Teaching Mathematical Reasoning in Secondary School Classrooms

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Author :
Publisher : Springer Science & Business Media
ISBN 13 : 0387097422
Total Pages : 231 pages
Book Rating : 4.3/5 (87 download)

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Book Synopsis Teaching Mathematical Reasoning in Secondary School Classrooms by : Karin Brodie

Download or read book Teaching Mathematical Reasoning in Secondary School Classrooms written by Karin Brodie and published by Springer Science & Business Media. This book was released on 2009-10-08 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Teaching mathematical reasoning in secondary school classrooms

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Publisher :
ISBN 13 :
Total Pages : 225 pages
Book Rating : 4.:/5 (646 download)

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Book Synopsis Teaching mathematical reasoning in secondary school classrooms by : Karin Brodie

Download or read book Teaching mathematical reasoning in secondary school classrooms written by Karin Brodie and published by . This book was released on 2010 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Building Thinking Classrooms in Mathematics, Grades K-12

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Author :
Publisher : Corwin Press
ISBN 13 : 1544374844
Total Pages : 454 pages
Book Rating : 4.5/5 (443 download)

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Book Synopsis Building Thinking Classrooms in Mathematics, Grades K-12 by : Peter Liljedahl

Download or read book Building Thinking Classrooms in Mathematics, Grades K-12 written by Peter Liljedahl and published by Corwin Press. This book was released on 2020-09-28 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical Thinking

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Author :
Publisher : World Scientific
ISBN 13 : 9814350834
Total Pages : 318 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis Mathematical Thinking by : Masami Isoda

Download or read book Mathematical Thinking written by Masami Isoda and published by World Scientific. This book was released on 2012 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developing mathematical thinking is one of major aims of mathematics education. In mathematics education research, there are a number of researches which describe what it is and how we can observe in experimental research. However, teachers have difficulties developing it in the classrooms. This book is the result of lesson studies over the past 50 years. It describes three perspectives of mathematical thinking: Mathematical Attitude (Minds set), Mathematical Methods in General and Mathematical Ideas with Content and explains how to develop them in the classroom with illuminating examples.

Reasoning, Communication and Connections in Mathematics

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Author :
Publisher : World Scientific
ISBN 13 : 9814405434
Total Pages : 335 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Reasoning, Communication and Connections in Mathematics by : Berinderjeet Kaur

Download or read book Reasoning, Communication and Connections in Mathematics written by Berinderjeet Kaur and published by World Scientific. This book was released on 2012 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: This fourth volume in the series of yearbooks by the Association of Mathematics Educators in Singapore entitled Reasoning, Communication and Connections in Mathematics is unique in that it focuses on a single theme in mathematics education. The objective is to encourage teachers and researchers to advance reasoning, communication and connections in mathematics classrooms. Several renowned international researchers in the field have published their work in this volume. The fifteen chapters of the book illustrate evidence-based practices that school teachers and researchers can experiment with in their own classrooms to bring about meaningful learning outcomes. Three major themes: mathematical tasks, classroom discourse, and connectivity within and beyond mathematics, shape the ideas underpinning reasoning, communication and connections in these chapters. The book makes a significant contribution towards mathematical processes essential for learners of mathematics. It is a good resource for mathematics educators and research students.

Teaching and Learning Secondary School Mathematics

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Author :
Publisher : Springer
ISBN 13 : 3319923900
Total Pages : 695 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Teaching and Learning Secondary School Mathematics by : Ann Kajander

Download or read book Teaching and Learning Secondary School Mathematics written by Ann Kajander and published by Springer. This book was released on 2018-10-24 with total page 695 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume brings together recent research and commentary in secondary school mathematics from a breadth of contemporary Canadian and International researchers and educators. It is both representative of mathematics education generally, as well as unique to the particular geography and culture of Canada. The chapters address topics of broad applicability such as technology in learning mathematics, recent interest in social justice contexts in the learning of mathematics, as well as Indigenous education. The voices of classroom practitioners, the group ultimately responsible for implementing this new vision of mathematics teaching and learning, are not forgotten. Each section includes a chapter written by a classroom teacher, making this volume unique in its approach. We have much to learn from one another, and this volume takes the stance that the development of a united vision, supported by both research and professional dialog, provides the first step.

Making Sense of Mathematics for Teaching High School

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Author :
Publisher : Solution Tree Press
ISBN 13 : 1942496494
Total Pages : 231 pages
Book Rating : 4.9/5 (424 download)

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Book Synopsis Making Sense of Mathematics for Teaching High School by : Edward C. Nolan

Download or read book Making Sense of Mathematics for Teaching High School written by Edward C. Nolan and published by Solution Tree Press. This book was released on 2016-05-19 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Mathematical Reasoning in Secondary School Classrooms

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Author :
Publisher : Springer
ISBN 13 : 9780387097428
Total Pages : 225 pages
Book Rating : 4.0/5 (974 download)

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Book Synopsis Teaching Mathematical Reasoning in Secondary School Classrooms by : Karin Brodie

Download or read book Teaching Mathematical Reasoning in Secondary School Classrooms written by Karin Brodie and published by Springer. This book was released on 2009-10-08 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Developing Essential Understanding of Mathematical Reasoning for Teaching Mathematics in Prekindergarten-grade 8

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Author :
Publisher : National Council of Teachers of English
ISBN 13 : 9780873536660
Total Pages : 95 pages
Book Rating : 4.5/5 (366 download)

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Book Synopsis Developing Essential Understanding of Mathematical Reasoning for Teaching Mathematics in Prekindergarten-grade 8 by : John K. Lannin

Download or read book Developing Essential Understanding of Mathematical Reasoning for Teaching Mathematics in Prekindergarten-grade 8 written by John K. Lannin and published by National Council of Teachers of English. This book was released on 2011 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: How do your students determine whether a mathematical statement is true? Do they rely on a teacher, a textbook or various examples? How can you encourage them to connect examples, extend their ideas to new situations that they have not yet considered and reason more generally? How much do you know...and how much do you need to know? Helping your students develop a robust understanding of mathematical reasoning requires that you understand this mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about mathematical reasoning. It is organised around one big idea, supported by multiple smaller, interconnected ideas - essential understandings.Taking you beyond a simple introduction to mathematical reasoning, 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.

International Perspectives on the Teaching and Learning of Geometry in Secondary Schools

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Author :
Publisher : Springer
ISBN 13 : 331977476X
Total Pages : 386 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis International Perspectives on the Teaching and Learning of Geometry in Secondary Schools by : Patricio Herbst

Download or read book International Perspectives on the Teaching and Learning of Geometry in Secondary Schools written by Patricio Herbst and published by Springer. This book was released on 2018-04-27 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents current perspectives on theoretical and empirical issues related to the teaching and learning of geometry at secondary schools. It contains chapters contributing to three main areas. A first set of chapters examines mathematical, epistemological, and curricular perspectives. A second set of chapters presents studies on geometry instruction and teacher knowledge, and a third set of chapters offers studies on geometry thinking and learning. Specific research topics addressed also include teaching practice, learning trajectories, learning difficulties, technological resources, instructional design, assessments, textbook analyses, and teacher education in geometry. Geometry remains an essential and critical topic in school mathematics. As they learn geometry, students develop essential mathematical thinking and visualization skills and learn a language that helps them relate to and interact with the physical world. Geometry has traditionally been included as a subject of study in secondary mathematics curricula, but it has also featured as a resource in out-of-school problem solving, and has been connected to various human activities such as sports, games, and artwork. Furthermore, geometry often plays a role in teacher preparation, undergraduate mathematics, and at the workplace. New technologies, including dynamic geometry software, computer-assisted design software, and geometric positioning systems, have provided more resources for teachers to design environments and tasks in which students can learn and use geometry. In this context, research on the teaching and learning of geometry will continue to be a key element on the research agendas of mathematics educators, as researchers continue to look for ways to enhance student learning and to understand student thinking and teachers’ decision making.

Developing Mathematical Thinking

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Author :
Publisher : Rowman & Littlefield
ISBN 13 : 147581058X
Total Pages : 145 pages
Book Rating : 4.4/5 (758 download)

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Book Synopsis Developing Mathematical Thinking by : Jonathan D. Katz

Download or read book Developing Mathematical Thinking written by Jonathan D. Katz and published by Rowman & Littlefield. This book was released on 2014-07-07 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this country we have done a poor job of helping students come to see the wonder, beauty and power of mathematics. Standards can be brought into the picture, but unless we think about what it means to truly engage students in mathematics we will continue to be unsuccessful. The goal of this book is to begin to change the way students experience mathematics in the middle and high school classrooms. In this book you will find a theoretical basis for this approach to teaching mathematics, multiple guides and questions for teachers to think about in relation to their everyday teaching, and over 30 examples of problems, lessons, tasks, and projects that been used effectively with urban students.

Mathematical Reasoning of Children and Adults

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Author :
Publisher : Springer Nature
ISBN 13 : 303069657X
Total Pages : 324 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Mathematical Reasoning of Children and Adults by : Alina Galvão Spinillo

Download or read book Mathematical Reasoning of Children and Adults written by Alina Galvão Spinillo and published by Springer Nature. This book was released on 2021-05-24 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book adopts an interdisciplinary approach to investigate the development of mathematical reasoning in both children and adults and to show how understanding the learner’s cognitive processes can help teachers develop better strategies to teach mathematics. This contributed volume departs from the interdisciplinary field of psychology of mathematics education and brings together contributions by researchers from different fields and disciplines, such as cognitive psychology, neuroscience and mathematics education. The chapters are presented in the light of the three instances that permeate the entire book: the learner, the teacher, and the teaching and learning process. Some of the chapters analyse the didactic challenges that teachers face in the classroom, such as how to interpret students' reasoning, the use of digital technologies, and their knowledge about mathematics. Other chapters examine students' opinions about mathematics, and others analyse the ways in which students solve situations that involve basic and complex mathematical concepts. The approaches adopted in the description and interpretation of the data obtained in the studies documented in this book point out the limits, the development, and the possibilities of students' thinking, and present didactic and cognitive perspectives to the learning scenarios in different school settings. Mathematical Reasoning of Children and Adults: Teaching and Learning from an Interdisciplinary Perspective will be a valuable resource for both mathematics teachers and researchers studying the development of mathematical reasoning in different fields, such as mathematics education, educational psychology, cognitive psychology, and developmental psychology.

Reasoning and Sense Making in the Elementary Grades, Prekindergarten-Grade 2

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Author :
Publisher : National Council of Teachers of English
ISBN 13 : 9780873537025
Total Pages : 151 pages
Book Rating : 4.5/5 (37 download)

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Book Synopsis Reasoning and Sense Making in the Elementary Grades, Prekindergarten-Grade 2 by : Michael T. Battista

Download or read book Reasoning and Sense Making in the Elementary Grades, Prekindergarten-Grade 2 written by Michael T. Battista and published by National Council of Teachers of English. This book was released on 2016 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on extensive research conducted by the authors, Reasoning and Sense Making in the Mathematics Classroom, Pre-K-Grade 2, is designed to help classroom teachers understand, monitor, and guide the development of students' reasoning and sense making about core ideas in elementary school mathematics. It describes and illustrates the nature of these skills using classroom vignettes and actual student work in conjunction with instructional tasks and learning progressions to show how reasoning and sense making develop and how instruction can support students in that development. Students who can make sense of mathematical ideas can apply those ideas in problem solving, even in unfamiliar situations, and can use them as a foundation for future learning. Without them, students are reduced to rote learning, often experiencing frustration and failure. But what do reasoning and sense making during learning and teaching look like? Each chapter of Reasoning and Sense Making in the Mathematics Classroom, Pre-K-Grade 2 explores a different topic that young children encounter in mathematics, demonstrating with actual student work and classroom dialogue how their mathematical knowledge and reasoning ability move through "levels of sophistication" or learning progressions: After opening with a discussion of the nature of reasoning and sense making and their critical importance in developing mathematical thinking, chapter 1 examines how young students attempt to make sense of the concepts of place value and length measurement. Chapter 2 focuses on how early childhood instruction can engage students in mathematical reasoning while helping them construct a rich sense of number and operations. Chapter 3 identifies core algebraic ideas and shows how students can engage with these ideas in ways that not only deepen their understanding of arithmetic but also lays the foundation for the future study of algebra. Children's reasoning and sense making as they decompose and compose geometric shapes--including reasoning about area--is examined in chapter 4. The use of learning progressions to understand students' reasoning and to guide their sense making with appropriate teaching is also discussed. Not just a theoretical discussion, the book also provides specific suggestions for related instructional activities for each topic. Supplementary online resources can be accessed at NCTM's More4U website. Reasoning and Sense Making in the Mathematics Classroom, Pre-K-Grade 2 will be a valuable and practical addition to your professional library.

We Reason & We Prove for ALL Mathematics

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Author :
Publisher : Corwin Press
ISBN 13 : 150637817X
Total Pages : 342 pages
Book Rating : 4.5/5 (63 download)

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Book Synopsis We Reason & We Prove for ALL Mathematics by : Fran Arbaugh

Download or read book We Reason & We Prove for ALL Mathematics written by Fran Arbaugh and published by Corwin Press. This book was released on 2018-08-08 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sharpen concrete teaching strategies that empower students to reason-and-prove How do teachers and students benefit from engaging in reasoning-and-proving? What strategies can teachers use to support students’ capacity to reason-and-prove? What does reasoning-and-proving instruction look like? We Reason & We Prove for ALL Mathematics helps mathematics teachers in grades 6-12 engage in the critical practice of reasoning-and-proving and support the development of reasoning-and-proving in their students. The phrase "reasoning-and-proving" describes the processes of identifying patterns, making conjectures, and providing arguments that may or may not qualify as proofs – processes that reflect the work of mathematicians. Going beyond the idea of "formal proof" traditionally relegated only to geometry, this book transcends all mathematical content areas with a variety of activities for teachers to learn more about reasoning-and-proving and about how to support students’ capacities to engage in this mathematical thinking through: Solving and discussing high-level mathematical tasks Analyzing narrative cases that make the relationship between teaching and learning salient Examining and interpreting student work that features a range of solution strategies, representations, and misconceptions Modifying tasks from curriculum materials so that they better support students to reason-and-prove Evaluating learning environments and making connections between key ideas about reasoning-and-proving and teaching strategies We Reason & We Prove for ALL Mathematics is designed as a learning tool for practicing and pre-service mathematics teachers and can be used individually or in a group. No other book tackles reasoning-and-proving with such breadth, depth, and practical applicability. Classroom examples, case studies, and sample problems help to sharpen concrete teaching strategies that empower students to reason-and-prove!

The Mathematics That Every Secondary School Math Teacher Needs to Know

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Author :
Publisher : Routledge
ISBN 13 : 1135157820
Total Pages : 1128 pages
Book Rating : 4.1/5 (351 download)

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Book Synopsis The Mathematics That Every Secondary School Math Teacher Needs to Know by : Alan Sultan

Download or read book The Mathematics That Every Secondary School Math Teacher Needs to Know written by Alan Sultan and published by Routledge. This book was released on 2010-09-13 with total page 1128 pages. Available in PDF, EPUB and Kindle. Book excerpt: What knowledge of mathematics do secondary school math teachers need to facilitate understanding, competency, and interest in mathematics for all of their students? This unique text and resource bridges the gap between the mathematics learned in college and the mathematics taught in secondary schools. Written in an informal, clear, and interactive learner-centered style, it is designed to help pre-service and in-service teachers gain the deep mathematical insight they need to engage their students in learning mathematics in a multifaceted way that is interesting, developmental, connected, deep, understandable, and often, surprising and entertaining. Features include Launch questions at the beginning of each section, Student Learning Opportunities, Questions from the Classroom, and highlighted themes throughout to aid readers in becoming teachers who have great "MATH-N-SIGHT": M Multiple Approaches/Representations A Applications to Real Life T Technology H History N Nature of Mathematics: Reasoning and Proof S Solving Problems I Interlinking Concepts: Connections G Grade Levels H Honing of Mathematical Skills T Typical Errors This text is aligned with the recently released Common Core State Standards, and is ideally suited for a capstone mathematics course in a secondary mathematics certification program. It is also appropriate for any methods or mathematics course for pre- or in-service secondary mathematics teachers, and is a valuable resource for classroom teachers.

Learning to Teach Mathematics in the Secondary School

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Author :
Publisher : Taylor & Francis
ISBN 13 : 1317372379
Total Pages : 346 pages
Book Rating : 4.3/5 (173 download)

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Book Synopsis Learning to Teach Mathematics in the Secondary School by : Sue Johnston-Wilder

Download or read book Learning to Teach Mathematics in the Secondary School written by Sue Johnston-Wilder and published by Taylor & Francis. This book was released on 2016-09-13 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Learning to Teach Mathematics in the Secondary School combines theory and practice to present a broad introduction to the opportunities and challenges of teaching mathematics in the secondary school classroom. This fourth edition has been fully updated to reflect the latest changes to the curriculum and research in the field, taking into account key developments in teacher training and education, including examinations and assessment. Written specifically with the new and student teacher in mind, the book covers a wide range of issues related to the teaching of mathematics, such as: why we teach mathematics the place of mathematics in the National Curriculum planning, teaching and assessing for mathematics learning how to communicate mathematically using digital technology to advance mathematical learning working with students with special educational needs post-16 teaching the importance of professional development the affective dimension when learning mathematics, including motivation, confidence and resilience Already a major text for many university teaching courses, this revised edition features a glossary of useful terms and carefully designed tasks to prompt critical reflection and support thinking and writing up to Masters Level. Issues of professional development are also examined, as well as a range of teaching approaches and styles from whole-class strategies to personalised learning, helping you to make the most of school experience, during your training and beyond. Designed for use as a core textbook, Learning to Teach Mathematics in the Secondary School provides essential guidance and advice for all those who aspire to be effective mathematics teachers.

Teaching Mathematics in Grades 6 - 12

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Author :
Publisher : SAGE
ISBN 13 : 141299568X
Total Pages : 513 pages
Book Rating : 4.4/5 (129 download)

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Book Synopsis Teaching Mathematics in Grades 6 - 12 by : Randall E. Groth

Download or read book Teaching Mathematics in Grades 6 - 12 written by Randall E. Groth and published by SAGE. This book was released on 2012-08-10 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: A journey into the vibrant and intriguing world of mathematics education Teaching Mathematics in Grades 6 - 12 explores how research in mathematics education can inform teaching practice in grades 6-12. The author shows secondary mathematics teachers the value of being a researcher in the classroom by constantly experimenting with methods for developing students′ mathematical thinking and then connecting this research to practices that enhance students′ understanding of the material.The chapters in Part I introduce secondary teachers to the field of mathematics education with cross-cutting issues that apply to teaching and learning in all mathematics content areas. The chapters in Part II are devoted to specific mathematics content strands and describe how students think about mathematical concepts. The goal of the text is to have secondary math teachers gain a deeper understanding of the types of mathematical knowledge their students bring to grade 6 - 12 classrooms, and how students′ thinking may develop in response to different teaching strategies.