National Council of Teachers of Mathematics,U.S. – förlag

Provides a model for facilitating discussions in mathematics classrooms based on the thinking of students. The model—anticipating, monitoring, selecting, sequencing and connecting—focuses on planning prior to the lesson and, in so doing, limits the amount of improvisation required during the lesson. This new edition is situated within current educational context (e.g., CCSSM and Principles to Actions) and offers details on how to plan for and engage students in K – grade 12 classrooms in discussions that advance the learning of all students in the classroom. Included are a detailed lesson plan, lesson planning protocol, completed monitoring chart, and a list of task resources. What’s new?Guidance on what is involved in anticipating, including elaboration on assessing and advancing questions Details on what is involved in anticipating, including elaboration on assessing and advancing questionsExpanded lesson planning discussionSituated in the current educational context of the Common Core State Standards for Mathematics and NCTM’s Principles to Actions, 5 Practices 2nd edition remains relevant for K – grade 12 mathematics teachers and the coaches, teacher educators, professional developers, and supervisors that support them.

Are you ready to take your teaching to the next level? Taking Action: Implementing Effective Mathematics Teaching Practices in K—Grade 5 offers a coherent set of professional learning experiences designed to foster teachers’ understanding of the effective mathematics teaching practices and their ability to apply those practices in their own classrooms. The book examines in depth what each teaching practice would look like in an elementary school classroom, with narrative cases, classroom videos, and real student work, presenting a rich array of experiences that bring the practices to life. Chapters are sequenced to scaffold teachers’ exploration of the effective mathematics teaching practices and furnish activities and materials for hands-on learning experiences around each individual teaching practice and across the set of the eight effective practices as a whole. Specific examples of each practice are presented in context, providing real-life instantiations of what the practice “looks” and “sounds” like in the classroom, with a careful analysis that links the practice to student learning and equity. The reader is invited to personally engage in two types of activities that run throughout the book: Analyzing Teaching and Learning, in which tasks or situations are presented to the reader to consider, work out, and reflect on, and Taking Action in Your Classroom, in which concrete suggestions are provided for exploring specific teaching practices in the classroom. Tools, such as a lesson plan template, a task analysis guide, and practices for orchestrating productive discussions, are offered to assist teachers in applying the ideas discussed in the book to their own practices. For teachers who aspire to ambitious teaching that will provide each and every one of their students with more opportunities to experience mathematics as meaningful, challenging, and worthwhile, Taking Action: Implementing Effective Mathematics Teaching Practices in K—Grade 5 is certain to be your number one go-to resource.

Are you ready to take your teaching to the next level? Taking Action: Implementing Effective Mathematics Teaching Practices in Grades 9-12 offers a coherent set of professional learning experiences designed to foster teachers' understanding of the effective mathematics teaching practices and their ability to apply those practices in their own classrooms. The book examines in depth what each teaching practice would look like in a high school classroom, with narrative cases, classroom videos, and real student work, presenting a rich array of experiences that bring the practices to life.Chapters are sequenced to scaffold teachers' exploration of the effective mathematics teaching practices and furnish activities and materials for hands-on learning experiences around each individual teaching practice and across the set of the eight effective practices as a whole. Specific examples of each practice are presented in context, providing real-life instantiations of what the practice “looks” and “sounds” like in the classroom, with a careful analysis that links the practice to student learning and equity.The reader is invited to personally engage in two types of activities that run throughout the book: Analysing Teaching and Learning, in which tasks or situations are presented to the reader to consider, work out, and reflect on, and Taking Action in Your Classroom, in which concrete suggestions are provided for exploring specific teaching practices in the classroom. Tools, such as a lesson plan template, a task analysis guide, and five practices for orchestrating productive discussions are offered to assist teachers in applying the ideas discussed in the book to their own practices.For teachers who aspire to ambitious teaching that will provide each and every one of their students with more opportunities to experience mathematics as meaningful, challenging, and worthwhile, Taking Action: Implementing Effective Mathematics Teaching Practices in Grades 9-12 is certain to be your number one go-to resource.

You just signed your first contract to teach secondary maths. You’re excited, but you probably have many questions and concerns: What do I do when students don’t “get” the lesson? How can I help students who struggle with math that they supposedly learned in elementary school? How do I arrange for students who are absent to make up the work? Do I assign seating or let students choose their seats? Should I have students work in groups? How much homework should I assign—and how much should I grade?Though you may envision your classroom as a place where students engage with mathematics and learn important content, you may also worry about how your teaching will actually play out—how you and your students will interact and what they will learn. Based on classroom observations and interviews with seasoned and beginning teachers, this highly useful book offers valuable suggestions to improve your teaching and your students’ opportunities to learn.The authors explore both the visible and invisible aspects of teaching and offer proven strategies to make the work meaningful—not merely manageable. Success from the start means being prepared from the start. This book not only teaches you how to be an effective maths teacher but also gives you the tools to do it well.

This book highlights how students learn math and the pedagogy behind it. Using vignettes based on real classroom discussions, the authors illustrate effective teaching practices to support math learning. Success from the Start: Your First Years Teaching Elementary Mathematics acts as a supportive and reassuring companion that you can return to throughout your journey as an elementary mathematics teacher. As a beginning elementary mathematics teacher you might already be asking yourself these questions:How can I differentiate my teaching to meet the diverse needs of my students? What assessments best advance student learning?How can students understand math if I do not show them different strategies and tell them about the underlying mathematical structures and properties?What advice do I give parents about how to support their children’s math learning?

Are you ready to take your teaching to the next level? Taking Action: Implementing Effective Mathematics Teaching Practices in Grades 6-8 offers a coherent set of professional learning experiences designed to foster teachers' understanding of the effective mathematics teaching practices and their ability to apply those practices in their own classrooms. The book examines in depth what each teaching practice would look like in a middle school classroom, with narrative cases, classroom videos, and real student work, presenting a rich array of experiences that bring the practices to life.Chapters are sequenced to scaffold teachers' exploration of the effective mathematics teaching practices and furnish activities and materials for hands-on learning experiences around each individual teaching practice and across the set of the eight effective practices as a whole. Specific examples of each practice are presented in context, providing real-life instantiations of what the practice “looks” and “sounds” like in the classroom, with a careful analysis that links the practice to student learning and equity.The reader is invited to personally engage in two types of activities that run throughout the book: Analysing Teaching and Learning, in which tasks or situations are presented to the reader to consider, work out, and reflect on, and Taking Action in Your Classroom, in which concrete suggestions are provided for exploring specific teaching practices in the classroom. Tools, such as a lesson plan template, a task analysis guide, and practices for orchestrating productive discussions are offered to assist teachers in applying the ideas discussed in the book to their own practices.For teachers who aspire to ambitious teaching that will provide each and every one of their students with more opportunities to experience mathematics as meaningful, challenging, and worthwhile, Taking Action: Implementing Effective Mathematics Teaching Practices in Grades 6-8 is certain to be your number one go-to resource.

Robust and effective classroom discussions are essential for providing students with opportunities to simultaneously engage in science practises while learning key science content. Using numerous examples and science learning tasks, the authors show how teachers can plan the lesson to encourage students to not only learn science content but employ disciplinary practises as well. This volume outlines the five practises teachers need for facilitating effective inquiry-oriented classrooms:Anticipate what students will do, what strategies they will use in solving a problem, monitor their work as they approach the problem in class, select students whose strategies are worth discussing in class, sequence those students’ presentations to maximise their potential to increase students’ learning, connect the strategies and ideas in a way that helps students understand the science learned.The 5 Practices framework identifies a set of instructional practises that will help teachers achieve high-demand learning objectives by using student work as the launching point for discussions in which important scientific ideas are brought to the surface, contradictions are exposed and understandings are developed or consolidated.

This annotated list of more than 550 titles analyses each book's content and accuracy, illustrations, style and any included activities. Highlights include a new section titled ""Series and Other Resources"" to accommodate the large number of books that have been issued in series, as well as a new subsection called ""Incidental Geometry–Quilting,"" which lists books that help students make connections among geometry, history and quilting.

This important tool for teachers and education professionals updates the messages of NCTM's previous Standards and shows how students' learning should grow across four grade bands: pre-K–2, 3–5, 6–8 and 9–12. It incorporates a clear set of principles and a sharper focus on how students' knowledge grows as shown by recent research. It also includes ways to incorporate the use of technology to make mathematics instruction relevant and effective in a technological world.The accompanying CD offers a searchable hypertext edition of Principles and Standards, which includes the full text of the printed volume along with interactive maths tools that support the vision of the Standards. The CD also contains a version of the Illuminations website, which includes hundreds of lessons, interactive tools and reviewed web sites that support Principles and Standards and the three previous Standards documents.

This easy-to-read summary is an excellent tool for introducing others to the messages contained in Principles and Standards.

Presents portraits of teaching by secondary school teachers who have closely observed classroom communication, conversation and discourse.

How do you refute the erroneous claim that all ratios are fractions? This book goes beyond a simple introduction to ratios, proportions and proportional reasoning. It will help broaden and deepen your mathematical understanding of one of the most challenging topics for students - and teachers - to grasp. It will help you engage your students, anticipate their perplexities, help them avoid pitfalls and dispel misconceptions. You will also learn to develop appropriate tasks, techniques and tools for assessing your students’ understanding of the topic.Essential Understanding series topics include:Number and Numeration for Grades Pre-K-2Addition and Subtraction for Grades Pre-K-2Geometry for Grades Pre-K-2Reasoning and Proof for Grades Pre-K-8Multiplication and Division for Grades 3-5Rational Numbers for Grades 3-5Algebraic Ideas and Readiness for Grades 3-5Geometric Shapes and Solids for Grades 3-5Ratio, Proportion and Proportionality for Grades 6-8Expressions and Equations for Grades 6-8Measurement for Grades 6-8Data Analysis and Statistics for Grades 6-8Function for Grades 9-12Geometric Relationships for Grades 9-12Reasoning and Proof for Grades 9-12Statistics for Grades 9—12

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-2Addition and Subtraction for Grades Pre-K-2Geometry for Grades Pre-K-2Reasoning and Proof for Grades Pre-K-8Multiplication and Division for Grades 3-5Rational Numbers for Grades 3-5Algebraic Ideas and Readiness for Grades 3-5Geometric Shapes and Solids for Grades 3-5Ratio, Proportion and Proportionality for Grades 6-8Expressions and Equations for Grades 6-8Measurement for Grades 6-8Data Analysis and Statistics for Grades 6-8Function for Grades 9-12Geometric Relationships for Grades 9-12Reasoning and Proof for Grades 9-12Statistics for Grades 9-12

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.

Good teaching is responsive to individual differences, tailoring instruction to meet the needs of individual learners. In gifted education, students need a curriculum that is differentiated (by level, complexity, breadth and depth), developmentally appropriate and conducted at a more rapid rate. This collection of essays from experts in the field addresses the particular needs educational institutions have in serving their gifted students. Topics include policy and philosophy; specific programme models; supplemental materials and programmes; knowledge and skills that teachers need in their work; international opportunities and possibilities and equity.Many of the points raised are as valid for general education students as for gifted students. Many relate equally well to high school or elementary school. And many apply across the curriculum - not just to mathematics.

One of the boys in the group responded, “That’s so smart! That’s so smart! That’s what we should do!” Complex Instruction (CI) is a response to the paradox that group work offers much potential but often creates circumstances where few students seem to learn. CI is a set of ideas and strategies that address the problems that confound group work, but that create powerful learning for children. This book offers guidance to readers on how to use these strategies and ideas. The authors describe the lessons they learned using group work, explain how complex instruction helps unsuccessful students and analyse how to design assignments that support group learning - using group-worthy tasks - giving readers examples of good tasks and help in adapting math problems from their own curricula.

How can you build on young children’s interactions with the world to develop their geometric thinking? What can you say to a student who claims that a diamond isn’t a square because it “stands on a point”? How can knowing what does not change when shapes are transformed help you extend your students’ thinking about the area of geometric figures?How much do you know … and how much do you need to know?Helping your students develop a robust understanding of geometry and measurement requires that you understand this mathematics deeply. But what does that mean?This book focuses on essential knowledge for teachers about geometry and measurement. It is organized around four big ideas, supported by multiple smaller, interconnected ideas—essential understandings.Taking you beyond a simple introduction to geometry and measurement, 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.About the Series: 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.

Unpacking"" the ideas related to multiplication and division is a critical step in developing a deeper understanding. To those without specialised training, many of these ideas might appear to be easy to teach. But those who teach in grades 3-5 are aware of their subtleties and complexities.This book identifies and examines two big ideas and related essential understandings for teaching multiplication and division in grades 3–5. Big Idea 1 captures the notion that multiplication is usefully defined as a scalar operation. Problem situations modelled by multiplication have an element that represents the scalar and an element that represents the quantity to which the scalar applies. Big Idea 2 relates to the algorithms that problem solvers have invented - some of which have become “standard” - for multiplying and dividing. The authors examine the ways in which counting, adding and subtracting lead to multiplication and division, as well as the role that these operations play in algebraic expressions and other advanced topics. The book examines challenges in teaching, learning and assessment and is interspersed with questions for teachers’ reflection.

Like algebra at any level, early algebra is a way to explore, analyse, represent and generalise mathematical ideas and relationships. This book shows that children can and do engage in generalising about numbers and operations as their mathematical experiences expand. The authors identify and examine five big ideas and associated essential understandings for developing algebraic thinking in grades 3-5. The big ideas relate to the fundamental properties of number and operations, the use of the equals sign to represent equivalence, variables as efficient tools for representing mathematical ideas, quantitative reasoning as a way to understand mathematical relationships and functional thinking to generalise relationships between covarying quantities. The book examines challenges in teaching, learning and assessment and is interspersed with questions for teachers’ reflection.

How can you introduce terms from geometry and measurement so that your students’ vocabulary will enhance their understanding of concepts and definitions? What can you say to clarify the thinking of a student who claims that perimeter is always an even number? How does knowing what changes or stays the same when shapes are transformed help you support and extend your students’ understanding of shapes and the space that they occupy?How much do you know … and how much do you need to know?Helping your students develop a robust understanding of geometry and measurement requires that you understand fundamental statistical concepts deeply. But what does that mean?This book focuses on essential knowledge for mathematics teachers about geometry and measurement. It is organized around three big ideas, supported by multiple smaller, interconnected ideas—essential understandings. Taking you beyond a simple introduction to geometry and measurement, the book will broaden and deepen your 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.

Why do some equations have one solution, others two or even more solutions and some no solutions? Why do we sometimes need to ""switch"" the direction of an inequality symbol in solving an inequality? What could you say if a student described a function as an equation?How much do you know...and how much do you need to know?Helping your students develop a robust understanding of expressions, equations and functions requires that you understand this mathematics deeply. But what does that mean?This book focuses on essential knowledge for teachers about expressions, equations and functions. It is organised around five big ideas, supported by multiple smaller, interconnected ideas - essential understandings. Taking you beyond a simple introduction to expressions, equations and functions, 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.

How does working with data in statistics differ from working with numbers in mathematics? What is variability, and how can we describe and measure it? How can we display distributions of quantitative or categorical data? What is a data sample, and how can we choose one that will allow us to draw valid conclusions from data?How much do you know? and how much do you need to know?Helping your students develop a robust understanding of statistics requires that you understand fundamental statistical concepts deeply. But what does that mean?This book focuses on essential knowledge for mathematics teachers about statistics. It is organised around four big ideas, supported by multiple smaller, interconnected ideas. Taking you beyond a simple introduction to statistics, the book will broaden and deepen your 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.

How does a statistical model differ from a mathematical model? What are the differences among the sample distribution, the sampling distribution, and the population distribution? In an experiment, what effect does the sampling method have on the results? What are the implications of the use of processes of random selection and random assignment? Can a small sample yield accurate estimates of population parameters?This book examines five big ideas and twenty-four related essential understandings for teaching statistics in grades 9–12. The authors distinguish mathematical and statistical models, explore distributions as descriptions of variability in data, focus on the fundamentals of testing hypotheses to draw conclusions from data, highlight the importance of the data collection method, and recognise the need to examine bias, precision, and sampling method in evaluating statistical estimators. Recognising that analysing data is an important part of understanding the world, the authors discuss the growth of students’ ideas about statistics and examine challenges to teaching, learning, and assessment. They intersperse their discussion with questions for teachers’ reflection.

Educators increasingly recognise the important role that mathematics teaching plays in helping students to understand and overcome social injustice and inequality. This collection of original articles is the start of a compelling conversation among some of the leading figures in critical and social justice mathematics, a number of teachers and educators who have been inspired by them and who have inspiring stories of their own to tell—and any reader interested in the intersection of education and social justice.An important read for every educator, this book shows how to teach mathematics so that all students are given the tools they need to confront issues of social justice today and in the future.Included in The Top 75 New York Times Best-Selling Education Books of 2013.

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.

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.

Based on extensive research conducted by the authors, Reasoning and Sense Making in the Mathematics Classroom, Grades 3–5, 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, Grades 3–5 explores a different topic that 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 students attempt to make sense of the concept of length measurement.Chapter 2 focuses on student strategies that exemplify conceptually sound reasoning and sense making in the context of multiplication word problems, and discusses how instruction can support students’ growth in this reasoning. The critical topic of properties of numbers that underlie reasoning about multiplication is also examined.Chapter 3 describes how students in grades 3–5 extend their understanding of number to include fractions and how they can build reasoning and sense making for fractions through explorations of different representations such as physical materials, pictures, and story contexts.Discussions on the nature of early algebraic reasoning, including research-based descriptions of this reasoning in children, classroom practices that can support this reasoning, and how algebra can be appropriately integrated in elementary mathematical content are provided in chapter 4.Chapter 5 discusses practices and processes connected to reasoning about geometric decomposition and structuring as applied to arrays of squares and cubes and to area and volume problems. A learning progression for the development of such reasoning is examined, and instructional practices that are consistent with this learning progression are considered.Not just a theoretical discussion,the book also provides specific suggestions for related instructional activities for each topic. Reasoning and Sense Making in the Mathematics Classroom, Grades 3–5 will be a valuable and practical addition to your professional library.

Reasoning and Sense Making in the Mathematics Classroom, Grades 6–8, based on extensive research conducted by the authors, is designed to help classroom teachers understand, monitor, and guide the development of students’ reasoning and sense making about core ideas in middle 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 instruction can support students in their development of these competencies.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 this base of conceptual understanding, students are reduced to rote learning, often experiencing frustration and failure.But what do reasoning and sense making look like in learning and teaching?Each chapter of Reasoning and Sense Making in the Mathematics Classroom, Grades 6–8 explores a different topic that 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 students attempt to make sense of the concepts of fractions and geometric properties of shapes.Chapter 2 discusses how reasoning about ratios and proportional relationships involves deep understanding of the multiplicative relationships embedded in the comparisons of two quantities.Chapter 3 focuses on what it means to call algebra a “style of mathematical thinking” and illustrates how students can view it as a reasoning and sense-making activity rather than as an isolated set of concepts to be memorized without understanding and quickly forgotten.Reasoning and sense making are inextricably linked in statistics and probability. Discussion and examples are used in chapter 4 to illustrate pedagogical practices that recognize and address students’ development of statistical understanding, including some of the misunderstandings that students display along the way.Chapter 5 examines how students make sense of and reason about decomposing shapes, and discusses the mental processes underlying this reasoning in the context of area, surface area, and volume.Not just a theoretical treatise, the book provides specific suggestions for related instructional activities for each topic. Reasoning and Sense Making in the Mathematics Classroom, Grades 6–8 will be a valuable and practical addition to your professional library.

This volume, a comprehensive survey and critical analysis of today’s issues in mathematics education, distills research to build knowledge and capacity in the field.The compendium is a valuable new resource that provides the most comprehensive evidence about what is known about research in mathematics education.The 38 chapters present five sections that address research about (1) foundations, (2) methods, (3) mathematical processes and content, (4) students, teachers, and learning environments, and (5) futuristic issues. Each chapter offers a synthesis of research with an eye to the historical development of a research topic and, in particular, historical milestones of the research about the topic.