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Children's Mathematics: Cognitively Guided Instruction [Paperback]

Thomas P Carpenter , Elizabeth Fennema , Megan Loef Franke , Linda Levi , Susan B Empson
4.3 out of 5 stars  See all reviews (18 customer reviews)

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Book Description

March 17, 1999 0325001375 978-0325001371 1 5 - 8 years

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.


Frequently Bought Together

Children's Mathematics: Cognitively Guided Instruction + Extending Children's Mathematics: Fractions & Decimals: Innovations In Cognitively Guided Instruction + Thinking Mathematically: Integrating Arithmetic & Algebra in Elementary School
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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

  • Age Range: 5 - 8 years
  • Paperback: 112 pages
  • Publisher: Heinemann; 1 edition (March 17, 1999)
  • Language: English
  • ISBN-10: 0325001375
  • ISBN-13: 978-0325001371
  • Product Dimensions: 9.2 x 7.4 x 0.3 inches
  • Shipping Weight: 9.6 ounces (View shipping rates and policies)
  • Average Customer Review: 4.3 out of 5 stars  See all reviews (18 customer reviews)
  • Amazon Best Sellers Rank: #14,149 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews
15 of 15 people found the following review helpful
5.0 out of 5 stars An excellent tool June 13, 2008
Format: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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11 of 11 people found the following review helpful
5.0 out of 5 stars Amazing teaching resource August 20, 2010
By ashkaz
Format: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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8 of 8 people found the following review helpful
5.0 out of 5 stars Children's mathematics; Cognitive Guided Instruction October 10, 2007
Format:Paperback|Verified Purchase
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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1 of 1 people found the following review helpful
5.0 out of 5 stars Becoming a Better Teacher! November 26, 2013
Format:Paperback|Verified Purchase
This is a book that can help every elementary teacher become a better children's mathematics teacher. The DVD disc helps with the reading;
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1 of 1 people found the following review helpful
5.0 out of 5 stars Great resource April 8, 2013
Format:Paperback|Verified Purchase
As a student learning to become a teacher I found this book a great resource. It has changed the way I view mathematics myself and how I will teach it. The short chapters and jam packed with information and not with a lot of fluff.
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1 of 1 people found the following review helpful
5.0 out of 5 stars Great book! January 26, 2013
By mac6
Format:Paperback|Verified Purchase
For starting this type of math program for the first time this book is what you need. It really helped me as I taught.
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1 of 1 people found the following review helpful
5.0 out of 5 stars THE BEST! July 16, 2011
By Sara
Format:Paperback
First of all, this is research, not a "math curriculum" or "program". This is about how children think about and understand math. I was very skeptical at first. However, after seeing the results in the classroom - I am a believer! Children understand a lot about mathematics that we don't give them credit for because they don't express their understanding in standard algorithms or with typical math vocabulary. CGI encourages the teacher to work with a student's natural understanding of math and to build on that. There is a teacher training that goes with this - it takes about 24 days of training over 3 years to complete. One of the more difficult trainings I have taken, (besides this book it also required a bottle of aspirin!) but without a doubt one of the very best! It is well worth the effort! Read the book, and if at all possible, take a CGI class!
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1 of 1 people found the following review helpful
5.0 out of 5 stars Children's Mathematics July 12, 2010
By Cathy
Format:Paperback|Verified Purchase
This is an excellent resource for anyone who wishes to understand children's mathematical thinking. It is a great tool for teachers.
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Most Recent Customer Reviews
5.0 out of 5 stars Good book
quick shipping, great condition. thank you. great concept to teach math to children. my son has started loving it and we have good times every week.
Published 2 months ago by Anand Belaguly
5.0 out of 5 stars CGI
Great read!! Really helps meet the needs of my students in the classroom. I would highly recommend this book to anyone.
Published 4 months ago by Tamara
5.0 out of 5 stars Great math resource!
This book is an excellent resource for learning about how children solve problems and how to teach them to recognize problem types.
Published 7 months ago by HK
1.0 out of 5 stars Disapointed
When I got my shipment in the mail it was missing the cds and you can't buy them on their own so now I need to buy the book again.
Published 12 months ago by kelly gorcica
1.0 out of 5 stars "think system" from music man
this book implies that if children explore enough they can arrive at the answers on their own....what a load. Ever see the movie The Music Man? Read more
Published 14 months ago by Sarah S. Hamilton
5.0 out of 5 stars An "EVEN" Can't Wait to Read Another Review
Dear Sir and Talented Math Team,

I can't wait to save up my pennies to BUY this book. Even your highlighted sections were helpful. : )
Published 21 months ago by Steve
2.0 out of 5 stars Simplistic Thoughts
The idea behind CGI is that students intuitively understand mathematical concepts and they can develop a more refined understanding and make the math their own if allowed to work... Read more
Published on May 6, 2011 by Andrew Bell
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