Mathematics Classrooms That Promote Understanding

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Mathematics Classrooms That Promote Understanding

Elizabeth Fennema,Thomas A. Romberg
Mathematics Classrooms That Promote Understanding Book PDF

Author : Elizabeth Fennema,Thomas A. Romberg
Publisher : Routledge
Page : 217 pages
File Size : 55,9 Mb
Release : 1999-04-01
Category : Education
ISBN : 9781135676506

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Mathematics Classrooms That Promote Understanding by Elizabeth Fennema,Thomas A. Romberg Pdf

Mathematics Classrooms That Promote Understanding synthesizes the implications of research done by the National Center for Research in Mathematical Sciences on integrating two somewhat diverse bodies of scholarly inquiry: the study of teaching and the study of learning mathematics. This research was organized around content domains and/or continuing issues of education, such as equity and assessment of learning, and was guided by two common goals--defining the mathematics content of the K-12 curriculum in light of the changing mathematical needs of citizens for the 21st century, and identifying common components of classrooms that enable students to learn the redefined mathematics with understanding. To accomplish these goals, classrooms in which instruction facilitated the growth of understanding were established and/or studied. This volume reports and discusses the findings which grew out of this research, and subsequent papers and discussions among the scholars engaged in the endeavor. Section I, "Setting the Stage," focuses on three major threads: What mathematics should be taught; how we should define and increase students' understanding of that mathematics; and how learning with understanding can be facilitated for all students. Section II, "Classrooms That Promote Understanding," includes vignettes from diverse classrooms that illustrate classroom discourse, student work, and student engagement in the mathematics described in Chapter 1 as well as the mental activities described in Chapter 2. These chapters also illustrate how teachers deal with the equity concerns described in Chapter 3. Section III addresses "Developing Classrooms That Promote Understanding." The knowledge of the teaching/learning process gained from the research reported in this volume is a necessary prerequisite for implementing the revisions called for in the current reform movement. The classrooms described show that innovative reform in teaching and learning mathematics is possible. Unlike many volumes reporting research, this book is written at a level appropriate for master's degree students. Very few references are included in the chapters themselves; instead, each chapter includes a short annotated list of articles for expanded reading which provides the scholarly basis and research substantiation for this volume.

Teaching Mathematics in Diverse Classrooms for Grades K-4

Benny F. Tucker,Ann H. Singleton,Terry L. Weaver
Teaching Mathematics in Diverse Classrooms for Grades K 4 Book PDF

Author : Benny F. Tucker,Ann H. Singleton,Terry L. Weaver
Publisher : Unknown
Page : 0 pages
File Size : 44,9 Mb
Release : 2013
Category : Mathematics
ISBN : 0132907283

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Teaching Mathematics in Diverse Classrooms for Grades K-4 by Benny F. Tucker,Ann H. Singleton,Terry L. Weaver Pdf

"The book emphasizes that effective mathematics teachers plan lessons that include a more complete development of mathematical ideas, use visuals supporting mental imagery, present opportunities for kinesthetic learning activities, provide chances for children to communicate their understanding of mathematics, and allow for continual monitoring of student learning. Lessons include straightforward, easy-to-use learning activities illustrating specific mathematical concepts and skills, visuals to help develop mental imagery, and opportunities for active student learning."--publisher website.

Making Sense

James Hiebert
Making Sense Book PDF

Author : James Hiebert
Publisher : Heinemann Educational Books
Page : 214 pages
File Size : 54,9 Mb
Release : 1997
Category : Education
ISBN : STANFORD:36105019325369

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Making Sense by James Hiebert Pdf

This book presents several key principles for teaching mathematics for understanding that you can use to reflect on your own teaching, make more informed decisions, and develop more effective systems of instruction.

Making Sense of Mathematics for Teaching High School

Edward C. Nolan,Juli K. Dixon,Farhsid Safi,Erhan Selcuk Haciomeroglu
Making Sense of Mathematics for Teaching High School Book PDF

Author : Edward C. Nolan,Juli K. Dixon,Farhsid Safi,Erhan Selcuk Haciomeroglu
Publisher : Solution Tree Press
Page : 273 pages
File Size : 46,9 Mb
Release : 2016-05-19
Category : Education
ISBN : 9781942496496

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Making Sense of Mathematics for Teaching High School by Edward C. Nolan,Juli K. Dixon,Farhsid Safi,Erhan Selcuk Haciomeroglu Pdf

Develop a deep understanding of mathematics by grasping the context and purpose behind various strategies. This user-friendly resource presents high school teachers with a logical progression of pedagogical actions, classroom norms, and collaborative teacher team efforts to increase their knowledge and improve mathematics instruction. Explore strategies and techniques to effectively learn and teach significant mathematics concepts and provide all students with the precise, accurate information they need to achieve academic success. Combine student understanding of functions and algebraic concepts so that they can better decipher the world. Benefits Dig deep into mathematical modeling and reasoning to improve as both a learner and teacher of mathematics. Explore how to develop, select, or modify mathematics tasks in order to balance cognitive demand and engage students. Discover the three important norms to uphold in all mathematics classrooms. Learn to apply the tasks, questioning, and evidence (TQE) process to ensure mathematics instruction is focused, coherent, and rigorous. Gain clarity about the most productive progression of mathematical teaching and learning for high school. Watch short videos that show what classrooms that are developing mathematical understanding should look like. Contents Introduction Equations and Functions Structure of Equations Geometry Types of Functions Function Modeling Statistics and Probability Epilogue: Next Steps Appendix: Weight Loss Study Data References Index

Teaching Mathematics in Diverse Classrooms for Grades 5-8

Benny F. Tucker
Teaching Mathematics in Diverse Classrooms for Grades 5 8 Book PDF

Author : Benny F. Tucker
Publisher : Unknown
Page : 0 pages
File Size : 42,7 Mb
Release : 2013
Category : Mathematics
ISBN : OCLC:816340570

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Teaching Mathematics in Diverse Classrooms for Grades 5-8 by Benny F. Tucker Pdf

"With this guide, teaching mathematics is made more effective through straightforward, easy-to-use lesson plans and learning activities that illustrate specific mathematical concepts and skills, ideas for using visuals to develop mental imagery, and ways to promote active student learning using movement and student discussion. The development of the content is user-friendly and based on a small number of easy-to-understand and easy-to-teach big ideas, and the many activities help to emphasize and reinforce the development of the mathematical content"--Publisher website.

Teaching Mathematics in Diverse Classrooms

Benny F. Tucker,Ann H. Singleton,Terry L. Weaver
Teaching Mathematics in Diverse Classrooms Book PDF

Author : Benny F. Tucker,Ann H. Singleton,Terry L. Weaver
Publisher : Allyn & Bacon
Page : 0 pages
File Size : 48,5 Mb
Release : 2013
Category : Education
ISBN : 0132907291

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Teaching Mathematics in Diverse Classrooms by Benny F. Tucker,Ann H. Singleton,Terry L. Weaver Pdf

Through a variety of straight-forward, easy-to-use lesson plans and learning activities that illustrate specific mathematical concepts and skills, this title emphasizes the premise that effective mathematics teaching promotes understanding-and understanding provides sound bases for skill development and better retention of material.

Making Sense of Mathematics for Teaching, Grades 3-5

Juli K. Dixon,Edward C. Nolan
Making Sense of Mathematics for Teaching Grades 3 5 Book PDF

Author : Juli K. Dixon,Edward C. Nolan
Publisher : Solution Tree Press
Page : 386 pages
File Size : 53,8 Mb
Release : 2016-04-11
Category : Education
ISBN : 9781942496434

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Making Sense of Mathematics for Teaching, Grades 3-5 by Juli K. Dixon,Edward C. Nolan Pdf

Develop a deep understanding of mathematics. This user-friendly resource presents grades 3–5 teachers with a logical progression of pedagogical actions, classroom norms, and collaborative teacher team efforts to increase their knowledge and improve mathematics instruction. Focus on an understanding of and procedural fluency with multiplication and division. Address how to learn and teach fraction concepts and operations with depth. Thoroughly teach plane and solid geometry. Explore strategies and techniques to effectively learn and teach significant mathematics concepts and provide all students with the precise, accurate information they need to achieve academic success. Benefits Dig deep into mathematical modeling and reasoning to improve as both a learner and teacher of mathematics. Explore how to develop, select, and modify mathematics tasks in order to balance cognitive demand and engage students. Discover the three important norms to uphold in all mathematics classrooms. Learn to apply the tasks, questioning, and evidence (TQE) process to ensure mathematics instruction is focused, coherent, and rigorous. Use charts and diagrams for classifying shapes, which can engage students in important mathematical practices. Access short videos that show what classrooms that are developing mathematical understanding should look like. Contents Introduction 1 Place Value, Addition, and Subtraction 2 Multiplication and Division 3 Fraction Concepts 4 Fraction Operations 5 Geometry 6 Measurement Epilogue Next Steps Appendix A Completed Classification of Triangles Chart Appendix B Completed Diagram for Classifying Quadrilaterals

Strengths-Based Teaching and Learning in Mathematics

Beth McCord Kobett,Karen S. Karp
Strengths Based Teaching and Learning in Mathematics Book PDF

Author : Beth McCord Kobett,Karen S. Karp
Publisher : Corwin
Page : 273 pages
File Size : 41,6 Mb
Release : 2020-02-27
Category : Education
ISBN : 9781544374901

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Strengths-Based Teaching and Learning in Mathematics by Beth McCord Kobett,Karen S. Karp Pdf

"This book is a game changer! Strengths-Based Teaching and Learning in Mathematics: 5 Teaching Turnarounds for Grades K- 6 goes beyond simply providing information by sharing a pathway for changing practice. . . Focusing on our students’ strengths should be routine and can be lost in the day-to-day teaching demands. A teacher using these approaches can change the trajectory of students’ lives forever. All teachers need this resource! Connie S. Schrock Emporia State University National Council of Supervisors of Mathematics President, 2017-2019 NEW COVID RESOURCES ADDED: A Parent’s Toolkit to Strengths-Based Learning in Math is now available on the book’s companion website to support families engaged in math learning at home. This toolkit provides a variety of home-based activities and games for families to engage in together. Your game plan for unlocking mathematics by focusing on students’ strengths. We often evaluate student thinking and their work from a deficit point of view, particularly in mathematics, where many teachers have been taught that their role is to diagnose and eradicate students’ misconceptions. But what if instead of focusing on what students don’t know or haven’t mastered, we identify their mathematical strengths and build next instructional steps on students’ points of power? Beth McCord Kobett and Karen S. Karp answer this question and others by highlighting five key teaching turnarounds for improving students’ mathematics learning: identify teaching strengths, discover and leverage students’ strengths, design instruction from a strengths-based perspective, help students identify their points of power, and promote strengths in the school community and at home. Each chapter provides opportunities to stop and consider current practice, reflect, and transfer practice while also sharing · Downloadable resources, activities, and tools · Examples of student work within Grades K–6 · Real teachers’ notes and reflections for discussion It’s time to turn around our approach to mathematics instruction, end deficit thinking, and nurture each student’s mathematical strengths by emphasizing what makes them each unique and powerful.

Making Sense of Mathematics for Teaching Grades 6-8

Edward C. Nolan,Juli K. Dixon
Making Sense of Mathematics for Teaching Grades 6 8 Book PDF

Author : Edward C. Nolan,Juli K. Dixon
Publisher : Unknown
Page : 0 pages
File Size : 42,6 Mb
Release : 2016-10-17
Category : Mathematics
ISBN : 1942496478

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Making Sense of Mathematics for Teaching Grades 6-8 by Edward C. Nolan,Juli K. Dixon Pdf

"With Making sense of mathematics for teaching grades 6-8, participants have the opportunity to engage in mathematics as learners. This unscripted video program addresses three specific goals: (1) to explore meaningful tasks as learners of mathematics for teaching, (2) to make sense of the TQE process (tasks, questioning, and evidence), and (3) to create a shared vision of classrooms where teachers are supporting the TQE process and students are engaged in meaningful mathematics learning experiences. The program accomplishes these goals through the use of challenging tasks for teachers, effective questions related to classroom content, and classroom video showing tasks modeled during instruction."--Container

Building Thinking Classrooms in Mathematics, Grades K-12

Peter Liljedahl
Building Thinking Classrooms in Mathematics Grades K 12 Book PDF

Author : Peter Liljedahl
Publisher : Corwin Press
Page : 454 pages
File Size : 50,9 Mb
Release : 2020-09-28
Category : Education
ISBN : 9781544374840

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Building Thinking Classrooms in Mathematics, Grades K-12 by Peter Liljedahl Pdf

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.

Mathematics as the Science of Patterns

Patrick M. Jenlink
Mathematics as the Science of Patterns Book PDF

Author : Patrick M. Jenlink
Publisher : IAP
Page : 265 pages
File Size : 47,7 Mb
Release : 2022-02-01
Category : Education
ISBN : 9781648027468

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Mathematics as the Science of Patterns by Patrick M. Jenlink Pdf

Mathematics as the Science of Patterns: Making the Invisible Visible to Students through Teaching introduces the reader to a collection of thoughtful, research-based works by authors that represent current thinking about mathematics, mathematics education, and the preparation of mathematics teachers. Each chapter focuses on mathematics teaching and the preparation of teachers who will enter classrooms to instruct the next generation of students in mathematics. The value of patterns to the teaching and learning of mathematics is well understood, both in terms of research and application. When we involve or appeal to pattern in teaching mathematics, it is usually because we are trying to help students to extract greater meaning, or enjoyment, or both, from the experience of learning environments within which they are occupied, and perhaps also to facilitate remembering. As a general skill it is thought that the ability to discern a pattern is a precursor to the ability to generalize and abstract, a skill essential in the early years of learning and beyond. Research indicates that the larger problem in teaching mathematics does not lie primarily with students; rather it is with the teachers themselves. In order to make changes for students there first needs to be a process of change for teachers. Understanding the place of patterns in learning mathematics is a predicate to understanding how to teach mathematics and how to use pedagogical reasoning necessary in teaching mathematics. Importantly, the lack of distinction created by the pedagogical use of patterns is not immediately problematic to the student or the teacher. The deep-seated cognitive patterns that both teachers and students bring to the classroom require change. Chapter 1 opens the book with a focus on mathematics as the science of patterns and the importance of patterns in mathematical problem solving, providing the reader with an introduction. The authors of Chapter 2 revisit the work of Po lya and the development and implementation of problem solving in mathematics. In Chapter 3, the authors present an argument for core pedagogical content knowledge in mathematics teacher preparation. The authors of Chapter 4 focus on preservice teachers’ patterns of conception as related to understanding number and operation. In Chapter 5 the authors examine the role of visual representation in exploring proportional reasoning, denoting the importance of helping learners make their thinking visible. The authors of Chapter 6 examine patterns and relationships, and the importance of each in assisting students’ learning and development in mathematical understanding. The authors of Chapter 7 examine the use of worked examples as a scalable practice, with emphasis on the importance of worked examples in teaching fraction magnitude and computation is discussed. In Chapter 8, the authors expand on the zone of proximal development to investigate the potential of Zankov’s Lesson in terms of students analyzing numerical equalities. The authors of Chapter 9 focus on high leverage mathematical practices in elementary pre-service teacher preparation, drawing into specific relief the APEX cycle to develop deep thinking. In Chapter 10, the author focuses on number talks and the engagement of students in mathematical reasoning, which provides opportunities for students to be sensemakers of mathematics. Chapter 11 presents an epilogue, focusing on the importance of recognizing the special nature of mathematics knowledge for teaching.

Mathematical Tasks in Classrooms Around the World

Anonim
Mathematical Tasks in Classrooms Around the World Book PDF

Author : Anonim
Publisher : BRILL
Page : 253 pages
File Size : 50,9 Mb
Release : 2010-01-01
Category : Education
ISBN : 9789460911507

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Mathematical Tasks in Classrooms Around the World by Anonim Pdf

This book presents an international perspective on environmental educational and specifically the influence that context has on this aspect of curriculum. The focus is on environmental education both formal and non formal and the factors that impact upon its effectiveness, particularly in non-Western and non-English-speaking contexts (i.e., outside the UK, USA, Australia, NZ, etc. ).

Mathematical Understanding for Secondary Teaching

M. Kathleen Heid,Patricia S. Wilson,Glendon W. Blume
Mathematical Understanding for Secondary Teaching Book PDF

Author : M. Kathleen Heid,Patricia S. Wilson,Glendon W. Blume
Publisher : IAP
Page : 471 pages
File Size : 50,9 Mb
Release : 2015-12-01
Category : Education
ISBN : 9781681231150

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Mathematical Understanding for Secondary Teaching by M. Kathleen Heid,Patricia S. Wilson,Glendon W. Blume Pdf

A perennial discussion about teacher development is the optimal content background for teachers. In recent years, that discussion has taken center stage in the work of mathematics education researchers, mathematicians, mathematics professional developers, and mathematics education policymakers. Much of the existing and prior work in this area has been directed toward mathematical knowledge for teaching at the elementary level. The work described in this volume takes a sometimes-neglected approach, focusing on the dynamic nature of mathematical understanding rather than on a stable description of mathematical knowledge, and on mathematics for secondary teaching rather than mathematics for teaching at the elementary level. The work reported in Mathematical Understanding for Secondary Teaching: A Framework and Classroom-Based Situations is a practice-based response to the question of what mathematical understandings secondary teachers could productively use in their teaching. For each of more than 50 events, our team of almost 50 mathematics educators who were experienced mathematics teachers developed descriptions of the mathematics that teachers could use—each of those descriptions (consisting of the event and the mathematics related to the event) is what we call a Situation. We developed our Framework for Mathematical Understanding for Secondary Teaching (MUST) based on an analysis of our entire set of Situations. We call the work practice-based because the MUST framework is based on actual events that we witnessed in our observations of secondary mathematics practice. Groups of mathematics teachers can use this volume to enhance their own understandings of secondary mathematics. School leaders and professional developers in secondary mathematics will find our MUST Framework and Situations useful as they work with teachers in enhancing and deepening their understanding of secondary mathematics. Mathematics teacher educators and mathematicians who teach mathematics to prospective and in-service secondary teachers will be able to couch their mathematical discussions in the Situations—examples that arise from secondary mathematics classrooms. They will be able to use this volume as they design courses and programs that enhance mathematics from the perspectives identified in the MUST framework. Policymakers and researchers can use our MUST framework as they consider the mathematics background needed by teachers.

Teaching Mathematical Reasoning in Secondary School Classrooms

Karin Brodie
Teaching Mathematical Reasoning in Secondary School Classrooms Book PDF

Author : Karin Brodie
Publisher : Springer Science & Business Media
Page : 231 pages
File Size : 47,9 Mb
Release : 2009-10-08
Category : Education
ISBN : 9780387097428

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Teaching Mathematical Reasoning in Secondary School Classrooms by Karin Brodie Pdf

For too many students, mathematics consists of facts in a vacuum, to be memorized because the instructor says so, and to be forgotten when the course of study is completed. In this all-too-common scenario, young learners often miss the chance to develop skills—specifically, reasoning skills—that can serve them for a lifetime. The elegant pages of Teaching Mathematical Reasoning in Secondary School Classrooms propose a more positive solution by presenting a reasoning- and discussion-based approach to teaching mathematics, emphasizing the connections between ideas, or why math works. The teachers whose work forms the basis of the book create a powerful record of methods, interactions, and decisions (including dealing with challenges and impasses) involving this elusive topic. And because this approach shifts the locus of authority from the instructor to mathematics itself, students gain a system of knowledge that they can apply not only to discrete tasks relating to numbers, but also to the larger world of people and the humanities. A sampling of the topics covered: Whole-class discussion methods for teaching mathematics reasoning. Learning mathematical reasoning through tasks. Teaching mathematics using the five strands. Classroom strategies for promoting mathematical reasoning. Maximizing student contributions in the classroom. Overcoming student resistance to mathematical conversations. Teaching Mathematical Reasoning in Secondary School Classrooms makes a wealth of cutting-edge strategies available to mathematics teachers and teacher educators. This book is an invaluable resource for researchers in mathematics and curriculum reform and of great interest to teacher educators and teachers.

Teachers Engaged in Research

Laura R. Van Zoest
Teachers Engaged in Research Book PDF

Author : Laura R. Van Zoest
Publisher : IAP
Page : 293 pages
File Size : 42,7 Mb
Release : 2006-03-01
Category : Mathematics
ISBN : 9781607526612

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Teachers Engaged in Research by Laura R. Van Zoest Pdf

This book provides examples of the ways in which 9-12 grade mathematics teachers from across North America are engaging in research. It offers a glimpse of the questions that capture the attention of teachers, the methodologies that they use to gather data, and the ways in which they make sense of what they find. The focus of these teachers’ investigations into mathematics classrooms ranges from students’ understanding of content to pedagogical changes to social issues. Underlying the chapters is the common goal of enabling students to develop a deep understanding of the mathematics they learn in their classrooms.