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Numerical Development - From cognitive functions to neural underpinnings

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Book Series: Frontiers Research Topics ISSN: 16648714 ISBN: 9782889194247 Year: Pages: 281 DOI: 10.3389/978-2-88919-424-7 Language: English
Publisher: Frontiers Media SA
Subject: Psychology --- Science (General)
Added to DOAB on : 2016-01-19 14:05:46
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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.

Building the Foundation: Whole Numbers in the Primary Grades: The 23rd ICMI Study

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Book Series: New ICMI Study Series ISSN: 1387-6872 ISBN: 9783319635545 9783319635552 Year: Pages: 536 DOI: https://doi.org/10.1007/978-3-319-63555-2 Language: English
Publisher: Springer Grant: International Commission on Mathematical Instruction (ICMI); International Mathematical Union (IMU)
Subject: Education --- Mathematics
Added to DOAB on : 2018-06-22 15:48:51
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This twenty-third ICMI Study addresses for the first time mathematics teaching and learning in the primary school (and pre-school) setting, while also taking international perspectives, socio-cultural diversity and institutional constraints into account. One of the main challenges of designing the first ICMI primary school study of this kind is the complex nature of mathematics at the early level. Accordingly, a focus area that is central to the discussion was chosen, together with a number of related questions. The broad area of Whole Number Arithmetic (WNA), including operations and relations and arithmetic word problems, forms the core content of all primary mathematics curricula. The study of this core content area is often regarded as foundational for later mathematics learning. However, the principles and main goals of instruction on the foundational concepts and skills in WNA are far from universally agreed upon, and practice varies substantially from country to country. As such, this study presents a meta-level analysis and synthesis of what is currently known about WNA, providing a useful base from which to gauge gaps and shortcomings, as well as an opportunity to learn from the practices of different countries and contexts.

Linguistic Influences on Mathematical Cognition

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Book Series: Frontiers Research Topics ISSN: 16648714 ISBN: 9782889452002 Year: Pages: 173 DOI: 10.3389/978-2-88945-200-2 Language: English
Publisher: Frontiers Media SA
Subject: Psychology --- Science (General)
Added to DOAB on : 2017-10-13 14:57:01
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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 representationsWe 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.

Physical (A)Causality: Determinism, Randomness and Uncaused Events

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Book Series: Fundamental Theories of Physics ISSN: 0168-1222 ISBN: 9783319708140 9783319708157 Year: Volume: 192 Pages: 219 DOI: https://doi.org/10.1007/978-3-319-70815-7 Language: English
Publisher: Springer Grant: OpenAIRE
Subject: Physics (General)
Added to DOAB on : 2018-06-29 14:42:45
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This book addresses the physical phenomenon of events that seem to occur spontaneously and without any known cause. These are to be contrasted with events that happen in a (pre-)determined, predictable, lawful, and causal way.All our knowledge is based on self-reflexive theorizing, as well as on operational means of empirical perception. Some of the questions that arise are the following: are these limitations reflected by our models? Under what circumstances does chance kick in? Is chance in physics merely epistemic? In other words, do we simply not know enough, or use too crude levels of description for our predictions? Or are certain events "truly", that is, irreducibly, random? The book tries to answer some of these questions by introducing intrinsic, embedded observers and provable unknowns; that is, observables and procedures which are certified (relative to the assumptions) to be unknowable or undoable. A (somewhat iconoclastic) review of quantum mechanics is presented which is inspired by quantum logic. Postulated quantum (un-)knowables are reviewed. More exotic unknowns originate in the assumption of classical continua, and in finite automata and generalized urn models, which mimic complementarity and yet maintain value definiteness. Traditional conceptions of free will, miracles and dualistic interfaces are based on gaps in an otherwise deterministic universe.

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