Visual Thinking In Mathematics
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Visual Thinking In Mathematics
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Author : Marcus Giaquinto
language : en
Publisher: Clarendon Press
Release Date : 2007-07-05
Visual Thinking In Mathematics written by Marcus Giaquinto and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-05 with Philosophy categories.
Visual thinking - visual imagination or perception of diagrams and symbol arrays, and mental operations on them - is omnipresent in mathematics. Is this visual thinking merely a psychological aid, facilitating grasp of what is gathered by other means? Or does it also have epistemological functions, as a means of discovery, understanding, and even proof? By examining the many kinds of visual representation in mathematics and the diverse ways in which they are used, Marcus Giaquinto argues that visual thinking in mathematics is rarely just a superfluous aid; it usually has epistemological value, often as a means of discovery. Drawing from philosophical work on the nature of concepts and from empirical studies of visual perception, mental imagery, and numerical cognition, Giaquinto explores a major source of our grasp of mathematics, using examples from basic geometry, arithmetic, algebra, and real analysis. He shows how we can discern abstract general truths by means of specific images, how synthetic a priori knowledge is possible, and how visual means can help us grasp abstract structures. Visual Thinking in Mathematics reopens the investigation of earlier thinkers from Plato to Kant into the nature and epistemology of an individual's basic mathematical beliefs and abilities, in the new light shed by the maturing cognitive sciences. Clear and concise throughout, it will appeal to scholars and students of philosophy, mathematics, and psychology, as well as anyone with an interest in mathematical thinking.
Visual Thinking In Mathematics
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Author : Marcus Giaquinto
language : en
Publisher: Clarendon Press
Release Date : 2007-07-05
Visual Thinking In Mathematics written by Marcus Giaquinto and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-05 with Philosophy categories.
Visual thinking - visual imagination or perception of diagrams and symbol arrays, and mental operations on them - is omnipresent in mathematics. Is this visual thinking merely a psychological aid, facilitating grasp of what is gathered by other means? Or does it also have epistemological functions, as a means of discovery, understanding, and even proof? By examining the many kinds of visual representation in mathematics and the diverse ways in which they are used, Marcus Giaquintoargues that visual thinking in mathematics is rarely just a superfluous aid; it usually has epistemological value, often as a means of discovery. Drawing from philosophical work on the nature of concepts and from empirical studies of visual perception, mental imagery, and numerical cognition,Giaquinto explores a major source of our grasp of mathematics, using examples from basic geometry, arithmetic, algebra, and real analysis. He shows how we can discern abstract general truths by means of specific images, how synthetic a priori knowledge is possible, and how visual means can help us grasp abstract structures.Visual Thinking in Mathematics reopens the investigation of earlier thinkers from Plato to Kant into the nature and epistemology of an individual's basic mathematical beliefs and abilities, in the new light shed by the maturing cognitive sciences. Clear and concise throughout, it will appeal to scholars and students of philosophy, mathematics, and psychology, as well as anyone with an interest in mathematical thinking.
Visual Thinking In Mathematics
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Author : M. Giaquinto
language : en
Publisher:
Release Date : 2007
Visual Thinking In Mathematics written by M. Giaquinto and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Arithmetic categories.
Drawing from philosophical work on the nature of concepts and from empirical studies of visual perception, mental imagery, and numerical cognition, Giaquinto explores a major source of our grasp of mathematics, using examples from basic geometry, arithmetic, algebra, and real analysis.
Proofs Without Words
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Author : Roger B. Nelsen
language : en
Publisher:
Release Date : 2018
Proofs Without Words written by Roger B. Nelsen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Mathematics categories.
Shape Understanding System
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Author : Zbigniew Les
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-11
Shape Understanding System written by Zbigniew Les 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 2008-01-11 with Mathematics categories.
This book presents the results of research into one of the most complex and difficult areas - research into thinking and understanding. The research was carried out at the newly founded Queen Jadwiga Research Institute of Understanding and is focused on the problem of visual understanding and visual thinking. The authors believe this is the first book to attempt to investigate the complexity of visual thinking problems in the context of building the thinking machine.
Using Visual Thinking Strategies To Improve Mathematics Instruction
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Author : Teri Yvonne Campos
language : en
Publisher:
Release Date : 2018
Using Visual Thinking Strategies To Improve Mathematics Instruction written by Teri Yvonne Campos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Electronic dissertations categories.
The purpose of the study was to explore the use of Visual Thinking Strategies as it applied to mathematics instruction for teachers in a small, urban elementary school containing grades 1-6 in a large Midwestern metropolis. This study was implemented to address the problem of low math scores in urban schools that have students with low socioeconomic status compounded by the way math concepts are generally taught. This study was qualitative and followed the heuristic tradition of research. The unit of analysis was the experiences of teachers with VTS, as we explored their implementation of the visual thinking strategies in the classroom gathered from open-ended surveys, observations, informal reflective conversations, in-depth interviews, and reflective journals analyzed during the illumination step of the heuristic process in a focus group discussion. The central question that guided the study was, how can Visual Thinking Strategies (VTS) improve mathematics instruction? There were three contributing parts explored, teacher “moves,” restatements of evidence regarding explicit teaching of mathematical concepts, and academic vocabulary. Five teachers in the building became co-researchers from different grade levels, backgrounds, ages, and years of teaching experience, and who were similar in growth mindsets and established discourse procedures in their classroom. Initial engagement started the study with surveying knowledge and interest of the teachers in VTS specifically, and math in general. Then a schedule was devised to conduct observations, including introducing the VTS protocol expectations and methods to display the art and math images. Immersion in facilitating lessons in six classrooms first with art images and then math was reflected in conversations, journals, interviews, and living the phenomena of VTS for three months. Incubation for each participant brought personal clarity and codebooks for me. Guided by the research questions and theoretical framework of the study, the final themes I gleaned from the process include Cognitive Operations, Teacher Moves, Discourse with Vocabulary, and Visual Learning. The interpretive codes of cognition, facilitation, talking, and learning visually came from descriptive coding of the data. Illumination occurred in the focus group discussion when the participants answered the research questions. The explication step revealed that VTS can be used to improve math instruction with collaboration to create images, such as, graphs. Students were taught the visual thinking strategies using pictures and photographs to enable them to think creatively and critically. Those same strategies helped students make sense of bar, line, circle, and picture graphs. They were able to build deeper understanding as a community from diverse individual input when teachers got students engaged and confident. Facilitators restated evidence while bumping up vocabulary from student language to make the math concepts more clear.
Proofs Without Words Iii
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Author : Roger B. Nelsen
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-12-31
Proofs Without Words Iii written by Roger B. Nelsen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-31 with Mathematics categories.
Proofs without words (PWWs) are figures or diagrams that help the reader see why a particular mathematical statement is true, and how one might begin to formally prove it true. PWWs are not new, many date back to classical Greece, ancient China, and medieval Europe and the Middle East. PWWs have been regular features of the MAA journals Mathematics Magazine and The College Mathematics Journal for many years, and the MAA published the collections of PWWs Proofs Without Words: Exercises in Visual Thinking in 1993 and Proofs Without Words II: More Exercises in Visual Thinking in 2000. This book is the third such collection of PWWs.
Proofs Without Words
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Author : Roger B Nelsen
language : en
Publisher:
Release Date : 1993-01-01
Proofs Without Words written by Roger B Nelsen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-01-01 with categories.
Proofs Without Words Ii
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Author : Roger B. Nelsen
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-02-22
Proofs Without Words Ii written by Roger B. Nelsen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-22 with Mathematics categories.
Like its predecessor, Proofs without Words, this book is a collection of pictures or diagrams that help the reader see why a particular mathematical statement may be true and how one could begin to go about proving it. While in some proofs without words an equation or two may appear to help guide that process, the emphasis is clearly on providing visual clues to stimulate mathematical thought. The proofs in this collection are arranged by topic into five chapters: geometry and algebra; trigonometry, calculus and analytic geometry; inequalities; integer sums; and sequences and series. Teachers will find that many of the proofs in this collection are well suited for classroom discussion and for helping students to think visually in mathematics.
Proceedings Of The 4th Science And Mathematics International Conference Smic 2024
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Author : Tian Abdul Aziz
language : en
Publisher: Springer Nature
Release Date : 2024-12-26
Proceedings Of The 4th Science And Mathematics International Conference Smic 2024 written by Tian Abdul Aziz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-26 with Mathematics categories.
This is an Open Access publication. Welcome to the 4th Science and Mathematics International Conference (SMIC) 2024, which will be held in Jakarta, Indonesia, 23 to 24 September 2024. The theme of SMIC 2024 is “Connecting Sustainable World and Future Technologies: Opportunities and Challenges in Science, Mathematics, and Education”. SMIC 2024 aims to bring together researchers, academics, scientists, students, and practitioners to share and discuss theoretical and practical knowledge, new trends and application in the fields of Mathematics and Mathematics Education, Science and Science Education, Computer Science, and Statistics. SMIC 2024 is the fourth SMIC organized by the Faculty of Mathematics and Natural Sciences, Universitas Negeri Jakarta, after the huge success in SMIC 2018, SMIC 2020, and SMIC 2022 with more than 6 countries participants and resulting in an international reputable book as well as proceedings.