The book places particular emphasis on adult-initiated, number-focused activities and playful, challenging and sensitive teaching strategies to engage younger children. The strategies are based on research and work with practitioners, and are illustrated by children’s own responses, such as making number jokes. It covers key areas of mathematics, including number, shape and space, measures and problem solving, with appropriate expectations and common difficulties as well as suggested activities.
Selected as the Michigan Council of Teachers of Mathematics winter book club book! Rich tasks, collaborative work, number talks, problem-based learning, direct instruction...with so many possible approaches, how do we know which ones work the best? In Visible Learning for Mathematics, six acclaimed educators assert it’s not about which one—it’s about when—and show you how to design high-impact instruction so all students demonstrate more than a year’s worth of mathematics learning for a year spent in school. That’s a high bar, but with the amazing K-12 framework here, you choose the right approach at the right time, depending upon where learners are within three phases of learning: surface, deep, and transfer. This results in "visible" learning because the effect is tangible. The framework is forged out of current research in mathematics combined with John Hattie’s synthesis of more than 15 years of education research involving 300 million students. Chapter by chapter, and equipped with video clips, planning tools, rubrics, and templates, you get the inside track on which instructional strategies to use at each phase of the learning cycle: Surface learning phase: When—through carefully constructed experiences—students explore new concepts and make connections to procedural skills and vocabulary that give shape to developing conceptual understandings. Deep learning phase: When—through the solving of rich high-cognitive tasks and rigorous discussion—students make connections among conceptual ideas, form mathematical generalizations, and apply and practice procedural skills with fluency. Transfer phase: When students can independently think through more complex mathematics, and can plan, investigate, and elaborate as they apply what they know to new mathematical situations. To equip students for higher-level mathematics learning, we have to be clear about where students are, where they need to go, and what it looks like when they get there. Visible Learning for Math brings about powerful, precision teaching for K-12 through intentionally designed guided, collaborative, and independent learning.
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.
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
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.
"With freshness, humour and originality, Sue Gifford demonstrates the interactive strategies that are required to teach mathematics to young children. The text is both refreshingly free from conventional wisdom and solidly grounded in recent research on learning and teaching early mathematics.At the same time, it is unfailing in its accuracy in uncovering children's own humour and instinct for subverting 'teacherly' overtures. Given the demonstrated lack of spontaneous mathematics in early childhood setting, this assembled collage of children's own observations, activities and comments is in itself a work of art." Professor Carol Aubrey, Institute of Education, University of Warwick, UK. What are the most important aspects of mathematics for young children to learn? How do children learn mathematics? How can adults best ‘teach’ mathematics to children so young? The book informs practitioners, students and parents about how three– to five-year-olds learn mathematics, and shows them how best to develop enjoyable mathematical learning in early years settings. The book includes a summary of relevant research and considers issues relating to current practice. This book: Establishes principles for teaching mathematics to young children Takes into account the way children learn, including social, emotional, physical and cognitive aspects Helps practitioners find the middle ground between not initiating enough mathematical activity and being too directive Suggests principles and frameworks for planning and assessment. The book places particular emphasis on adult-initiated, number-focused activities and playful, challenging and sensitive teaching strategies to engage younger children. The strategies are based on research and work with practitioners, and are illustrated by children’s own responses, such as making number jokes. It covers key areas of mathematics, including number, shape and space, measures and problem solving, with appropriate expectations and common difficulties as well as suggested activities. Essential reading for those teaching or preparing to teach mathematics to young children, as well as parents interested in the mathematical education of their children.
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.
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.
Develop a deep understanding of mathematics. This user-friendly resource presents grades 6–8 teachers with a logical progression of pedagogical actions, classroom norms, and collaborative teacher team efforts to increase their knowledge and improve mathematics instruction. Make connections between elementary fraction-based content to fraction operations taught in the middle grades. 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 grow as both learners and teachers of mathematics. Gain clarity about the most productive progression of mathematical teaching and learning for grades 6–8. Access short videos that show what classrooms that are developing mathematical understanding should look like. Contents Introduction 1 Fraction Operations and Integer Concepts and Operations 2 Ratios and Proportional Relationships 3 Equations, Expressions, and Inequalities 4 Functions 5 Measurement and Geometry 6 Statistics and Probability Epilogue: Next Steps References and Resources Index
NOTE: Used books, rentals, and purchases made outside of Pearson If purchasing or renting from companies other than Pearson, the access codes for the Enhanced Pearson eText may not be included, may be incorrect, or may be previously redeemed. Check with the seller before completing your purchase. This access code card provides access to the Enhanced Pearson eText. Helping students make connections between mathematics and their worlds-and helping them feel empowered to use math in their lives-is the focus of this widely popular guide. Designed for classroom teachers, the book focuses on specific grade bands and includes information on creating an effective classroom environment, aligning teaching to various standards and practices, such as the Common Core State Standards and NCTM's teaching practices, and engaging families. The first portion of the book addresses how to build a student-centered environment in which children can become mathematically proficient, while the second portion focuses on practical ways to teach important concepts in a student-centered fashion. The new edition features a corresponding Enhanced Pearson eText version with links to embedded videos, blackline masters, downloadable teacher resource and activity pages, lesson plans, activities correlated to the CCSS, and tables of common errors and misconceptions. Invigorate learning with the Enhanced Pearson eText This access code card provides access to the new Enhanced Pearson eText, a rich, interactive learning environment designed to improve student mastery of content with the following multimedia features: NEW! Embedded videos. The Enhanced Pearson eText now includes links to videos throughout the text that provide examples of students' misconceptions, expand on key concepts, and demonstrate how to implement strategies and techniques in real classrooms. NEW! Downloadable Teacher Resource and Activity Pages that support teaching activities such as formative assessment and team-building are now available in the Enhanced Pearson eText at the point of use. NEW! Downloadable Blackline Masters in Part 2 Chapters. Readers may download Blackline Masters that support the activities and Expanded Lessons by clicking on hyperlinks embedded in the Enhanced Pearson eText. Appendix E includes a list of the Blackline Masters and a thumbnail version of each. *The Enhanced eText features are only available in the Pearson eText format. They are not available in third-party eTexts or downloads. *The Pearson eText App is available on Google Play and in the App Store. It requires Android OS 3.1-4, a 7" or 10" tablet, or iPad iOS 5.0 or later.
