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Language and Culture in Mathematical Cognition

Language and Culture in Mathematical Cognition
  • Author : Daniel B. Berch,David C. Geary,Kathleen Mann Koepke
  • Publisher :Unknown
  • Release Date :2018-07-27
  • Total pages :364
  • ISBN : 9780128125755
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Summary : Language and Culture in Mathematical Cognition, First Edition focuses on the role of linguistic and cultural factors in math cognition and development. It covers a wide range of topics, including analogical mapping in numerical development, arithmetic fact retrieval in the bilingual brain, cross-cultural comparisons of mathematics achievement, the shaping of numerical processing by number word construction, the influence of Head Start programs, the mathematical skills of children with specific language impairments, the role of culture and language in creating associations between number and space, and electrophysiological studies of linguistic traces in core knowledge at the neural level. Includes cutting-edge findings, innovative measures, recent methodological advances and groundbreaking theoretical developments Synthesizes research from various subdomains of math cognition research Covers the full complement of research in mathematical thinking and learning Informs researchers, scholars, educators, students and policymakers

The Oxford Handbook of Numerical Cognition

The Oxford Handbook of Numerical Cognition
  • Author : Roi Cohen Kadosh,Ann Dowker
  • Publisher :Unknown
  • Release Date :2015-03-15
  • Total pages :1144
  • ISBN : 9780199642342
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Summary : How do we understand numbers? Do animals and babies have numerical abilities? Why do some people fail to grasp numbers, and how we can improve numerical understanding? Numbers are vital to so many areas of life: in science, economics, sports, education, and many aspects of everyday life from infancy onwards. Numerical cognition is a vibrant area that brings together scientists from different and diverse research areas (e.g., neuropsychology, cognitive psychology, developmental psychology, comparative psychology, anthropology, education, and neuroscience) using different methodological approaches (e.g., behavioral studies of healthy children and adults and of patients; electrophysiology and brain imaging studies in humans; single-cell neurophysiology in non-human primates, habituation studies in human infants and animals, and computer modeling). While the study of numerical cognition had been relatively neglected for a long time, during the last decade there has been an explosion of studies and new findings. This has resulted in an enormous advance in our understanding of the neural and cognitive mechanisms of numerical cognition. In addition, there has recently been increasing interest and concern about pupils' mathematical achievement in many countries, resulting in attempts to use research to guide mathematics instruction in schools, and to develop interventions for children with mathematical difficulties. This handbook brings together the different research areas that make up the field of numerical cognition in one comprehensive and authoritative volume. The chapters provide a broad and extensive review that is written in an accessible form for scholars and students, as well as educationalists, clinicians, and policy makers. The book covers the most important aspects of research on numerical cognition from the areas of development psychology, cognitive psychology, neuropsychology and rehabilitation, learning disabilities, human and animal cognition and neuroscience, computational modeling, education and individual differences, and philosophy. Containing more than 60 chapters by leading specialists in their fields, the Oxford Handbook of Numerical Cognition is a state-of-the-art review of the current literature.

Linguistic Influences on Mathematical Cognition

Linguistic Influences on Mathematical Cognition
  • Author : Ann Dowker,Hans-Christoph Nuerk
  • Publisher :Unknown
  • Release Date :2017-06-16
  • Total pages :229
  • ISBN : 9782889452002
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Summary : 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.

On the Development of Space-Number Relations: Linguistic and Cognitive Determinants, Influences, and Associations

On the Development of Space-Number Relations: Linguistic and Cognitive Determinants, Influences, and Associations
  • Author : Hans-Christoph Nuerk,Krzysztof Cipora,Frank Domahs,Maciej Haman
  • Publisher :Unknown
  • Release Date :2020-03-30
  • Total pages :229
  • ISBN : 9782889635887
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Summary :

Linguistic Influences on Mathematical Cognition

Linguistic Influences on Mathematical Cognition
  • Author : Ann Dowker,Hans-Christoph Nuerk
  • Publisher :Unknown
  • Release Date :2017-06-16
  • Total pages :229
  • ISBN : 9782889452002
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Summary : 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.

Cultural Development of Mathematical Ideas

Cultural Development of Mathematical Ideas
  • Author : Geoffrey B. Saxe
  • Publisher :Unknown
  • Release Date :2012-09-28
  • Total pages :229
  • ISBN : 9781139560238
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Summary : Drawing upon field studies conducted in 1978, 1980 and 2001 with the Oksapmin, a remote Papua New Guinea group, Geoffrey B. Saxe traces the emergence of new forms of numerical representations and ideas in the social history of the community. In traditional life, the Oksapmin used a counting system that makes use of twenty-seven parts of the body; there is no evidence that the group used arithmetic in prehistory. As practices of economic exchange and schooling have shifted, children and adults unwittingly reproduced and altered the system in order to solve new kinds of numerical and arithmetical problems, a process that has led to new forms of collective representations in the community. While Dr Saxe's focus is on the Oksapmin, the insights and general framework he provides are useful for understanding shifting representational forms and emerging cognitive functions in any human community.

Understanding Emotions in Mathematical Thinking and Learning

Understanding Emotions in Mathematical Thinking and Learning
  • Author : Ulises Xolocotzin
  • Publisher :Unknown
  • Release Date :2017-05-12
  • Total pages :474
  • ISBN : 9780128024898
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Summary : Emotions play a critical role in mathematical cognition and learning. Understanding Emotions in Mathematical Thinking and Learning offers a multidisciplinary approach to the role of emotions in numerical cognition, mathematics education, learning sciences, and affective sciences. It addresses ways in which emotions relate to cognitive processes involved in learning and doing mathematics, including processing of numerical and physical magnitudes (e.g. time and space), performance in arithmetic and algebra, problem solving and reasoning attitudes, learning technologies, and mathematics achievement. Additionally, it covers social and affective issues such as identity and attitudes toward mathematics. Covers methodologies in studying emotion in mathematical knowledge Reflects the diverse and innovative nature of the methodological approaches and theoretical frameworks proposed by current investigations of emotions and mathematical cognition Includes perspectives from cognitive experimental psychology, neuroscience, and from sociocultural, semiotic, and discursive approaches Explores the role of anxiety in mathematical learning Synthesizes unifies the work of multiple sub-disciplines in one place

Cultural Models in Language and Thought

Cultural Models in Language and Thought
  • Author : Dorothy Holland,Naomi Quinn
  • Publisher :Unknown
  • Release Date :1987-01-30
  • Total pages :400
  • ISBN : 0521311683
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Summary : A multidisciplinary collaboration exploring the role of cultural knowledge in everyday language and understanding.

Cognition and Culture

Cognition and Culture
  • Author : J. Altarriba
  • Publisher :Unknown
  • Release Date :1993-11-17
  • Total pages :405
  • ISBN : UOM:39015029970632
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Summary : While the main source of knowledge of human cognition has come from studies of information processing in a single culture, primarily within the U.S. or within certain countries in Europe, much research has also been conducted in other parts of the world. Can the study of cognition across cultures lead us to interesting conclusions about human cognition in general? Surely any general theory of language processing, for example, must be able to explain phenomena observed across cultures and not just within a single one. This book is an attempt to look at this issue of universals in thinking and understanding by providing a compendium of cross cultural investigations in the four major areas of cognitive psychology: (1) memory and knowledge representation, (2) language processing, (3) perception, and (4) reasoning and problem solving. The differences found across cultures are also fascinating and extremely informative. A final chapter provides a summary of the major findings reported in each of these areas. The chapters included in this work were written for those interested in cross-cultural psychology and also those with an interest in cultural anthropology. The authors are well-known in the areas of cross-cultural psychology, cognitive psychology, linguistics, and anthropology. However, the reader need not be an expert in any one of these fields to understand the conclusions and implications of the work reported here.

Cognition, Metacognition, and Culture in STEM Education

Cognition, Metacognition, and Culture in STEM Education
  • Author : Yehudit Judy Dori,Zemira R. Mevarech,Dale R. Baker
  • Publisher :Unknown
  • Release Date :2017-12-01
  • Total pages :380
  • ISBN : 9783319666594
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Summary : This book addresses the point of intersection between cognition, metacognition, and culture in learning and teaching Science, Technology, Engineering, and Mathematics (STEM). We explore theoretical background and cutting-edge research about how various forms of cognitive and metacognitive instruction may enhance learning and thinking in STEM classrooms from K-12 to university and in different cultures and countries. Over the past several years, STEM education research has witnessed rapid growth, attracting considerable interest among scholars and educators. The book provides an updated collection of studies about cognition, metacognition and culture in the four STEM domains. The field of research, cognition and metacognition in STEM education still suffers from ambiguity in meanings of key concepts that various researchers use. This book is organized according to a unique manner: Each chapter features one of the four STEM domains and one of the three themes—cognition, metacognition, and culture—and defines key concepts. This matrix-type organization opens a new path to knowledge in STEM education and facilitates its understanding. The discussion at the end of the book integrates these definitions for analyzing and mapping the STEM education research.

Handbook of Mathematical Cognition

Handbook of Mathematical Cognition
  • Author : Jamie I. D. Campbell
  • Publisher :Unknown
  • Release Date :2005
  • Total pages :508
  • ISBN : 9781841694115
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Summary : Forlagsomtale: This collection of 27 chapters by leading researchers provides a state-of-the-art reference for mathematical cognition research

Development of Mathematical Cognition

Development of Mathematical Cognition
  • Author : Daniel B. Berch,David C. Geary,Kathleen Mann Koepke
  • Publisher :Unknown
  • Release Date :2015-10-03
  • Total pages :414
  • ISBN : 9780128019092
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Summary : 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

Where Mathematics Comes from

Where Mathematics Comes from
  • Author : George Lakoff,Rafael E. Núñez
  • Publisher :Unknown
  • Release Date :2000
  • Total pages :493
  • ISBN : UOM:39015049551552
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Summary : Provides an in-depth analysis of the cognitive science of mathematical ideas that argues that conceptual metaphor plays a definitive role in mathematical ideas, exploring such concepts as arithmetic, algebra, sets, logic, and infinity. 20,000 first printing.

Cognitive Foundations for Improving Mathematical Learning

Cognitive Foundations for Improving Mathematical Learning
  • Author : David C. Geary,Daniel B. Berch,Kathleen Mann Koepke
  • Publisher :Unknown
  • Release Date :2019-01-03
  • Total pages :377
  • ISBN : 9780128159538
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Summary : The fifth volume in the Mathematical Cognition and Learning series focuses on informal learning environments and other parental influences on numerical cognitive development and formal instructional interventions for improving mathematics learning and performance. The chapters cover the use of numerical play and games for improving foundational number knowledge as well as school math performance, the link between early math abilities and the approximate number system, and how families can help improve the early development of math skills. The book goes on to examine learning trajectories in early mathematics, the role of mathematical language in acquiring numeracy skills, evidence-based assessments of early math skills, approaches for intensifying early mathematics interventions, the use of analogies in mathematics instruction, schema-based diagrams for teaching ratios and proportions, the role of cognitive processes in treating mathematical learning difficulties, and addresses issues associated with intervention fadeout. Identifies the relative influence of school and family on math learning Discusses the efficacy of numerical play for improvement in math Features learning trajectories in math Examines the role of math language in numeracy skills Includes assessments of math skills Explores the role of cognition in treating math-based learning difficulties

Why is Math So Hard for Some Children?

Why is Math So Hard for Some Children?
  • Author : Daniel B. Berch,Michèle M. M. Mazzocco
  • Publisher :Unknown
  • Release Date :2007
  • Total pages :457
  • ISBN : UOM:39015069337130
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Summary : This landmark resource gives educational decision–makers and researchers theoretical and practical insight into mathematical learning difficulties and disabilities, combining diverse perspectives from fields such as special education, developmental

Children’s Logical and Mathematical Cognition

Children’s Logical and Mathematical Cognition
  • Author : C.J. Brainerd
  • Publisher :Unknown
  • Release Date :2012-12-06
  • Total pages :216
  • ISBN : 9781461394662
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Summary : For some time now, the study of cognitive development has been far and away the most active discipline within developmental psychology. Although there would be much disagreement as to the exact proportion of papers published in developmen tal journals that could be considered cognitive, 50% seems like a conservative estimate. Hence, a series of scholarly books to be devoted to work in cognitive development is especially appropriate at this time. The Springer Series in Cognitive Development contains two basic types of books, namely, edited collections of original chapters by several authors, and original volumes written by one author or a small group of authors. The flagship for the Springer Series will be a serial publication of the "advances" type, carrying the subtitle Progress in Cognitive Development Research. Each volume in the Progress sequence will be strongly thematic, in that it will be limited to some well-defined domain of cognitive-developmental research (e. g. , logical and mathematical de velopment, semantic development). All Progress volumes will be edited collec tions. Editors of such collections, upon consultation with the Series Editor, may elect to have their books published either as contributions to the Progress sequence or as separate volumes. All books written by one author or a small group of authors will be published as separate volumes within the series. A fairly broad definition of cognitive development is being used in the selection of books for this series.

The Number Sense

The Number Sense
  • Author : Stanislas Dehaene
  • Publisher :Unknown
  • Release Date :2011-04-29
  • Total pages :316
  • ISBN : 9780199753871
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Summary : "Our understanding of how the human brain performs mathematical calculations is far from complete. In The Number Sense, Stanislas Dehaene offers readers an enlightening exploration of the mathematical mind. Using research showing that human infants have a rudimentary number sense, Dehaene suggests that this sense is as basic as our perception of color, and that it is wired into the brain. But how then did we leap from this basic number ability to trigonometry, calculus, and beyond? Dehaene shows that it was the invention of symbolic systems of numerals that started us on the climb to higher mathematics. Tracing the history of numbers, we learn that in early times, people indicated numbers by pointing to part of their bodies, and how Roman numerals were replaced by modern numbers. On the way, we also discover many fascinating facts: for example, because Chinese names for numbers are short, Chinese people can remember up to nine or ten digits at a time, while English-speaking people can only remember seven. A fascinating look at the crossroads where numbers and neurons intersect, The Number Sense offers an intriguing tour of how the structure of the brain shapes our mathematical abilities, and how math can open up a window on the human mind"--Provided by publisher.

Mathematics Under the Microscope

Mathematics Under the Microscope
  • Author : Alexandre Borovik
  • Publisher :Unknown
  • Release Date :2010
  • Total pages :317
  • ISBN : 9780821847619
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Summary : The author's goal is to start a dialogue between mathematicians and cognitive scientists. He discusses, from a working mathematician's point of view, the mystery of mathematical intuition: why are certain mathematical concepts more intuitive than others? To what extent does the ``small scale'' structure of mathematical concepts and algorithms reflect the workings of the human brain? What are the ``elementary particles'' of mathematics that build up the mathematical universe? The book is saturated with amusing examples from a wide range of disciplines--from turbulence to error-correcting codes to logic--as well as with just puzzles and brainteasers. Despite the very serious subject matter, the author's approach is lighthearted and entertaining. This is an unusual and unusually fascinating book. Readers who never thought about mathematics after their school years will be amazed to discover how many habits of mind, ideas, and even material objects that are inherently mathematical serve as building blocks of our civilization and everyday life. A professional mathematician, reluctantly breaking the daily routine, or pondering on some resisting problem, will open this book and enjoy a sudden return to his or her young days when mathematics was fresh, exciting, and holding all promises. And do not take the word ``microscope'' in the title too literally: in fact, the author looks around, in time and space, focusing in turn on a tremendous variety of motives, from mathematical ``memes'' (genes of culture) to an unusual life of a Hollywood star. --Yuri I. Manin, Max-Planck Institute of Mathematics, Bonn, and Northwestern University

Getting to "Got It!"

Getting to 'Got It!'
  • Author : Betty K. Garner
  • Publisher :Unknown
  • Release Date :2007-11-15
  • Total pages :168
  • ISBN : 9781416612421
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Summary : It's one of the great mysteries of teaching: Why do some students "get it" and some students don't? In this book, Betty K. Garner focuses on why students struggle and what teachers can do to help them become self-directed learners. Difficulty reading, remembering, paying attention, or following directions are not the reasons students fail but symptoms of the true problem: underdeveloped cognitive structures—the mental processes necessary to connect new information with prior knowledge; organize information into patterns and relationships; formulate rules that make information processing automatic, fast, and predictable; and abstract generalizable principles that allow them to transfer and apply learning. Each chapter focuses on a key cognitive structure and uses real-life accounts to illustrate how learners construct meaning by using recognition, memorization, conservation of constancy, classification, spatial orientation, temporal orientation, and metaphorical thinking. The author's simple techniques stress reflective awareness and visualization. It's by helping students to be conscious of what their senses are telling them, encouraging them to visualize the information for processing, and then prompting them to ask questions and figure out solutions on their own that teachers can best help students develop the tools they need to * Gather, organize, and make sense of information, * Become cognitively engaged and internally motivated to achieve, and * Experience learning as a dynamic process of creating and changing. Suggestions for using these techniques in daily classroom practice, advice on lesson planning for cognitive engagement, and guidelines for conducting reflective research expand this book's practical applications. Use it not only to help struggling students break through hidden barriers but to empower all students with tools that will last a lifetime.

Evolutionary Epistemology, Language and Culture

Evolutionary Epistemology, Language and Culture
  • Author : Nathalie Gontier,Jean Paul van Bendegem,Diederik Aerts
  • Publisher :Unknown
  • Release Date :2006-07-25
  • Total pages :494
  • ISBN : 9781402033957
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Summary : For the first time in history, scholars working on language and culture from within an evolutionary epistemological framework, and thereby emphasizing complementary or deviating theories of the Modern Synthesis, were brought together. Of course there have been excellent conferences on Evolutionary Epistemology in the past, as well as numerous conferences on the topics of Language and Culture. However, until now these disciplines had not been brought together into one all-encompassing conference. Moreover, previously there never had been such stress on alternative and complementary theories of the Modern Synthesis. Today we know that natural selection and evolution are far from synonymous and that they do not explain isomorphic phenomena in the world. ‘Taking Darwin seriously’ is the way to go, but today the time has come to take alternative and complementary theories that developed after the Modern Synthesis, equally seriously, and, furthermore, to examine how language and culture can merit from these diverse disciplines. As this volume will make clear, a specific inter- and transdisciplinary approach is one of the next crucial steps that needs to be taken, if we ever want to unravel the secrets of phenomena such as language and culture.

Multiple Perspectives on Difficulties in Learning Literacy and Numeracy

Multiple Perspectives on Difficulties in Learning Literacy and Numeracy
  • Author : Claire Wyatt-Smith,John Elkins,Stephanie Gunn
  • Publisher :Unknown
  • Release Date :2010-10-28
  • Total pages :375
  • ISBN : 1402088647
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Summary : There are many approaches to researching the difficulties in learning that students experience in the key areas of literacy and numeracy. This book seeks to advance understanding of these difficulties and the interventions that have been used to improve outcomes. The book addresses the sometimes complementary and sometimes contradictory results, and generates new approaches to understanding and serving students with difficulties in literacy and numeracy. The book represents a departure from conventional wisdom as most scholars and graduate students draw upon ideas from only one of the three domains focal in the book and usually from one single or dominant theoretical frame. Typically, readers will affiliate with reading education, mathematics education, or learning disabilities and belong to one of the corresponding professional associations such as IRA, NCTM, or CLD. This book’s scope will open a scholarly forum for engaging readers with a familiarity with one of these domains while providing insight into the others on offer in the book.