Mathematics Classrooms That Promote Understanding

Mathematics Classrooms That Promote Understanding PDF

Author: Elizabeth Fennema

Publisher: Routledge

Published: 1999-04-01

Total Pages: 217

ISBN-13: 113567650X

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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.

Making Sense

Making Sense PDF

Author: James Hiebert

Publisher: Heinemann Educational Books

Published: 1997

Total Pages: 214

ISBN-13:

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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.

Teaching Mathematics in Diverse Classrooms for Grades K-4

Teaching Mathematics in Diverse Classrooms for Grades K-4 PDF

Author: Benny F. Tucker

Publisher:

Published: 2013

Total Pages: 0

ISBN-13: 9780132907286

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"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 of Mathematics for Teaching High School

Making Sense of Mathematics for Teaching High School PDF

Author: Edward C. Nolan

Publisher: Solution Tree Press

Published: 2016-05-19

Total Pages: 231

ISBN-13: 1942496494

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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

Strengths-Based Teaching and Learning in Mathematics

Strengths-Based Teaching and Learning in Mathematics PDF

Author: Beth McCord Kobett

Publisher: Corwin Press

Published: 2020-02-27

Total Pages: 189

ISBN-13: 1544374925

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"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.

Helping Children Learn Mathematics

Helping Children Learn Mathematics PDF

Author: National Research Council

Publisher: National Academies Press

Published: 2002-07-31

Total Pages: 53

ISBN-13: 0309131987

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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.

Teaching Mathematics in Diverse Classrooms

Teaching Mathematics in Diverse Classrooms PDF

Author: Benny F. Tucker

Publisher: Allyn & Bacon

Published: 2013

Total Pages: 0

ISBN-13: 9780132907293

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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.

High School Mathematics Lessons to Explore, Understand, and Respond to Social Injustice

High School Mathematics Lessons to Explore, Understand, and Respond to Social Injustice PDF

Author: Robert Q. Berry III

Publisher: Corwin Press

Published: 2020-03-09

Total Pages: 328

ISBN-13: 1071806467

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Empower students to be the change—join the teaching mathematics for social justice movement! We live in an era in which students have —through various media and their lived experiences— a more visceral experience of social, economic, and environmental injustices. However, when people think of social justice, mathematics is rarely the first thing that comes to mind. Through model lessons developed by over 30 diverse contributors, this book brings seemingly abstract high school mathematics content to life by connecting it to the issues students see and want to change in the world. Along with expert guidance from the lead authors, the lessons in this book explain how to teach mathematics for self- and community-empowerment. It walks teachers step-by-step through the process of using mathematics—across all high school content domains—as a tool to explore, understand, and respond to issues of social injustice including: environmental injustice; wealth inequality; food insecurity; and gender, LGBTQ, and racial discrimination. This book features: Content cross-referenced by mathematical concept and social issues Downloadable instructional materials for student use User-friendly and logical interior design for daily use Guidance for designing and implementing social justice lessons driven by your own students’ unique passions and challenges Timelier than ever, teaching mathematics through the lens of social justice will connect content to students’ daily lives, fortify their mathematical understanding, and expose them to issues that will make them responsive citizens and leaders in the future.

Making Sense of Mathematics for Teaching, Grades 3-5

Making Sense of Mathematics for Teaching, Grades 3-5 PDF

Author: Juli K. Dixon

Publisher: Solution Tree Press

Published: 2016-04-11

Total Pages: 386

ISBN-13: 1942496435

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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

Teaching Mathematics through Problem-Solving in K–12 Classrooms

Teaching Mathematics through Problem-Solving in K–12 Classrooms PDF

Author: Matthew Oldridge

Publisher: Rowman & Littlefield

Published: 2018-10-31

Total Pages: 135

ISBN-13: 1475843348

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“Teaching through problem-solving” is a commonly used phrase for mathematics educators. This book shows how to use worthwhile and interesting mathematics tasks and problems to build a classroom culture based on students’ reasoning and thinking. It develops a set of axioms about problem-solving classrooms to show teachers that mathematics is playful and engaging. It presents an aspirational vision for school mathematics, one which all teachers can bring into being in their classrooms.