children s mathematics second edition cognitively guided instruction

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Children S Mathematics

Author : Thomas P. Carpenter
ISBN : 0325052875
Genre : Education
File Size : 32. 90 MB
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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.

Extending Children S Mathematics

Author : Susan B. Empson
ISBN : 0325030537
Genre : Education
File Size : 36. 1 MB
Format : PDF
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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.

Children S Mathematics

Author : Thomas P. Carpenter
ISBN : 0325006415
Genre : Education
File Size : 73. 54 MB
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Contained in this Guide is suggestions for implementing a Professional Development Program, a selected annotated bibliography, and a selection of resources such as sample workshop agendas and worksheets.

Thinking Mathematically

Author : Thomas P. Carpenter
ISBN : 0325005656
Genre : Education
File Size : 42. 19 MB
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In this book the authors reveal how children's developing knowledge of the powerful unifying ideas of mathematics can deepen their understanding of arithmetic

Math Exchanges

Author : Kassia Omohundro Wedekind
ISBN : 9781571108265
Genre : Education
File Size : 67. 84 MB
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Traditionally, small-group math instruction has been used as a format for reaching children who struggle to understand. Math coach Kassia Omohundro Wedekind uses small-group instruction as the centerpiece of her math workshop approach, engaging all students in rigorous "math exchanges." The key characteristics of these mathematical conversations are that they are: 1) short, focused sessions that bring all mathematical minds together, 2) responsive to the needs of the specific group of mathematicians, and 3) designed for meaningful, guided reflection. As in reading and writing workshop, students in Kassia's math workshop are becoming self-directed and independent while participating in a classroom community of learners. Through the math exchanges, students focus on number sense and the big ideas of mathematics. Teachers guide the conversations with small groups of students, mediating talk and thinking as students share problem-solving strategies, discuss how math works, and move toward more effective and efficient approaches and greater mathematical understanding. Although grounded in theory and research, Math Exchanges is written for practicing teachers and answers such questions as the following: How can I use a math workshop approach and follow a certain textbook or set of standards? How should I form small groups? and How often should I meet with small groups? What should I focus on in small groups? How can I tell if my groups are making progress? What do small-group math exchanges look like, sound like, and feel like?

Implementing Standards Based Mathematics Instruction

Author : Mary Kay Stein
ISBN : 0807739073
Genre : Education
File Size : 33. 2 MB
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Presents prevalent cases of maths instruction drawn from research of classroom lessons. The "Mathematical Tasks Framework", developed by the authors, offers teachers the means to evaluate instructional decisions, choice of materials and learning outcomes.

Creativity And The Arts With Young Children

Author : Rebecca Isbell
ISBN : 9781285225524
Genre : Education
File Size : 41. 57 MB
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CREATIVITY AND THE ARTS WITH YOUNG CHILDREN, Third Edition, is written for early childhood educators as well as those who work with children from birth through age eight. The text focuses on helping educators make the vital connection to the arts--including music, movement, drama, and the visual arts--throughout all areas of the classroom and curriculum, and on developing creative teachers who will be able to foster an artistic environment. Observations and photos of teachers and children demonstrate practical ways the arts can be used to help children reach their potential. Educators will find many ideas for open-ended activities that are important for the development of young children, and which will encourage them to think in new ways. Discussion of professional standards and recommendations allows teachers to be cognizant of goals that are important in the early years. Thorough in its coverage, the text speaks to children with special needs and cultural diversity, leaving readers with a complete information resource regarding arts in the young child's classroom. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Knowing And Teaching Elementary Mathematics

Author : Liping Ma
ISBN : 9781135149499
Genre : Education
File Size : 69. 9 MB
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Studies of teachers in the U.S. often document insufficient subject matter knowledge in mathematics. Yet, these studies give few examples of the knowledge teachers need to support teaching, particularly the kind of teaching demanded by recent reforms in mathematics education. Knowing and Teaching Elementary Mathematics describes the nature and development of the knowledge that elementary teachers need to become accomplished mathematics teachers, and suggests why such knowledge seems more common in China than in the United States, despite the fact that Chinese teachers have less formal education than their U.S. counterparts. The anniversary edition of this bestselling volume includes the original studies that compare U.S and Chinese elementary school teachers’ mathematical understanding and offers a powerful framework for grasping the mathematical content necessary to understand and develop the thinking of school children. Highlighting notable changes in the field and the author’s work, this new edition includes an updated preface, introduction, and key journal articles that frame and contextualize this seminal work.

How People Learn

Author : National Research Council
ISBN : 9780309131971
Genre : Education
File Size : 84. 11 MB
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First released in the Spring of 1999, How People Learn has been expanded to show how the theories and insights from the original book can translate into actions and practice, now making a real connection between classroom activities and learning behavior. This edition includes far-reaching suggestions for research that could increase the impact that classroom teaching has on actual learning. Like the original edition, this book offers exciting new research about the mind and the brain that provides answers to a number of compelling questions. When do infants begin to learn? How do experts learn and how is this different from non-experts? What can teachers and schools do-with curricula, classroom settings, and teaching methods--to help children learn most effectively? New evidence from many branches of science has significantly added to our understanding of what it means to know, from the neural processes that occur during learning to the influence of culture on what people see and absorb. How People Learn examines these findings and their implications for what we teach, how we teach it, and how we assess what our children learn. The book uses exemplary teaching to illustrate how approaches based on what we now know result in in-depth learning. This new knowledge calls into question concepts and practices firmly entrenched in our current education system. Topics include: How learning actually changes the physical structure of the brain. How existing knowledge affects what people notice and how they learn. What the thought processes of experts tell us about how to teach. The amazing learning potential of infants. The relationship of classroom learning and everyday settings of community and workplace. Learning needs and opportunities for teachers. A realistic look at the role of technology in education.

Learning And Teaching Early Math

Author : Douglas H. Clements
ISBN : 9781134080717
Genre : Education
File Size : 75. 10 MB
Format : PDF, Kindle
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In this important book for pre- and in-service teachers, early math experts Douglas Clements and Julie Sarama show how "learning trajectories" help diagnose a child’s level of mathematical understanding and provide guidance for teaching. By focusing on the inherent delight and curiosity behind young children’s mathematical reasoning, learning trajectories ultimately make teaching more joyous. They help teachers understand the varying levels of knowledge exhibited by individual students, which in turn allows them to better meet the learning needs of all children. Using straightforward, no-nonsense language, this book summarizes the current research about how children learn mathematics, and how to build on what children already know to realize more effective teaching. This second edition of Learning and Teaching Early Math remains the definitive, research-based resource to help teachers understand the learning trajectories of early mathematics and become quintessential professionals. Updates to the new edition include: • Explicit connections between Learning Trajectories and the new Common Core State Standards. • New coverage of patterns and patterning. • Incorporation of hundreds of recent research studies.

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