Visual Thinking in Mathematics

Visual Thinking in Mathematics
Author: Marcus Giaquinto
Publisher: Oxford University Press
Total Pages: 298
Release: 2007-07-05
Genre: Mathematics
ISBN: 0199285942

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.

Visible Thinking in the K–8 Mathematics Classroom

Visible Thinking in the K–8 Mathematics Classroom
Author: Ted H. Hull
Publisher: Corwin Press
Total Pages: 185
Release: 2011-01-21
Genre: Education
ISBN: 1452269408

"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.

Proofs Without Words

Proofs Without Words
Author: Roger B. Nelsen
Publisher: MAA
Total Pages: 166
Release: 1993
Genre: Logic, Symbolic and mathematical
ISBN: 9780883857007

Making Thinking Visible

Making Thinking Visible
Author: Ron Ritchhart
Publisher: John Wiley & Sons
Total Pages: 325
Release: 2011-05-03
Genre: Education
ISBN: 047091551X

A proven program for enhancing students' thinking and comprehension abilities Visible Thinking is a research-based approach to teaching thinking, begun at Harvard's Project Zero, that develops students' thinking dispositions, while at the same time deepening their understanding of the topics they study. Rather than a set of fixed lessons, Visible Thinking is a varied collection of practices, including thinking routines?small sets of questions or a short sequence of steps?as well as the documentation of student thinking. Using this process thinking becomes visible as the students' different viewpoints are expressed, documented, discussed and reflected upon. Helps direct student thinking and structure classroom discussion Can be applied with students at all grade levels and in all content areas Includes easy-to-implement classroom strategies The book also comes with a DVD of video clips featuring Visible Thinking in practice in different classrooms.

Math Made Visual

Math Made Visual
Author: Claudi Alsina
Publisher: MAA
Total Pages: 202
Release: 2006-07-06
Genre: Education
ISBN: 9780883857465

The object of this book is to show how visualization techniques may be employed to produce pictures that have interest for the creation, communication and teaching of mathematics. Mathematical drawings related to proofs have been produced since antiquity in China, Arabia, Greece and India but only in the last thirty years has there been a growing interest in so-called 'proofs without words.' In this book the authors show that behind most of the pictures 'proving' mathematical relations are some well-understood methods. The first part of the book consists of twenty short chapters, each one describing a method to visualize some mathematical idea (a proof, a concept, an operation,...) and several applications to concrete cases. Following this the book examines general pedagogical considerations concerning the development of visual thinking, practical approaches for making visualizations in the classroom and a discussion of the role that hands-on material plays in this process.

Opt Art

Opt Art
Author: Robert Bosch (mathématicien)
Publisher: Princeton University Press
Total Pages: 200
Release: 2019-11-12
Genre: Art
ISBN: 0691164061

Bosch provides a lively and accessible introduction to the geometric, algebraic, and algorithmic foundations of optimization. He presents classical applications, such as the legendary Traveling Salesman Problem, and shows how to adapt them to make optimization art--opt art. art.

Proofs Without Words II

Proofs Without Words II
Author: Roger B. Nelsen
Publisher: American Mathematical Soc.
Total Pages: 130
Release: 2020-02-22
Genre: Mathematics
ISBN: 1470451891

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.

Mathematical Mindsets

Mathematical Mindsets
Author: Jo Boaler
Publisher: John Wiley & Sons
Total Pages: 320
Release: 2015-10-12
Genre: Education
ISBN: 1118415531

Banish math anxiety and give students of all ages a clear roadmap to success Mathematical Mindsets provides practical strategies and activities to help teachers and parents show all children, even those who are convinced that they are bad at math, that they can enjoy and succeed in math. Jo Boaler—Stanford researcher, professor of math education, and expert on math learning—has studied why students don't like math and often fail in math classes. She's followed thousands of students through middle and high schools to study how they learn and to find the most effective ways to unleash the math potential in all students. There is a clear gap between what research has shown to work in teaching math and what happens in schools and at home. This book bridges that gap by turning research findings into practical activities and advice. Boaler translates Carol Dweck's concept of 'mindset' into math teaching and parenting strategies, showing how students can go from self-doubt to strong self-confidence, which is so important to math learning. Boaler reveals the steps that must be taken by schools and parents to improve math education for all. Mathematical Mindsets: Explains how the brain processes mathematics learning Reveals how to turn mistakes and struggles into valuable learning experiences Provides examples of rich mathematical activities to replace rote learning Explains ways to give students a positive math mindset Gives examples of how assessment and grading policies need to change to support real understanding Scores of students hate and fear math, so they end up leaving school without an understanding of basic mathematical concepts. Their evasion and departure hinders math-related pathways and STEM career opportunities. Research has shown very clear methods to change this phenomena, but the information has been confined to research journals—until now. Mathematical Mindsets provides a proven, practical roadmap to mathematics success for any student at any age.

Mindset Mathematics

Mindset Mathematics
Author: Jo Boaler
Publisher: John Wiley & Sons
Total Pages: 288
Release: 2017-08-28
Genre: Education
ISBN: 1119358809

Engage students in mathematics using growth mindset techniques The most challenging parts of teaching mathematics are engaging students and helping them understand the connections between mathematics concepts. In this volume, you'll find a collection of low floor, high ceiling tasks that will help you do just that, by looking at the big ideas at the first-grade level through visualization, play, and investigation. During their work with tens of thousands of teachers, authors Jo Boaler, Jen Munson, and Cathy Williams heard the same message—that they want to incorporate more brain science into their math instruction, but they need guidance in the techniques that work best to get across the concepts they needed to teach. So the authors designed Mindset Mathematics around the principle of active student engagement, with tasks that reflect the latest brain science on learning. Open, creative, and visual math tasks have been shown to improve student test scores, and more importantly change their relationship with mathematics and start believing in their own potential. The tasks in Mindset Mathematics reflect the lessons from brain science that: There is no such thing as a math person - anyone can learn mathematics to high levels. Mistakes, struggle and challenge are the most important times for brain growth. Speed is unimportant in mathematics. Mathematics is a visual and beautiful subject, and our brains want to think visually about mathematics. With engaging questions, open-ended tasks, and four-color visuals that will help kids get excited about mathematics, Mindset Mathematics is organized around nine big ideas which emphasize the connections within the Common Core State Standards (CCSS) and can be used with any current curriculum.

Visual Thinking for Design

Visual Thinking for Design
Author: Colin Ware
Publisher: Elsevier
Total Pages: 210
Release: 2010-07-27
Genre: Computers
ISBN: 0080558410

Visual Thinking brings the science of perception to the art of design. Designers increasingly need to present information in ways that aid their audience's thinking process. Fortunately, results from the relatively new science of human visual perception provide valuable guidance. In this book, Colin Ware takes what we now know about perception, cognition, and attention and transforms it into concrete advice that designers can directly apply. He demonstrates how designs can be considered as tools for cognition – extensions of the viewer's brain in much the same way that a hammer is an extension of the user's hand. The book includes hundreds of examples, many in the form of integrated text and full-color diagrams. Experienced professional designers and students alike will learn how to maximize the power of the information tools they design for the people who use them. - Presents visual thinking as a complex process that can be supported in every stage using specific design techniques - Provides practical, task-oriented information for designers and software developers charged with design responsibilities - Includes hundreds of examples, many in the form of integrated text and full-color diagrams - Steeped in the principles of "active vision, which views graphic designs as cognitive tools