Does Mathematical Study Develop Logical Thinking Testing The Theory Of Formal Discipline

Author : Matthew Inglis,Nina Attridge
Publisher : World Scientific
Page : 204 pages
File Size : 41,9 Mb
Release : 2016-09-06
Category : Mathematics
ISBN : 9781786340702

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Does Mathematical Study Develop Logical Thinking?: Testing The Theory Of Formal Discipline by Matthew Inglis,Nina Attridge Pdf

For centuries, educational policymakers have believed that studying mathematics is important, in part because it develops general thinking skills that are useful throughout life. This 'Theory of Formal Discipline' (TFD) has been used as a justification for mathematics education globally. Despite this, few empirical studies have directly investigated the issue, and those which have showed mixed results.Does Mathematical Study Develop Logical Thinking? describes a rigorous investigation of the TFD. It reviews the theory's history and prior research on the topic, followed by reports on a series of recent empirical studies. It argues that, contrary to the position held by sceptics, advanced mathematical study does develop certain general thinking skills, however these are much more restricted than those typically claimed by TFD proponents.Perfect for students, researchers and policymakers in education, further education and mathematics, this book provides much needed insight into the theory and practice of the foundations of modern educational policy.

Author : Andrew Aberdein,Matthew Inglis
Publisher : Bloomsbury Publishing
Page : 293 pages
File Size : 53,7 Mb
Release : 2019-05-02
Category : Philosophy
ISBN : 9781350039032

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Advances in Experimental Philosophy of Logic and Mathematics by Andrew Aberdein,Matthew Inglis Pdf

This book explores the results of applying empirical methods to the philosophy of logic and mathematics. Much of the work that has earned experimental philosophy a prominent place in twenty-first century philosophy is concerned with ethics or epistemology. But, as this book shows, empirical methods are just as much at home in logic and the philosophy of mathematics. Chapters demonstrate and discuss the applicability of a wide range of empirical methods including experiments, surveys, interviews, and data-mining. Distinct themes emerge that reflect recent developments in the field, such as issues concerning the logic of conditionals and the role played by visual elements in some mathematical proofs. Featuring leading figures from experimental philosophy and the fields of philosophy of logic and mathematics, this collection reveals that empirical work in these disciplines has been quietly thriving for some time and stresses the importance of collaboration between philosophers and researchers in mathematics education and mathematical cognition.

Author : Lidia Gonzalez
Publisher : Corwin Press
Page : 173 pages
File Size : 49,7 Mb
Release : 2023-02-03
Category : Education
ISBN : 9781071907498

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Bad at Math? by Lidia Gonzalez Pdf

Math really is for everyone—so let’s prove it. You’ve heard it from kids, from friends, and from celebrities: "I’m bad at math." It’s a line that society tends to accept without examination—after all, some people just aren’t "math people," right? Wrong. As we do with other essential skills, we need to expose the stereotypes, challenge the negative mindsets, and finally confront the systemic opportunity gaps in math education, and replace them with a new vision for what math is, who it’s for, and who can excel at it. In this book you’ll find Research on teacher and student mindsets and their effect on student achievement Audience-specific and differentiated tools, reflection questions, and suggested actions for educators at all levels of the system Examples from popular media, as well as personal stories and anecdotes Quotes, data-driven figures, and suggestions for deeper learning on all aspects of a positive and equitable vision of math education Both social commentary and a toolkit of solutions, this bold new book directly challenges the constructs that have historically dictated our perceptions of what makes someone a "math person". Only by dismantling those misplaced assumptions can we reform math education so it works for everyone. Because in truth, we are all math people.

Author : Olivier Houdé,Grégoire Borst
Publisher : Cambridge Handbooks in Psychol
Page : 727 pages
File Size : 42,8 Mb
Release : 2022-03-03
Category : Psychology
ISBN : 9781108423878

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The Cambridge Handbook of Cognitive Development by Olivier Houdé,Grégoire Borst Pdf

This handbook presents a cutting-edge overview of cognitive development, spanning methodology, key domain-based findings and applications.

Author : Wim Fias,Avishai Henik
Publisher : Academic Press
Page : 422 pages
File Size : 43,6 Mb
Release : 2021-05-28
Category : Medical
ISBN : 9780128174159

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Heterogeneous Contributions to Numerical Cognition by Wim Fias,Avishai Henik Pdf

Arithmetic disability stems from deficits in neurodevelopment, with great individual differences in development or function of an individual at neuroanatomical, neuropsychological, behavioral, and interactional levels. Heterogeneous Contributions to Numerical Cognition: Learning and Education in Mathematical Cognition examines research in mathematical education methods and their neurodevelopmental basis, focusing on the underlying neurodevelopmental features that must be taken into account when teaching and learning mathematics. Cognitive domains and functions such as executive functions, memory, attention, and language contribute to numerical cognition and are essential for its proper development. These lines of research and thinking in neuroscience are discussed in this book to further the understanding of the neurodevelopmental and cognitive basis of more complex forms of mathematics – and how to best teach them. By unravelling the basic building blocks of numerical thinking and the developmental basis of human capacity for arithmetic, this book and the discussions within are important for the achievement of a comprehensive understanding of numerical cognition, its brain basis, development, breakdown in brain-injured individuals, and failures to master mathematical skills. A novel innovative reference on the emerging field of numerical cognition and neurodevelopment underlying mathematical education Includes an overview of the multiple disciplines that comprise numerical cognition written by world-leading researchers in the numerical cognition and neurodevelopment fields Features an innovative organization with each section providing a general overview, developmental research, neurocognitive mechanisms, and discussion about relevant studies

Author : Lara Alcock
Publisher : Oxford University Press
Page : 270 pages
File Size : 41,8 Mb
Release : 2021-02-04
Category : Science
ISBN : 9780192581426

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How to Think About Abstract Algebra by Lara Alcock Pdf

How to Think about Abstract Algebra provides an engaging and readable introduction to its subject, which encompasses group theory and ring theory. Abstract Algebra is central in most undergraduate mathematics degrees, and it captures regularities that appear across diverse mathematical structures - many people find it beautiful for this reason. But its abstraction can make its central ideas hard to grasp, and even the best students might find that they can follow some of the reasoning without really understanding what it is all about. This book aims to solve that problem. It is not like other Abstract Algebra texts and is not a textbook containing standard content. Rather, it is designed to be read before starting an Abstract Algebra course, or as a companion text once a course has begun. It builds up key information on five topics: binary operations, groups, quotient groups, isomorphisms and homomorphisms, and rings. It provides numerous examples, tables and diagrams, and its explanations are informed by research in mathematics education. The book also provides study advice focused on the skills that students need in order to learn successfully in their own Abstract Algebra courses. It explains how to interact productively with axioms, definitions, theorems and proofs, and how research in psychology should inform our beliefs about effective learning.

Author : Mircea Pitici
Publisher : Princeton University Press
Page : 304 pages
File Size : 49,8 Mb
Release : 2019-11-05
Category : Mathematics
ISBN : 9780691197944

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The Best Writing on Mathematics 2019 by Mircea Pitici Pdf

The year's finest mathematical writing from around the world This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2019 makes available to a wide audience many articles not easily found anywhere else—and you don't need to be a mathematician to enjoy them. These essays delve into the history, philosophy, teaching, and everyday aspects of math, offering surprising insights into its nature, meaning, and practice—and taking readers behind the scenes of today's hottest mathematical debates. In this volume, Moon Duchin explains how geometric-statistical methods can be used to combat gerrymandering, Jeremy Avigad illustrates the growing use of computation in making and verifying mathematical hypotheses, and Kokichi Sugihara describes how to construct geometrical objects with unusual visual properties. In other essays, Neil Sloane presents some recent additions to the vast database of integer sequences he has catalogued, and Alessandro Di Bucchianico and his colleagues highlight how mathematical methods have been successfully applied to big-data problems. And there's much, much more. In addition to presenting the year's most memorable math writing, this must-have anthology includes an introduction by the editor and a bibliography of other notable writings on mathematics. This is a must-read for anyone interested in where math has taken us—and where it is headed.

Author : Camilla Gilmore,Silke M. Göbel,Matthew Inglis
Publisher : Routledge
Page : 248 pages
File Size : 50,5 Mb
Release : 2018-06-13
Category : Psychology
ISBN : 9781317410102

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An Introduction to Mathematical Cognition by Camilla Gilmore,Silke M. Göbel,Matthew Inglis Pdf

The last decade has seen a rapid growth in our understanding of the cognitive systems that underlie mathematical learning and performance, and an increased recognition of the importance of this topic. This book showcases international research on the most important cognitive issues that affect mathematical performance across a wide age range, from early childhood to adulthood. The book considers the foundational competencies of nonsymbolic and symbolic number processing before discussing arithmetic, conceptual understanding, individual differences and dyscalculia, algebra, number systems, reasoning and higher-level mathematics such as formal proof. Drawing on diverse methodology from behavioural experiments to brain imaging, each chapter discusses key theories and empirical findings and introduces key tasks used by researchers. The final chapter discusses challenges facing the future development of the field of mathematical cognition and reviews a set of open questions that mathematical cognition researchers should address to move the field forward. This book is ideal for undergraduate or graduate students of psychology, education, cognitive sciences, cognitive neuroscience and other academic and clinical audiences including mathematics educators and educational psychologists.

Author : Lorna Uden,Dario Liberona,Galo Sanchez,Sara Rodríguez-González
Publisher : Springer
Page : 488 pages
File Size : 48,9 Mb
Release : 2019-05-27
Category : Education
ISBN : 9783030207984

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Learning Technology for Education Challenges by Lorna Uden,Dario Liberona,Galo Sanchez,Sara Rodríguez-González Pdf

This book constitutes the refereed proceedings of the 8th International Workshop on Learning Technology for Education Challenges, LTEC 2019, held in Zamora, Spain, in July 2019. The 41 revised full papers presented were carefully reviewed and selected from 83 submissions. The papers are organized in the following topical sections: learning technolgies; learning tools and environment; e-learning and MOOCs; learning practices; social media learning tools; machine learning and evaluation support programs. LTEC 2019 examines how these technologies and pedagogical advances can be used to change the way teachers teach and students learn, while giving special emphasis to the pedagogically effective ways we can harness these new technologies in education.

Author : John D. McNeil
Publisher : John Wiley & Sons
Page : 354 pages
File Size : 48,6 Mb
Release : 2014-11-17
Category : Education
ISBN : 9781118916513

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Contemporary Curriculum by John D. McNeil Pdf

The Eighth Edition of Contemporary Curriculum: In Thought and Action prepares readers to participate in the discussion of curriculum control and other matters important to K-12 and university educators. The text highlights major philosophies and principles, examines conflicting conceptions of curriculum, and provides the intellectual and technical tools educators and administrators need for constructing and implementing curriculum.

Author : Johan van Benthem
Publisher : MIT Press
Page : 390 pages
File Size : 42,5 Mb
Release : 1995
Category : Language Arts & Disciplines
ISBN : 0262720248

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Language in Action by Johan van Benthem Pdf

Language in Action demonstrates the viability of mathematical research into the foundations of categorial grammar, a topic at the border between logic and linguistics. Since its initial publication it has become the classic work in the foundations of categorial grammar. A new introduction to this paperback edition updates the open research problems and records relevant results through pointers to the literature. Van Benthem presents the categorial processing of syntax and semantics as a central component in a more general dynamic logic of information flow, in tune with computational developments in artificial intelligence and cognitive science. Using the paradigm of categorial grammar, he describes the substructural logics driving the dynamics of natural language syntax and semantics. This is a general type-theoretic approach that lends itself easily to proof-theoretic and semantic studies in tandem with standard logic. The emphasis is on a broad landscape of substructural categorial logics and their proof-theoretical and semantic peculiarities. This provides a systematic theory for natural language understanding, admitting of significant mathematical results. Moreover, the theory makes possible dynamic interpretations that view natural languages as programming formalisms for various cognitive activities.

Author : Barry J. Zimmerman,Dale H. Schunk
Publisher : Routledge
Page : 527 pages
File Size : 46,9 Mb
Release : 2014-08-13
Category : Education
ISBN : 9781317560418

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Educational Psychology by Barry J. Zimmerman,Dale H. Schunk Pdf

Educational Psychology: A Century of Contributions--the first comprehensive book-length treatment of this topic--looks at the historic contributions of 16 leading psychologists, as well as others, who influenced the field of educational psychology from its philosophical moorings in the late 19th century to its current scientific status at the dawn of the 21st. It presents information regarding these individuals' ideas and scientific discoveries, along with a sense of the historical context in which they lived. The book is divided into three sections that correspond to three eras in the history of the discipline: *the founding period (1880s to 1920); *the rise to prominence period (1920 to1960); and *the modern period (1960 to the present). Each section begins with an overview chapter describing the period in terms of key social, political, and historical events affecting educational theory, research, and practice. In addition, the overview chapters discuss major theoretical, methodological, and instructional contributions of the period and how they changed the course of educational psychology. The biographical chapters describe the scholar's major contribution in terms of theory, research, and practice and his or her legacy and impact. These descriptions portray these individuals as real human beings responding to historical events and social influences of their time in personal and collective ways that changed the nature and direction of the field. Educational Psychology: A Century of Contributions is a cohesive collection appropriate for graduate and advanced undergraduate students in educational psychology.

Author : Arihant Experts
Publisher : Arihant Publications India limited
Page : 616 pages
File Size : 49,9 Mb
Release : 2020-01-02
Category : Electronic
ISBN : 9789324195043

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CTET Success Master Social Science/Studies Paper-2 for Class 6 to 8 2020 by Arihant Experts Pdf

Throughout the world, teaching is looked at as one of the most respected and noble profession a person could have. A great teacher not only shows the right path that a student should follow but also prepares the human resources for the further development of the nation. Among various exams CTET is the most popular teaching exam in the country. Central Teaching Eligibility Test (CTET) is a national level test conducted by CBSE twice a year to recruit the eligible candidates as teacher. The exam is conducted into 2 papers: Paper 1 for class 1-5 and Paper 2 for class 6-8. Any candidate who is interested to become a teacher for classes 6 to 8 then they have to appear for both the papers. The new the edition of Study Guide ‘Success Master CTET Social Science/ Studies Paper – II’ has been prepared completely on the latest exam pattern. The book has been divided into 5 key sections and further divided into chapters providing the focused study material. After covering theoretical part this book also concentrates on the practice part, it provides Previous Years’ Solved Paper, 2 practice sets and more than 3000 MCQs for thorough practice. Ample numbers of questions have been given which are covered in a Chapterwise manner that allows candidates to understand the trend of the questions as well as the exam. This book will prove to be highly useful for the CTET Paper 2 exam as it will help in achieving the good rank in the exam. TABLE OF CONTENT Solved Paper 2019 (December), Solved Paper 2019 (July), Solved Paper 2018 (December), Solved Paper 2016 (September), Child Development and Pedagogy, English Language and Pedagogy, Hindi Bhasha evm Shiksha Shastra, Social Science/ Studies Pedagogy, Pedagogy, Practice Sets (1-2).

Author : Lee C. Deighton
Publisher : Unknown
Page : 616 pages
File Size : 52,8 Mb
Release : 1971
Category : Education
ISBN : UOM:39076001051791

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The Encyclopedia of Education by Lee C. Deighton Pdf

Author : EduGorilla Prep Experts
Publisher : EduGorilla Community Pvt. Ltd.
Page : 212 pages
File Size : 51,8 Mb
Release : 2023-10-01
Category : Education
ISBN : 9789355569417

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West Bengal TET Paper - II (Social Studies) Exam Book 2023 (English Edition) | Teacher Eligibility Test | 10 Practice Tests (1800 Solved MCQs) by EduGorilla Prep Experts Pdf

• Best Selling Book in English Edition for West Bengal TET Paper - II (Social Studies) Exam 2023 with objective-type questions as per the latest syllabus. • West Bengal TET Paper - II Preparation Kit comes with 10 Practice Tests with the best quality content. • Increase your chances of selection by 16X. •West Bengal TET Paper - II Exam Prep Kit comes with well-structured and 100% detailed solutions for all the questions. • Clear exam with good grades using thoroughly Researched Content by experts.