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"With the collaboration of a number of dedicated teachers and their students, Susan Empson and Linda Levi have produced a volume that is faithful to the basic principles of CGI while at the same time covering new ground with insight and innovation." -Thomas P. Carpenter This highly anticipated follow-up volume to the landmark Children's Mathematics: Cognitively Guided Instruction addresses the urgent need to help teachers understand and teach fraction concepts. Fractions remain one of the key stumbling blocks in math education, and here Empson and Levi lay a foundation for understanding fractions and decimals in ways that build conceptual learning. They show how the same kinds of intuitive knowledge and sense making that provides the basis for children's learning of whole number arithmetic can be extended to fractions and decimals. Just as they did in Children's Mathematics and Thinking Mathematically, Empson and Levi provide important insights into children's thinking and alternative approaches to solving problems. Three themes appear throughout the book: building meaning for fractions and decimals through discussing and solving word problems the progression of children's strategies for solving fraction word problems and equations from direct modeling through relational thinking designing instruction that capitalizes on students' relational thinking strategies to integrate algebra into teaching and learning fractions. With illuminating examples of student work, classroom vignettes, "Teacher Commentaries" from the field, sample problems and instructional guides provided in each chapter, you'll have all the tools you need to teach fractions and decimals with understanding and confidence.
With a focus on children's mathematical thinking, this second edition adds new material on the mathematical principles underlying children's strategies, a new online video that illustrates student teacher interaction, and examines the relationship between CGI and the Common Core State Standards for Mathematics.
In this book the authors reveal how children's developing knowledge of the powerful unifying ideas of mathematics can deepen their understanding of arithmetic
Tap into the Power of Child-Led Math Teaching and Learning Everything a child does has mathematical value--these words are at the heart of this completely revised and updated third edition of The Young Child and Mathematics. Grounded in current research, this classic book focuses on how teachers working with children ages 3 to 6 can find and build on the math inherent in children's ideas in ways that are playful and intentional. This resource - Illustrates through detailed vignettes how math concepts can be explored in planned learning experiences as well as informal spaces - Highlights in-the-moment instructional decision-making and child-teacher interactions that meaningfully and dynamically support children in making math connections - Provides an overview of what children know about counting and operations, spatial relations, measurement and data, and patterns and algebra - Offers examples of informal documentation and assessment approaches that are embedded within classroom practice Deepen your understanding of how math is an integral part of your classroom all day, every day. Includes online video!
"The best source I have seen challenging mathematically talented students. The activities are thought provoking and enjoyable. I will recommend this book to parents as well as educators of mathematically talented students!" Sally Reis Past President of The National Association for Gifted Children Challenge, engage, and inspire your mathematically promising students! Combining theory and practice, Sheffield expertly guides the reader through the process of mathematical talent development from identifying students with mathematical potential, to finding and creating first-rate problems for exploration and strategies for assessment. The multi-level investigations in this book are designed to challenge students and inspire deeper and more original mathematical thinking in Number and Operations, Algebra, Geometry and Measurement, and Data Analysis and Probability. Each investigation is developed in the following easy-to-follow format: Relate—sets the stage for the investigation by connecting it to prior learning and the NCTM Principles and Standards Investigate—poses the initial problem to start students thinking about the investigation Evaluate and Communicate—provides solutions, probing assessment questions, and suggestions for teacher responses Create—offers ideas for extending and deepening the investigation, allowing even the most accomplished students to add depth and complexity to their reasoning Discussion—gives teachers hints on what to look for in student solutions, as well as ideas for encouraging students to dig more deeply into the mathematical concepts that are presented Mathematically promising students have the potential to become the leaders and problem solvers of the future. Extending the Challenge in Mathematics provides the practical tips and tools educators need to help their students develop this potential to the fullest.
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.
Explore STEM concepts through making and tinkering!
Use the powerful strategies of play and storytelling to help young children develop their "math brains." This easy-to-use resource includes fun activities, routines, and games inspired by children's books that challenge children to recognize and think more logically about the math all around them.
With small steps and our carefully crafted questions, every pupil will achieve greater progress. Designed to be used flexibly, this second edition textbook has been updated to include more Mastery-style questions and whole-class activities. Whether you follow a full Mastery scheme, choose to use Mastery aspects or you're just looking for quality resources, our three textbooks support the way you want to teach. Each book gradually builds on prior knowledge, developing pupils' confidence, fluency, reasoning and problem-solving skills. · Secure understanding with differentiated questions and worked examples that build on prior knowledge, following the 'do it, secure it, deepen it' Mastery structure · Recap skills and topics from Key Stage 2, ensuring a smooth transition to Key Stage 3 · Target key skills using the fluency, reasoning and problem-solving markers in the margin · Build confidence with starter activities and warm-up questions to introduce each concept · Develop reasoning skills using non-examples, where pupils identify mistakes in sample answers · Track progress through review questions, building key skills and knowledge · Benefit from the expertise of UK Mastery trained subject specialists with over 30 years of teaching experience · Cover the full UK National Curriculum and all four strands - number, algebra, geometry and measures, statistics and probability - within our three restructured textbooks for Key Stage 3 Our flexible, Mastery-led approach Our flexible approach allows you to teach maths your way. You can choose to focus on building understanding using the graduated questions or take a Mastery approach to exposition using manipulatives and 'concrete, pictorial, abstract' in the optional class activities. Answers will be provided online.
Minilessons for Extending Multiplication and Division is one of two yearlong resource guides in Contexts for Learning Mathematics' Investigating Multiplication and Division (3 - 5) Minilessons for Extending Multiplication and Division can be helpful in grades 4 - 5 as students work with multiplication and division beyond the basic facts. This guide contains 77 minilessons structured as strings of related computation problems. They are likely to generate discussion of certain strategies or big ideas that are landmarks on the landscape of learning for multiplication and division, particularly using numbers with two and three digits. Although the emphasis is on the development of mental arithmetic strategies, this does not mean learners have to solve the problems in their heads - but it is important for them to do the problems with their heads In other words, as you use this guide, encourage students to examine the numbers in each problem and think about clever, efficient ways to solve it. The relationships between the problems in the minilesson will support students as they progress through the string. The open array is used throughout to represent student strategies. To learn more visit http: //www.contextsforlearning.com