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Author : Leo John Brueckner
Publisher :
ISBN 13 :
Total Pages : 584 pages
Book Rating : 4.:/5 (33 download)
Download or read book Developing Mathematical Understandings in the Upper Grades written by Leo John Brueckner and published by . This book was released on 1957 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : David K. Pugalee
Publisher : Christopher-Gordon Pub
ISBN 13 : 9781929024865
Total Pages : 195 pages
Book Rating : 4.0/5 (248 download)
Download or read book Writing to Develop Mathematical Understanding written by David K. Pugalee and published by Christopher-Gordon Pub. This book was released on 2005-01-01 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt:
![Download Developing Mathematical Understandings in the Upper Grades. [By] L.J. Brueckner ... Foster E. Grossnickle ... John Reckzeh. [With Illustrations.]. PDF Online Free](https://books.google.com/books/content/images/frontcover/d-kQMwEACAAJ?fife=w200-h370)
Author : Leo John Brueckner
Publisher :
ISBN 13 :
Total Pages : 567 pages
Book Rating : 4.:/5 (558 download)
Download or read book Developing Mathematical Understandings in the Upper Grades. [By] L.J. Brueckner ... Foster E. Grossnickle ... John Reckzeh. [With Illustrations.]. written by Leo John Brueckner and published by . This book was released on 1957 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Leo John Brueckner
Publisher :
ISBN 13 :
Total Pages : 588 pages
Book Rating : 4.3/5 (91 download)
Download or read book Developing Mathematical Understandings in the Upper Grades written by Leo John Brueckner and published by . This book was released on 1957 with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Thomas J. Cooney
Publisher :
ISBN 13 : 9780873536233
Total Pages : 109 pages
Book Rating : 4.5/5 (362 download)
Download or read book Developing Essential Understanding of Functions for Teaching Mathematics in Grades 9-12 written by Thomas J. Cooney and published by . This book was released on 2010 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: Are sequences functions? Why can’t the popular “vertical line test” be applied in some cases to determine if a relation is a function? How does the idea of rate of change connect with simpler ideas about proportionality as well as more advanced topics in calculus? How much do you know… and how much do you need to know? Helping your high school students develop a robust understanding of functions requires that you understand mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about functions. It is organised around five big ideas, supported by multiple smaller, interconnected ideas-essential understandings. Taking you beyond a simple introduction to functions, this book will broaden and deepen your mathematical understanding of one of the most challenging topics for students and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls and dispel misconceptions. You will also learn to develop appropriate tasks, techniques and tools for assessing students’ understanding of the topic. Focus on the ideas that you need to understand thoroughly to teach confidently.
Author :
Publisher :
ISBN 13 :
Total Pages : 567 pages
Book Rating : 4.:/5 (299 download)
Download or read book Developing Mathematical Understanding written by and published by . This book was released on 1961 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Carne Barnett-Clarke
Publisher : National Council of Teachers of English
ISBN 13 : 9780873536301
Total Pages : 83 pages
Book Rating : 4.5/5 (363 download)
Download or read book Developing Essential Understanding of Rational Numbers for Teaching Mathematics in Grades 3/5 written by Carne Barnett-Clarke and published by National Council of Teachers of English. This book was released on 2010 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is the relationship between fractions and rational numbers? Can you explain why the product of two fractions between 0 and 1 is less than either factor? How are rational numbers related to irrational numbers, which your students will study in later grades? How much do you know… and how much do you need to know? Helping your upper elementary school students develop a robust understanding of rational numbers requires that you understand this mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about rational numbers. It is organised around four big ideas, supported by multiple smaller, interconnected ideas-essential understandings. Taking you beyond a simple introduction to rational numbers, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls and dispel misconceptions. You will also learn to develop appropriate tasks, techniques and tools for assessing students’ understanding of the topic. Focus on the ideas that you need to understand thoroughly to teach confidently.
Author : Barbara J. Dougherty
Publisher :
ISBN 13 : 9780873536295
Total Pages : 60 pages
Book Rating : 4.5/5 (362 download)
Download or read book Developing Essential Understanding of Number and Numeration for Teaching Mathematics in Prekindergarten--grade 2 written by Barbara J. Dougherty and published by . This book was released on 2010 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt: How do composing and decomposing numbers connect with the properties of addition? Focus on the ideas that you need to thoroughly understand in order to teach with confidence. The mathematical content of this book focuses on essential knowledge for teachers about numbers and number systems. It is organised around one big idea and supported by smaller, more specific, interconnected ideas (essential understandings). Gaining this understanding is essential because numbers and numeration are building blocks for other mathematical concepts and for thinking quantitatively about the real-world. Essential Understanding series topics include: Number and Numeration for Grades Pre-K-2 Addition and Subtraction for Grades Pre-K-2 Geometry for Grades Pre-K-2 Reasoning and Proof for Grades Pre-K-8 Multiplication and Division for Grades 3-5 Rational Numbers for Grades 3-5 Algebraic Ideas and Readiness for Grades 3-5 Geometric Shapes and Solids for Grades 3-5 Ratio, Proportion and Proportionality for Grades 6-8 Expressions and Equations for Grades 6-8 Measurement for Grades 6-8 Data Analysis and Statistics for Grades 6-8 Function for Grades 9-12 Geometric Relationships for Grades 9-12 Reasoning and Proof for Grades 9-12 Statistics for Grades 9-12
Author : Jennifer M. Bay-Williams
Publisher : Corwin
ISBN 13 : 1071818430
Total Pages : 265 pages
Book Rating : 4.0/5 (718 download)
Download or read book Figuring Out Fluency in Mathematics Teaching and Learning, Grades K-8 written by Jennifer M. Bay-Williams and published by Corwin. This book was released on 2021-03-02 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Because fluency practice is not a worksheet. Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. Real fluency involves reasoning and creativity, and it varies by the situation at hand. Figuring Out Fluency in Mathematics Teaching and Learning offers educators the inspiration to develop a deeper understanding of procedural fluency, along with a plethora of pragmatic tools for shifting classrooms toward a fluency approach. In a friendly and accessible style, this hands-on guide empowers educators to support students in acquiring the repertoire of reasoning strategies necessary to becoming versatile and nimble mathematical thinkers. It includes: "Seven Significant Strategies" to teach to students as they work toward procedural fluency. Activities, fluency routines, and games that encourage learning the efficiency, flexibility, and accuracy essential to real fluency. Reflection questions, connections to mathematical standards, and techniques for assessing all components of fluency. Suggestions for engaging families in understanding and supporting fluency. Fluency is more than a toolbox of strategies to choose from; it’s also a matter of equity and access for all learners. Give your students the knowledge and power to become confident mathematical thinkers.
Author : National Research Council
Publisher : National Academies Press
ISBN 13 : 0309131987
Total Pages : 53 pages
Book Rating : 4.3/5 (91 download)
Download or read book Helping Children Learn Mathematics written by National Research Council and published by National Academies Press. This book was released on 2002-07-31 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: Results from national and international assessments indicate that school children in the United States are not learning mathematics well enough. Many students cannot correctly apply computational algorithms to solve problems. Their understanding and use of decimals and fractions are especially weak. Indeed, helping all children succeed in mathematics is an imperative national goal. However, for our youth to succeed, we need to change how we're teaching this discipline. Helping Children Learn Mathematics provides comprehensive and reliable information that will guide efforts to improve school mathematics from pre-kindergarten through eighth grade. The authors explain the five strands of mathematical proficiency and discuss the major changes that need to be made in mathematics instruction, instructional materials, assessments, teacher education, and the broader educational system and answers some of the frequently asked questions when it comes to mathematics instruction. The book concludes by providing recommended actions for parents and caregivers, teachers, administrators, and policy makers, stressing the importance that everyone work together to ensure a mathematically literate society.
Author : Jessica F. Shumway
Publisher : Stenhouse Publishers
ISBN 13 : 1625310889
Total Pages : 152 pages
Book Rating : 4.6/5 (253 download)
Download or read book Number Sense Routines written by Jessica F. Shumway and published by Stenhouse Publishers. This book was released on 2018 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: Upper elementary teachers have a big job: to help students deepen their mathematical understanding and become more efficient mathematicians. Number Sense Routines: Developing Mathematical Understanding Every Day in Grades 3-5 is about tapping into every child's innate number sense and providing daily, connected experiences that are responsive to children's learning needs. Through familiar five-, ten-, or fifteen-minute warm-up routines, author Jessica Shumway offers both beginner and veteran teachers easy and effective ways to build and solidify students' number sense foundations. No matter how familiar the routine, Jessica infuses each with new joy, depth, and life. She reveals the careful thinking and planning that goes into each routine and provides detailed vignettes and dialogues of how they unfold in real classrooms. She gives teachers a clear view into her nuanced facilitation. Each routine becomes an exciting opportunity to understand where students are in their understanding and to help students articulate and extend their mathematical thinking. Not only will these routines help develop students' mathematical understanding as they move towards using standard algorithms, but teachers will learn to better recognize the big ideas that emerge in discussions, how to encourage important strategies based in number sense, and how to facilitate discussions on key mathematical concepts.
Author : Beth McCord Kobett
Publisher : Corwin Press
ISBN 13 : 1071841068
Total Pages : 348 pages
Book Rating : 4.0/5 (718 download)
Download or read book Classroom-Ready Rich Math Tasks, Grades 4-5 written by Beth McCord Kobett and published by Corwin Press. This book was released on 2021-04-14 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Detailed plans for helping elementary students experience deep mathematical learning Do you work tirelessly to make your math lessons meaningful, challenging, accessible, and engaging? Do you spend hours you don’t have searching for, adapting, and creating tasks to provide rich experiences for your students that supplement your mathematics curriculum? Help has arrived! Classroom Ready-Rich Math Tasks for Grades 4-5 details more than 50 research- and standards-aligned, high-cognitive-demand tasks that will have your students doing deep-problem-based learning. These ready-to-implement, engaging tasks connect skills, concepts and practices, while encouraging students to reason, problem-solve, discuss, explore multiple solution pathways, connect multiple representations, and justify their thinking. They help students monitor their own thinking and connect the mathematics they know to new situations. In other words, these tasks allow students to truly do mathematics! Written with a strengths-based lens and an attentiveness to all students, this guide includes: • Complete task-based lessons, referencing mathematics standards and practices, vocabulary, and materials • Downloadable planning tools, student resource pages, and thoughtful questions, and formative assessment prompts • Guidance on preparing, launching, facilitating, and reflecting on each task • Notes on access and equity, focusing on students’ strengths, productive struggle, and distance or alternative learning environments. With concluding guidance on adapting or creating additional rich tasks for your students, this guide will help you give all of your students the deepest, most enriching and engaging mathematics learning experience possible.
Author : Jessica Shumway
Publisher : Taylor & Francis
ISBN 13 : 100383986X
Total Pages : 150 pages
Book Rating : 4.0/5 (38 download)
Download or read book Number Sense Routines written by Jessica Shumway and published by Taylor & Francis. This book was released on 2023-10-10 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: Following up her' best-selling book, Number Sense Routines: Building Numerical Literacy Every Day in Grades K-3, Jessica Shumway turns her focus to upper elementary classrooms. Number Sense Routines: Developing Mathematical Understanding Every Day in Grades 3-5 is about tapping into every child' s innate number sense and providing daily, connected experiences that are responsive to children's learning needs. Consistent, Daily Routines Work:' Adaptable to any curriculum, Shumway' s 5, 10, or 15 minute warm-up routines are an easy and effective way to build and solidify students' number sense foundations as a supplement to any program Planning and Facilitating Your Classroom:' No matter how familiar the routine, Shumway provides insight on how to keep daily warm-ups fresh. She reveals careful thinking and planning that goes into each routine and offers detailed vignettes and dialogues of how they unfold in real classrooms Assessment Strategies:' As students engage in the process, each routine becomes an exciting opportunity to gain insight into where they are in their understanding and help students articulate their mathematical thinking Identify Big Ideas: Not only will these math routines help develop students' mathematical understanding as they move towards using standard algorithms, but teachers will learn to better recognize the big ideas that emerge in discussions, how to encourage important strategies based in number sense, and how to facilitate conversations on key mathematical concepts. ' 'These routines may appear in other places, [but] I have never seen them written in such detail and with so many variations.. . .. Although she makes what she does sound easy, we all know that teaching math well is anything but easy. It is challenging and complex. Unpacking what students are saying, helping them make connections not only to the math but to each other's ideas, while simultaneously recording their ideas using mathematical models, visuals, or equations is no easy task. Jessica provides wonderful visuals, examples of student work, and so much more to help educators develop the tools they need to improve their practice and in so doing improve student learning. ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' – From the Foreword by math coach and consultant Lucy West
Author : National Research Council
Publisher : National Academies Press
ISBN 13 : 0309074339
Total Pages : 633 pages
Book Rating : 4.3/5 (9 download)
Download or read book How Students Learn written by National Research Council and published by National Academies Press. This book was released on 2005-01-23 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: How do you get a fourth-grader excited about history? How do you even begin to persuade high school students that mathematical functions are relevant to their everyday lives? In this volume, practical questions that confront every classroom teacher are addressed using the latest exciting research on cognition, teaching, and learning. How Students Learn: History, Mathematics, and Science in the Classroom builds on the discoveries detailed in the bestselling How People Learn. Now, these findings are presented in a way that teachers can use immediately, to revitalize their work in the classroom for even greater effectiveness. Organized for utility, the book explores how the principles of learning can be applied in teaching history, science, and math topics at three levels: elementary, middle, and high school. Leading educators explain in detail how they developed successful curricula and teaching approaches, presenting strategies that serve as models for curriculum development and classroom instruction. Their recounting of personal teaching experiences lends strength and warmth to this volume. The book explores the importance of balancing students' knowledge of historical fact against their understanding of concepts, such as change and cause, and their skills in assessing historical accounts. It discusses how to build straightforward science experiments into true understanding of scientific principles. And it shows how to overcome the difficulties in teaching math to generate real insight and reasoning in math students. It also features illustrated suggestions for classroom activities. How Students Learn offers a highly useful blend of principle and practice. It will be important not only to teachers, administrators, curriculum designers, and teacher educators, but also to parents and the larger community concerned about children's education.
Author : Nathalie Sinclair
Publisher : National Council of Teachers of English
ISBN 13 : 9780873536929
Total Pages : 95 pages
Book Rating : 4.5/5 (369 download)
Download or read book Developing Essential Understanding of Geometry for Teaching Mathematics in Grades 9-12 written by Nathalie Sinclair and published by National Council of Teachers of English. This book was released on 2012 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: Why does it matter whether we state definitions carefully when we all know what particular geometric figures look like? What does it mean to say that a reflection is a transformation—a function? How does the study of transformations and matrices in high school connect with later work with vector spaces in linear algebra? How much do you know… and how much do you need to know? Helping your students develop a robust understanding of geometry requires that you understand this mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about geometry. It is organised around four big ideas, supported by multiple smaller, interconnected ideas—essential understandings. Taking you beyond a simple introduction to geometry, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students—and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls, and dispel misconceptions. You will also learn to develop appropriate tasks, techniques, and tools for assessing students’ understanding of the topic. Focus on the ideas that you need to understand thoroughly to teach confidently. Move beyond the mathematics you expect your students to learn. Students who fail to get a solid grounding in pivotal concepts struggle in subsequent work in mathematics and related disciplines. By bringing a deeper understanding to your teaching, you can help students who don’t get it the first time by presenting the mathematics in multiple ways. The Essential Understanding Series addresses topics in school mathematics that are critical to the mathematical development of students but are often difficult to teach. Each book in the series gives an overview of the topic, highlights the differences between what teachers and students need to know, examines the big ideas and related essential understandings, reconsiders the ideas presented in light of connections with other mathematical ideas, and includes questions for readers’ reflection.
Author : Nathalie Sinclair
Publisher : National Council of Teachers of English
ISBN 13 : 9780873536912
Total Pages : 96 pages
Book Rating : 4.5/5 (369 download)
Download or read book Developing Essential Understanding of Geometry for Teaching Mathematics in Grades 6-8 written by Nathalie Sinclair and published by National Council of Teachers of English. This book was released on 2012-01 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: Why are there so many formulas for area and volume, and why do some of them look alike? Why does one quadrilateral have no special name while another has several, like square, rectangle, rhombus, and parallelogram—and why are all these names useful? How much do you know … and how much do you need to know? Helping your students develop a robust understanding of geometry requires that you understand this mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about geometry. It is organized around four big ideas, supported by multiple smaller, interconnected ideas—essential understandings. Taking you beyond a simple introduction to geometry, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students—and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls, and dispel misconceptions. You will also learn to develop appropriate tasks, techniques, and tools for assessing students’ understanding of the topic.
Author : Tim Rowland
Publisher : SAGE
ISBN 13 : 1446207315
Total Pages : 257 pages
Book Rating : 4.4/5 (462 download)
Download or read book Developing Primary Mathematics Teaching written by Tim Rowland and published by SAGE. This book was released on 2009-03-09 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: How can KS1/2 teachers improve their mathematics teaching? This book helps readers to become better, more confident teachers of mathematics by enabling them to focus critically on what they know and what they do in the classroom. Building on their close observation of primary mathematics classrooms, the authors provide those starting out in the teaching profession with a four-stage framework which acts as a tool of support for developing their teaching: - making sense of foundation knowledge - focusing on what teachers know about mathematics - transforming knowledge - representing mathematics to learners through examples, analogies, illustrations and demonstrations - connection - helping learners to make sense of mathematics through understanding how ideas and concepts are linked to each other - contingency - what to do when the unexpected happens Each chapter includes practical activities, lesson descriptions and extracts of classroom transcripts to help teachers reflect on effective practice.
