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Visual Thinking in Mathematics

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Release : 2007-07-05
Genre : Mathematics
Kind : eBook
Book Rating : 942/5 ( reviews)

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Book Synopsis Visual Thinking in Mathematics by : Marcus Giaquinto

Download or read book Visual Thinking in Mathematics written by Marcus Giaquinto. This book was released on 2007-07-05. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Visual Thinking in Mathematics

Download Visual Thinking in Mathematics PDF Online Free

Author :
Release : 2007-07-05
Genre : Philosophy
Kind : eBook
Book Rating : 61X/5 ( reviews)

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Book Synopsis Visual Thinking in Mathematics by : Marcus Giaquinto

Download or read book Visual Thinking in Mathematics written by Marcus Giaquinto. This book was released on 2007-07-05. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Visible Thinking in the K–8 Mathematics Classroom

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Author :
Release : 2011-01-21
Genre : Education
Kind : eBook
Book Rating : 408/5 ( reviews)

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Book Synopsis Visible Thinking in the K–8 Mathematics Classroom by : Ted H. Hull

Download or read book Visible Thinking in the K–8 Mathematics Classroom written by Ted H. Hull. This book was released on 2011-01-21. Available in PDF, EPUB and Kindle. Book excerpt: "This book is a crucial tool for meeting NCTM mathematical content and process standards. Through the useful problems and strategies presented within, teachers will definitely know how well their students will comprehend. If comprehension is an issue in your class, this book is a must have!" —Therese Gessler Rodammer, Math Coach Thomas W. Dixon Elementary School, Staunton, VA Seeing is believing with this interactive approach to math instruction Do you ever wish your students could read each other′s thoughts? Now they can—and so can you! Veteran mathematics educators Ted Hull, Don Balka, and Ruth Harbin Miles explain why making students′ thought processes visible is the key to effective mathematics instruction. Their newest book contains numerous grade-specific sample problems and instructional strategies for teaching essential concepts such as number sense, fractions, and estimation. Among the many benefits of visible thinking are: Interactive student-to-student learning Increased class participation Development of metacognitive thinking and problem-solving skills Helpful features include vignettes, relevant word problems, classroom scenarios, sample problems, lesson adaptations, and easy-to-follow examples of each strategy in action. The authors also explain how students can demonstrate their thinking using calculators and online tools. The final chapter outlines steps math leaders can take to implement visible thinking and maximize mathematics comprehension for all students.

Visible Learning for Mathematics, Grades K-12

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Release : 2016-09-15
Genre : Education
Kind : eBook
Book Rating : 958/5 ( reviews)

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Book Synopsis Visible Learning for Mathematics, Grades K-12 by : John Hattie

Download or read book Visible Learning for Mathematics, Grades K-12 written by John Hattie. This book was released on 2016-09-15. Available in PDF, EPUB and Kindle. Book excerpt: Selected as the Michigan Council of Teachers of Mathematics winter book club book! Rich tasks, collaborative work, number talks, problem-based learning, direct instruction...with so many possible approaches, how do we know which ones work the best? In Visible Learning for Mathematics, six acclaimed educators assert it’s not about which one—it’s about when—and show you how to design high-impact instruction so all students demonstrate more than a year’s worth of mathematics learning for a year spent in school. That’s a high bar, but with the amazing K-12 framework here, you choose the right approach at the right time, depending upon where learners are within three phases of learning: surface, deep, and transfer. This results in "visible" learning because the effect is tangible. The framework is forged out of current research in mathematics combined with John Hattie’s synthesis of more than 15 years of education research involving 300 million students. Chapter by chapter, and equipped with video clips, planning tools, rubrics, and templates, you get the inside track on which instructional strategies to use at each phase of the learning cycle: Surface learning phase: When—through carefully constructed experiences—students explore new concepts and make connections to procedural skills and vocabulary that give shape to developing conceptual understandings. Deep learning phase: When—through the solving of rich high-cognitive tasks and rigorous discussion—students make connections among conceptual ideas, form mathematical generalizations, and apply and practice procedural skills with fluency. Transfer phase: When students can independently think through more complex mathematics, and can plan, investigate, and elaborate as they apply what they know to new mathematical situations. To equip students for higher-level mathematics learning, we have to be clear about where students are, where they need to go, and what it looks like when they get there. Visible Learning for Math brings about powerful, precision teaching for K-12 through intentionally designed guided, collaborative, and independent learning.

Visual Math

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Author :
Release : 2002
Genre : Mathematics
Kind : eBook
Book Rating : 044/5 ( reviews)

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Book Synopsis Visual Math by : Jessika Sobanski

Download or read book Visual Math written by Jessika Sobanski. This book was released on 2002. Available in PDF, EPUB and Kindle. Book excerpt: Visual Math has been designed to allow learners to "see" why math makes sense. By combining logical math concepts with pictures, previously unclear images will fade and math will suddenly click for you. Pictures, graphs, and diagrams help you understand math questions in the areas of number concepts and properties, fractions and decimals, ratios and proportions, percents, algebra, geometry, and much more. Designed especially for students who have difficulty with conventional math rules, this book gives you step-by step instructions with pictures to help you solve math problems.

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