Foundations Of Geometric Cognition
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Foundations Of Geometric Cognition
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Author : Mateusz Hohol
language : en
Publisher: Routledge
Release Date : 2019-09-12
Foundations Of Geometric Cognition written by Mateusz Hohol and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-12 with Psychology categories.
The cognitive foundations of geometry have puzzled academics for a long time, and even today are mostly unknown to many scholars, including mathematical cognition researchers. Foundations of Geometric Cognition shows that basic geometric skills are deeply hardwired in the visuospatial cognitive capacities of our brains, namely spatial navigation and object recognition. These capacities, shared with non-human animals and appearing in early stages of the human ontogeny, cannot, however, fully explain a uniquely human form of geometric cognition. In the book, Hohol argues that Euclidean geometry would not be possible without the human capacity to create and use abstract concepts, demonstrating how language and diagrams provide cognitive scaffolding for abstract geometric thinking, within a context of a Euclidean system of thought. Taking an interdisciplinary approach and drawing on research from diverse fields including psychology, cognitive science, and mathematics, this book is a must-read for cognitive psychologists and cognitive scientists of mathematics, alongside anyone interested in mathematical education or the philosophical and historical aspects of geometry.
Cognitive Foundations For Improving Mathematical Learning
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Author : David C. Geary
language : en
Publisher: Academic Press
Release Date : 2019-01-03
Cognitive Foundations For Improving Mathematical Learning written by David C. Geary and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-03 with Psychology categories.
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
Geometries Of Nature Living Systems And Human Cognition New Interactions Of Mathematics With Natural Sciences And Humanities
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Author : Luciano Boi
language : en
Publisher: World Scientific
Release Date : 2005-11-02
Geometries Of Nature Living Systems And Human Cognition New Interactions Of Mathematics With Natural Sciences And Humanities written by Luciano Boi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-02 with Science categories.
The collection of papers forming this volume is intended to provide a deeper study of some mathematical and physical subjects which are at the core of recent developments in the natural and living sciences. The book explores some far-reaching interfaces where mathematics, theoretical physics, and natural sciences seem to interact profoundly. The main goal is to show that an accomplished movement of geometrisation has enabled the discovery of a great variety of amazing structures and behaviors in physical reality and in living matter. The diverse group of expert mathematicians, physicists and natural scientists present numerous new results and original ideas, methods and techniques. Both academic and interdisciplinary, the book investigates a number of important connections between mathematics, theoretical physics and natural sciences including biology.
Where Mathematics Come From How The Embodied Mind Brings Mathematics Into Being
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Author : George Lakoff
language : en
Publisher:
Release Date : 2000-11-02
Where Mathematics Come From How The Embodied Mind Brings Mathematics Into Being written by George Lakoff and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-11-02 with Mathematics categories.
A study of the cognitive science of mathematical ideas.
Cognition Based Assessment Teaching Of Fractions
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Author : Michael T. Battista
language : en
Publisher: Heinemann Educational Books
Release Date : 2012
Cognition Based Assessment Teaching Of Fractions written by Michael T. Battista and has been published by Heinemann Educational Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Education categories.
Designed to work with any curriculum, Cognition-Based Assessment and Teaching will enable you to better understand and respond to your students' learning needs and help you choose instructional activities that are best for them. Michael Battista offers a learning-progressions model for maximizing each student's progress&— helping students who are behind catch up, preventing future failures from occurring, and helping students who are ready move quickly ahead. Cognition-Based Assessment and Teaching will help you will all three tiers in RTI. Battista's approach emphasizes three key components that support students' mathematical sense making and proficiency: Determining students' levels of sophistication in reasoning Assessing and monitoring the development of students' understanding of core ideas Differentiating instruction to meet individual students' learning needs Using a research-based framework that describes the development of students' thinking and learning in terms of levels of sophistication, a “cognitive terrain” that includes ascents and plateaus, Battista shows how teachers can build on their students' reasoning with instruction that keeps them moving ever upwards.--Publisher.
Space Time And Number In The Brain
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Author : Elizabeth Brannon
language : en
Publisher: Academic Press
Release Date : 2011-05-31
Space Time And Number In The Brain written by Elizabeth Brannon and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-31 with Mathematics categories.
The study of mathematical cognition and the ways in which the ideas of space, time and number are encoded in brain circuitry has become a fundamental issue for neuroscience. How such encoding differs across cultures and educational level is of further interest in education and neuropsychology. This rapidly expanding field of research is overdue for an interdisciplinary volume such as this, which deals with the neurological and psychological foundations of human numeric capacity. A uniquely integrative work, this volume provides a much needed compilation of primary source material to researchers from basic neuroscience, psychology, developmental science, neuroimaging, neuropsychology and theoretical biology. The first comprehensive and authoritative volume dealing with neurological and psychological foundations of mathematical cognition Uniquely integrative volume at the frontier of a rapidly expanding interdisciplinary field Features outstanding and truly international scholarship, with chapters written by leading experts in a variety of fields
The Geometry Of Meaning
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Author : Peter Gärdenfors
language : en
Publisher: MIT Press
Release Date : 2014-01-17
The Geometry Of Meaning written by Peter Gärdenfors and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-17 with Language Arts & Disciplines categories.
A novel cognitive theory of semantics that proposes that the meanings of words can be described in terms of geometric structures.
Numerical Cognition And The Epistemology Of Arithmetic
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Author : Markus Pantsar
language : en
Publisher: Cambridge University Press
Release Date : 2024-03-31
Numerical Cognition And The Epistemology Of Arithmetic written by Markus Pantsar and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-31 with Science categories.
The first book-length philosophical account of arithmetical knowledge that is based on the state-of-the-art empirical studies of numerical cognition.
Proof And Proving In Mathematics Education
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Author : Gila Hanna
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-06-14
Proof And Proving In Mathematics Education written by Gila Hanna and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-14 with Education categories.
*THIS BOOK IS AVAILABLE AS OPEN ACCESS BOOK ON SPRINGERLINK* One of the most significant tasks facing mathematics educators is to understand the role of mathematical reasoning and proving in mathematics teaching, so that its presence in instruction can be enhanced. This challenge has been given even greater importance by the assignment to proof of a more prominent place in the mathematics curriculum at all levels. Along with this renewed emphasis, there has been an upsurge in research on the teaching and learning of proof at all grade levels, leading to a re-examination of the role of proof in the curriculum and of its relation to other forms of explanation, illustration and justification. This book, resulting from the 19th ICMI Study, brings together a variety of viewpoints on issues such as: The potential role of reasoning and proof in deepening mathematical understanding in the classroom as it does in mathematical practice. The developmental nature of mathematical reasoning and proof in teaching and learning from the earliest grades. The development of suitable curriculum materials and teacher education programs to support the teaching of proof and proving. The book considers proof and proving as complex but foundational in mathematics. Through the systematic examination of recent research this volume offers new ideas aimed at enhancing the place of proof and proving in our classrooms.
Interdisciplinary Perspectives On Math Cognition
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Author : Marcel Danesi
language : en
Publisher: Springer Nature
Release Date : 2019-09-14
Interdisciplinary Perspectives On Math Cognition written by Marcel Danesi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-14 with Mathematics categories.
This is an anthology of contemporary studies from various disciplinary perspectives written by some of the world's most renowned experts in each of the areas of mathematics, neuroscience, psychology, linguistics, semiotics, education, and more. Its purpose is not to add merely to the accumulation of studies, but to show that math cognition is best approached from various disciplinary angles, with the goal of broadening the general understanding of mathematical cognition through the different theoretical threads that can be woven into an overall understanding. This volume will be of interest to mathematicians, cognitive scientists, educators of mathematics, philosophers of mathematics, semioticians, psychologists, linguists, anthropologists, and all other kinds of scholars who are interested in the nature, origin, and development of mathematical cognition.