Visible Thinking in the K–8 Mathematics Classroom

Visible Thinking in the K–8 Mathematics Classroom

Author: Ted H. Hull

Publisher: Corwin Press

Published: 2011-01-21

Total Pages: 185

ISBN-13: 1452269408

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"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.


Making Thinking Visible

Making Thinking Visible

Author: Ron Ritchhart

Publisher: John Wiley & Sons

Published: 2011-05-03

Total Pages: 325

ISBN-13: 047091551X

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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.


Visible Learning for Mathematics, Grades K-12

Visible Learning for Mathematics, Grades K-12

Author: John Hattie

Publisher: Corwin Press

Published: 2016-09-15

Total Pages: 209

ISBN-13: 1506362958

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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.


Building Thinking Classrooms in Mathematics, Grades K-12

Building Thinking Classrooms in Mathematics, Grades K-12

Author: Peter Liljedahl

Publisher: Corwin Press

Published: 2020-09-28

Total Pages: 454

ISBN-13: 1544374844

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A thinking student is an engaged student Teachers often find it difficult to implement lessons that help students go beyond rote memorization and repetitive calculations. In fact, institutional norms and habits that permeate all classrooms can actually be enabling "non-thinking" student behavior. Sparked by observing teachers struggle to implement rich mathematics tasks to engage students in deep thinking, Peter Liljedahl has translated his 15 years of research into this practical guide on how to move toward a thinking classroom. Building Thinking Classrooms in Mathematics, Grades K–12 helps teachers implement 14 optimal practices for thinking that create an ideal setting for deep mathematics learning to occur. This guide Provides the what, why, and how of each practice and answers teachers’ most frequently asked questions Includes firsthand accounts of how these practices foster thinking through teacher and student interviews and student work samples Offers a plethora of macro moves, micro moves, and rich tasks to get started Organizes the 14 practices into four toolkits that can be implemented in order and built on throughout the year When combined, these unique research-based practices create the optimal conditions for learner-centered, student-owned deep mathematical thinking and learning, and have the power to transform mathematics classrooms like never before.


The Power of Making Thinking Visible

The Power of Making Thinking Visible

Author: Ron Ritchhart

Publisher: John Wiley & Sons

Published: 2020-05-19

Total Pages: 279

ISBN-13: 1119626048

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The long-awaited follow-up to Making Thinking Visible, provides new thinking routines, original research, and unique global case studies Visible Thinking—a research-based approach developed at Harvard’s Project Zero – prompts and promotes students’ thinking. This approach has been shown to positively impact student engagement, learning, and development as thinkers. Visible Thinking involves using thinking routines, documentation, and effective questioning and listening techniques to enhance learning and collaboration in any learning environment. The Power of Making Thinking Visible explains how educators can effectively use thinking routines and other tools to engage and empower students as learners and transform classrooms into places of deep learning. Building on the success of the bestselling Making Thinking Visible, this highly-anticipated new book expands the work of the original by providing 18 new thinking routines based on new research and work with teachers and students around the world. Original content explains how to use thinking routines to maximum effect in the classroom, engage students exploration of big ideas, link thinking routines to formative assessment, and more. Providing new research, new global case studies, and new practices, this book: Focuses on the power that thinking routines can bring to learning Provides practical insights on using thinking routines to facilitate student engagement Highlights the most effective techniques for using thinking routines in the classroom Identifies the skillsets and mindsets needed to truly make thinking visible Features actionable classroom strategies that can be applied across grade levels and content areas Written by researchers from Harvard’s Project Zero, The Power of Making Thinking Visible: Using Routines to Engage and Empower Learners is an indispensable resource for K-12 educators and curriculum designers, higher education instructional designers and educators, and professional learning course developers.


Number Sense Routines

Number Sense Routines

Author: Jessica F. Shumway

Publisher: Stenhouse Publishers

Published: 2011

Total Pages: 194

ISBN-13: 1571107908

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Just as athletes stretch their muscles before every game and musicians play scales to keep their technique in tune, mathematical thinkers and problem solvers can benefit from daily warm-up exercises. Jessica Shumway has developed a series of routines designed to help young students internalize and deepen their facility with numbers. The daily use of these quick five-, ten-, or fifteen-minute experiences at the beginning of math class will help build students' number sense. Students with strong number sense understand numbers, ways to represent numbers, relationships among numbers, and number systems. They make reasonable estimates, compute fluently, use reasoning strategies (e.g., relate operations, such as addition and subtraction, to each other), and use visual models based on their number sense to solve problems. Students who never develop strong number sense will struggle with nearly all mathematical strands, from measurement and geometry to data and equations. In Number Sense Routines, Jessica shows that number sense can be taught to all students. Dozens of classroom examples -- including conversations among students engaging in number sense routines -- illustrate how the routines work, how children's number sense develops, and how to implement responsive routines. Additionally, teachers will gain a deeper understanding of the underlying math -- the big ideas, skills, and strategies children learn as they develop numerical literacy.


Singapore Math Challenge, Grades 2 - 5

Singapore Math Challenge, Grades 2 - 5

Author: Frank Schaffer Publications

Publisher: Carson-Dellosa Publishing

Published: 2013-02-01

Total Pages: 354

ISBN-13: 1623990726

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Get ready to take the Math Challenge! Singapore Math Challenge will provide second grade students with skill-building practice based on the leading math program in the world, Singapore Math! Common Core Standards accelerate math expectations for all students, creating a need for challenging supplementary math practice. Singapore Math Challenge is the ideal solution, with problems, puzzles, and brainteasers that strengthen mathematical thinking. Step-by-step strategies are clearly explained for solving problems at varied levels of difficulty. A complete, worked solution is also provided for each problem. -- Singapore Math Challenge includes the tools and practice needed to provide a strong mathematical foundation and ongoing success for your students. The Common Core State Standards cite Singapore math standards as worldwide benchmarks for excellence in mathematics.


Visual Thinking in Mathematics

Visual Thinking in Mathematics

Author: Marcus Giaquinto

Publisher: Oxford University Press

Published: 2007-07-05

Total Pages: 298

ISBN-13: 0199285942

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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

Published: 2011-01-21

Total Pages: 185

ISBN-13: 1412992052

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The key to students' success in math lies in a way of teaching that provides clear evidence of how students are thinking about problems and builds on that thinking to take them to a deeper level of understanding. Seasoned math educators Ted Hull, Don Balka, and Ruth Harbin Miles offer teachers a sequential and developmental plan for integrating visual thinking into current classroom practices, and gradually, but steadily, initiating successful instructional changes in mathematics. Their new book provides teachers with numerous sample problems and classroom scenarios, showing successful teacher interventions at work, and offers guidance on how teachers can adapt traditional problems to promote visible thinking in their own classrooms.


Proofs Without Words: Exercises in Visual Thinking

Proofs Without Words: Exercises in Visual Thinking

Author: Roger B. Nelsen

Publisher: American Mathematical Soc.

Published: 2020-02-18

Total Pages: 164

ISBN-13: 1470451867

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Proofs without words are generally 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.