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Children's Mathematics: Cognitively Guided Instruction [Paperback]

Thomas P. Carpenter (Author), Elizabeth Fennema (Author), Megan Loef Franke (Author), Linda Levi (Author), Susan B. Empson (Author)
4.4 out of 5 stars  See all reviews (9 customer reviews)

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Book Description

0325001375 978-0325001371 March 17, 1999

By the time they begin school, most children have already developed a sophisticated, informal understanding of basic mathematical concepts and problem-solving strategies. Too often, however, the mathematics instruction that we impose upon them in the classroom fails to connect with this informal knowledge. Children's Mathematics was written to help you understand children's intuitive mathematical thinking and use that knowledge to help children learn mathematics with understanding.

Based on more than twenty years of research, this book portrays the development of children's understanding of basic number concepts. The authors offer a detailed explanation and numerous examples of the problem-solving and computational processes that virtually all children use as their numerical thinking develops. They also describe how classrooms can be organized to foster that development. Two accompanying CDs provide a remarkable inside look at students and teachers in real classrooms implementing the teaching and learning strategies described in the text. Together, the book and CDs provide you with the foundation necessary to engage children in discussions of how they think through problems-providing suggestions for what problems to give and insight into what responses to expect, and how children's thinking will evolve.


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Editorial Reviews

About the Author

Thomas Carpenter is Professor of Curriculum and Instruction at the University of Wisconsin-Madison, where he has taught for twenty-five years. He is the former editor of the National Council of Teachers of Mathematics (NCTM) Journal for Research in Mathematics Education, and has received the NCTM Lifetime Achievement award for Distinguished Service to Mathematics Education among other awards.

Elizabeth Fennema is Emerita Professor of Curriculum and Instruction and Senior Scientist at the Wisconsin Center for Education Research at the University of Wisconsin-Madison. She has studied the teaching and learning of mathematics throughout her professional career, and is well known for her work on gender and mathematics.

Megan Loef Franke is an Associate Professor in the Department of Education at the University of California-Los Angeles and Director of Center X: Where Research and Practice Intersect for Urban School Professionals. Her work focuses on understanding and supporting teacher learning through professional development.

Linda Levi is the Director of Cognitively Guided Instruction (CGI) Initiatives at Teachers Development Group, a nonprofit organization dedicated to increasing all students' understanding and achievement through teacher professional development. She currently works with schools, districts, education cooperatives and State Departments of Education to provide CGI professional development. Linda was coauthor of Thinking Mathematically (Heinemann 2003), and coauthor of Heinemann's top selling math title Children's Mathematics: Cognitively Guided Instruction, which has helped tens of thousands of teachers understand children's intuitive problem-solving and computational skills. Children's Mathematics remains a hallmark contribution to mathematics education since its publication in 1999.

Susan B. Empson is an Associate Professor of Science and Mathematics Education at The University of Texas at Austin. Her research has been supported by the National Science Foundation and the Spencer Foundation, and has been published in numerous journals including Cognition and Construction, Journal for Research in Mathematics Education, Teaching Children Mathematics, and Journal of Mathematics Teacher Education. Susan was coauthor of Heinemann's top selling math title Children's Mathematics: Cognitively Guided Instruction, which has helped tens of thousands of teachers understand children's intuitive problem-solving and computational skills. Children's Mathematics remains a hallmark contribution to mathematics education since its publication in 1999.

Product Details

  • Paperback: 128 pages
  • Publisher: Heinemann (March 17, 1999)
  • Language: English
  • ISBN-10: 0325001375
  • ISBN-13: 978-0325001371
  • Product Dimensions: 9.1 x 7.2 x 0.4 inches
  • Shipping Weight: 9.6 ounces (View shipping rates and policies)
  • Average Customer Review: 4.4 out of 5 stars  See all reviews (9 customer reviews)
  • Amazon Best Sellers Rank: #12,407 in Books (See Top 100 in Books)

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11 of 11 people found the following review helpful:
5.0 out of 5 stars An excellent tool, June 13, 2008
This review is from: Children's Mathematics: Cognitively Guided Instruction (Paperback)
This book revolutionized the way that I taught math in my classroom. I was a more informed instructor, and it allowed me to group, scaffold, and individualize my instruction. The year that I implemented these techniques into my fifth grade class, we made an average of two years growth in one year! Highly recommend this one!
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7 of 7 people found the following review helpful:
5.0 out of 5 stars Children's mathematics; Cognitive Guided Instruction, October 10, 2007
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This review is from: Children's Mathematics: Cognitively Guided Instruction (Paperback)
Excellent resource for those wishing to guide students from informal understanding of solving word problems to problem solving. The authors' examples of the various problem types coupled with explanations and strategically placed video clips (CD included) guide even the most novice CGI instructor to a clear understanding of the problems and expected student strategies, classroom environment and expectations needed to implement this teaching strategy.
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2 of 2 people found the following review helpful:
5.0 out of 5 stars Amazing teaching resource, August 20, 2010
This review is from: Children's Mathematics: Cognitively Guided Instruction (Paperback)
As a fourth and fifth grade teacher I was always under the impression that CGI was only for Kindergarten through third grade. However, once kids started filtering into my class who had recieved CGI instruction, I was blown away! Their critical thinking and ability to solve math problems (all the different types of word problems that the book recommends)was the most incedible thing I had ever seen students do. I immediately read this book and even went through some workshops and training through my school district.

The book explains the different types of math problems contexts for addition, subtraction, multiplication, and division, which most college of education programs do not include. For example: when creating subtraction word problems we need to pose some where the start is unknown (x - 5 = 6), some where the change is unknown (11- x = 6), and others where the result is unknown (11-6= x). When posed in a word context, contrary to our beliefs, students ARE able to reason through the problems and solve them. The book teaches you what types of solutions to expect from your students and how to implement CGI in your classroom.

When starting CGI for the first time, I highly recommend playing around with a few problem types at first so you do not get overwhelmed. It is a lot of fun and you can learn a lot about how your kids think if you just DON'T TELL THEM HOW TO SOLVE THE PROBLEMS, but let them explore and be critical thinkers. :)

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Inside This Book (learn more)
First Sentence:
Initially, young children have quite different conceptions of addition, subtraction, multiplication, and division than adults do. Read the first page
Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
partitive division, direct modeling, direct modeling strategies, finger with each count, direct modelers, more toy cars, loose cubes, invented algorithms, many guppies, many toy cars, linking cubes, division word problems, counting strategies, many cupcakes, ten cubes, counting sequence, individual cubes, many stickers, many more dollars, join problems, written algorithms, division problems, multidigit numbers
Key Phrases - Capitalized Phrases (CAPs): (learn more)
Result Unknown, Change Unknown, Measurement Division, Start Unknown, Whole Unknown, Difference Unknown, Joining All, Susan Gehn, Counting Down, Multiplicative Comparison, Ann Badeau, Mazie Jenkins, Kathy Statz, Sue Ellen, Invented Algorithm, Derived Facts
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Front Cover | Table of Contents | First Pages | Back Cover | Surprise Me!
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