro-scientific, educational, cross-cultural, and neuropsychological studies addressing this issue. Additionally, our understanding of how numerical competencies develop has also benefitted considerably from the advent of different neuro-imaging techniques allowing for an evaluation of developmental changes in the human brain. In sum, we are now starting to put together a more and more coherent picture of how numerical competencies develop and how this development is associated with neural changes as well. In the end, this knowledge might also lead to a better understanding of the reasons for atypical numerical development which often has grieve consequences for those who suffer from developmental dyscalculia or mathematics learning disabilities. Therefore, this Research Topic deals with all aspects of numerical development: findings from behavioural performance to underlying neural substrates, from cross-sectional to longitudinal evaluations, from healthy to clinical populations. To this end, we included empirical contributions using different experimental methodologies, but also theoretical contributions, review articles, or opinion papers.

This volume is a collection of all papers published in Volume One of the journal "Mathematical Cognition". The aim of the journal is to provide a forum for explorations of how we understand mathematics and how we acquire and use mathematical concepts. The journal encourages an interdisciplinary approach to the field, and publishes advances in the study of the mental representation and use of mathematical concepts from a range of disciplines.; This first volume features contributions from cognitive psychology, developmental psychology, philosophy, neuroscience, education, computational modelling, and neuropsychology.

Numerical Cognition: The Basics provides an understanding of the neural and cognitive mechanisms that enable us to perceive, process, and memorize numerical information. Starting from basic numerical competencies that humans share with other species, the book explores the mental coding of numbers and their neural representation. It explains the strategies of mental calculation, their pitfalls and their development, as well as the developmental steps children make while learning about numbers. The book gradually builds our understanding of the underlying mental processes of numeracy and concludes with an insightful examination of the diagnosis, etiology and treatment of dyscalculia. Written in an accessible manner, the book summarizes and critically evaluates the major psychological explanations for various empirical phenomena in numerical cognition. Containing a wealth of student-friendly features including end of chapter summaries, informative figures, further reading lists, and links to relevant websites, Numerical Cognition: The Basics is an essential starting point for anybody new to the field.

For many years, an abstract, amodal semantic magnitude representation, largely independent of verbal linguistic representations, has been viewed as the core numerical or mathematical representation This assumption has been substantially challenged in recent years. Linguistic properties affect not only verbal representations of numbers,but also numerical magnitude representation, spatial magnitude representations, calculation, parity representation, place-value representation and even early number acquisition. Thus, we postulate that numerical and arithmetic processing are not fully independent of linguistic processing. This is not to say, that in patients, magnitude processing cannot function independently of linguistic processing we just suppose, these functions are connected in the functioning brain. So far, much research about linguistic influences on numerical cognition has simply demonstrated that language influences number without investigating the level at which a particular language influence operates. After an overview, we present new findings on language influences on seven language levels: - Conceptual: Conceptual properties of language - Syntactic: The grammatical structure of languages beyond the word level influences - Semantic: The semantic meaning or existence of words - Lexical: The lexical composition of words, in particular number words - Visuo-spatial-orthographic: Orthographic properties, such as the writing/reading direction of a language. - Phonological: Phonological/phonetic properties of languages - Other language-related skills: Verbal working memory and other cognitive skills related to language representations We hope that this book provides a new and structured overview on the exciting influences of linguistic processing on numerical cognition at almost all levels of language processing.

Development of Mathematical Cognition: Neural Substrates and Genetic Influences reviews advances in extant imaging modalities and the application of brain stimulation techniques for improving mathematical learning. It goes on to explore the role genetics and environmental influences have in the development of math abilities and disabilities. Focusing on the neural substrates and genetic factors associated with both the typical and atypical development of mathematical thinking and learning, this second volume in the Mathematical Cognition and Learning series integrates the latest in innovative measures and methodological advances from the top researchers in the field. - Provides details about new progress made in the study of neural correlates of numerical and arithmetic cognition - Addresses recent work in quantitative and molecular genetics - Works to improve instruction in numerical, arithmetical, and algebraic thinking and learning - Informs policy to help increase the level of mathematical proficiency among the general public

Provides an introduction to the neural network modeling of complex cognitive and neuropsychological processes. Over the past few years, computer modeling has become more prevalent in the clinical sciences as an alternative to traditional symbol-processing models. This book provides an introduction to the neural network modeling of complex cognitive and neuropsychological processes. It is intended to make the neural network approach accessible to practicing neuropsychologists, psychologists, neurologists, and psychiatrists. It will also be a useful resource for computer scientists, mathematicians, and interdisciplinary cognitive neuroscientists. The editors (in their introduction) and contributors explain the basic concepts behind modeling and avoid the use of high-level mathematics. The book is divided into four parts. Part I provides an extensive but basic overview of neural network modeling, including its history, present, and future trends. It also includes chapters on attention, memory, and primate studies. Part II discusses neural network models of behavioral states such as alcohol dependence, learned helplessness, depression, and waking and sleeping. Part III presents neural network models of neuropsychological tests such as the Wisconsin Card Sorting Task, the Tower of Hanoi, and the Stroop Test. Finally, part IV describes the application of neural network models to dementia: models of acetycholine and memory, verbal fluency, Parkinsons disease, and Alzheimer's disease. Contributors J. Wesson Ashford, Rajendra D. Badgaiyan, Jean P. Banquet, Yves Burnod, Nelson Butters, John Cardoso, Agnes S. Chan, Jean-Pierre Changeux, Kerry L. Coburn, Jonathan D. Cohen, Laurent Cohen, Jose L. Contreras-Vidal, Antonio R. Damasio, Hanna Damasio, Stanislas Dehaene, Martha J. Farah, Joaquin M. Fuster, Philippe Gaussier, Angelika Gissler, Dylan G. Harwood, Michael E. Hasselmo, J, Allan Hobson, Sam Leven, Daniel S. Levine, Debra L. Long, Roderick K. Mahurin, Raymond L. Ownby, Randolph W. Parks, Michael I. Posner, David P. Salmon, David Servan-Schreiber, Chantal E. Stern, Jeffrey P. Sutton, Lynette J. Tippett, Daniel Tranel, Bradley Wyble