Children's Mathematics: Cognitively Guided Instruction

by Thomas P. Carpenter, Elizabeth Fennema, Megan Loef L. Franke

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

Genres: Education, Teaching, Professional Development, School, Mathematics, Nonfiction

Paperback

First published March 17, 1999

Reviews

[Sarah · Rating 4 out of 5]

elemetary school mathematics with a freirian twist... think five-year-olds can't solve complex division problems? think again. but more importantly, here's a methodology that embraces non-hierarchical and anti-oppressive learning techniques.

when public school math education is typically about placing children into boxes, and when math knowledge is cultivated for the purposes of amassing capital and war technology, it is refreshing to be exposed to a framework that is about communal learning, disrupting authority, and children's empowerment. the text is not explicitly radical, but nevertheless has the potential to rock my future fourth grade classroom... i'll just have to tweak it a little bit here.... add a few gay penguins there...

[Agie Cummings · Rating 5 out of 5]

Another book I read for work. Clear, actionable examples and explanation of the Cognitively Guided Instruction approach to teaching mathematics. Definitely recommend to teachers looking to ensure their math practice is best aligned to meeting student needs and pushing their strategical thinking.

[Meg]

This book discusses the CGI strategy. The CGI strategy is to approach mathematics from a discovery/problem solving angle. The goal is to get students to explore through metacognition and become life long problem solvers. CGI teachers prompt students to discover their own understanding of mathematics and apply these to problem solving.

[Lori · Rating 4 out of 5]

This is an excellent book for any teacher who wants to understand how math concepts progress developmentally in children. It serves as a guide to understand their thinking so instruction can match and move them forward. Excellent!

[Maya · Rating 2 out of 5]

a little too basic, good for readers new to cognitively guided instruction

[Annie · Rating 5 out of 5]

Originally posted on my blog Nonstop Reader.

Children's Mathematics: Cognitively Guided Instruction is a clearly written supportive and accessible guide for facilitators and teachers to help children succeed with learning mathematical concepts with minimal frustration. Released in this edition in 2014 by Heinemann, it's 240 pages and is available in paperback format. It's unclear from the publisher's info, but the book is full of links and support videos which would be more accessible in ebook format, if it's available in electronic format. The electronic ARC provided for review contains hyperlinked table of contents and links to online resources, so if possible, I recommend at least one copy of the ebook for ease of navigation.

I've been an advocate for STE(A)M for decades. Our capacity for innovation and probably future survival are dependent on the critical reasoning skills we foster in the next generation(s). They're literally our future. When I find books which support learning styles and techniques which actually work and are logical and have practice based data to back them up, I am thrilled. This is a sensible and very accessible guide to using children's natural developmental understanding to build math skills in the classroom.

This book is aimed at professional educators although it will also be appropriate for some homeschooling/hybrid resource people. The book is based on CGI techniques (Cognitively Guided Instruction) and uses the differing ways children's cognitive development occurs to creatively support their learning styles to foster *understanding* of concepts as opposed to rote learning (which gives no firm basis to build on).

The introductory chapters explain the ways children formulate mathematical problems differently than adults, and how teachers can utilize those differences to help them succeed at problem solving. The book contains concrete techniques for tool building and retention.

The book contains the methodology and techniques for classroom practice as well as appendices containing research data and resource links.

This is a well written and practical guide to using natural psychological development to enhance students' understanding and facility with math.

Four and a half stars.

Disclosure: I received an ARC at no cost from the author/publisher for review purposes.

[Jamie · Rating 5 out of 5]

This book should be required reading for all educators teaching math (and their coaches)! As children enter school, we typically see them using manipulatives to begin learning a concept and quickly move them into using standard algorithms. Carpenter et. al posit that, to truly have an understanding of numbers and mathematics we should tell stories and let children work through the phases of learning (with manipulatives, drawings, invented algorithms, and standard algorithms) at their own pace. Children who are given multiple opportunities to solve story problems in ways of their own choosing are better able to describe their actions and thinking, leading to better understanding. This is true of prekindergarten through high school-aged students. The authors show how students move along a continuum of learning from simple addition and subtraction stories, through an understanding of the base ten system, and into more advanced concepts such as multiplication and division. This book provides QR codes that link to video examples of the practices being described, as well as exercises to help teachers create their own math stories that are appropriate to their students' levels of learning.

[Stephanie Rossman · Rating 5 out of 5]

In terms of a mathematical textbook, this is about as good as it gets. This book focuses on cognitively guided instruction in grades Pre-K through 3, although many of these strategies can be extended into a middle school or high school class. My favorite parts of this book were the QR codes that could be scanned to watch videos of the strategies in action. It definitely felt made me curious about how students think about and interpret mathematical problems and I definitely had to try some of them out on my own children.

Perhaps this book was so interesting to me since I’m a high school math teacher and the young learner is a relatively new concept for me? Either way, I appreciate this strategy and can see its value in mathematics education. The goal is not to learn a procedure to solve a problem, it is to solve a problem and learn efficient procedures in the process.

[Markwoods · Rating 2 out of 5]

I’d like to think we can teach like this.

Various issues though. It’s another of these approaches that will solve your problems. I get tired of hearing how wonderful approach x is. The promises tend to repeat themselves. I wonder if teachers who’ve made marvellous progress in one of these wonder approaches find a second approach. What do they make of the second approach’s claims?

Also, there little peer review. The references are mainly to research done by the main man. It’s like a cult leader referring to more of his own books.

Reading this- that’s part of my life I’m never getting back.

[Mary Beth]

This book is a helpful resource to learn about the CGI strategy used to help with problem-solving and explaining. The goal of teaching like this is to become a lifelong problem solve. It provides information on the development of children’s mathematical thinking and the importance of not boxing our children into specific strategies and methods. There are ways for teachers to promote flexible thinking. We can expose kids way earlier on to complex thinking needed but need to set the environment up for it. When using CGI, the goal is to have students explore.

[Alicia Bayer · Rating 3 out of 5]

This is a good book, just very dry. It’ll make a great textbook for elementary ed majors but while I often enjoy reading educational books for pleasure, this one was hard to make myself keep picking up. Recommended more for teachers and those going into the field rather than homeschool parents looking for engaging ways to teach math.

I read a digital version of this book for review.

[Reagan Suzanne · Rating 4 out of 5]

As a veteran teacher (now instructional coach), the first few chapters dragged for me. BUT I think they should be necessary reading for pre service and beginning teachers. After the first few chapters, I thought the information was great no matter how long you’ve been teaching. I also love that there are videos and pictures of student work included!

[kar · Rating 4 out of 5]

This text is a well-written, supportive, and accessible guide to helping children succeed in mathematics with minimal frustration, using children's natural developmental understanding to build math skills in the classroom.
Very handy! Thank you to Heinemann and NetGalley for this advanced copy.

[Shelli · Rating 4 out of 5]

Learned a lot about the operations! Whoa.

[Libni Berenice · Rating 5 out of 5]

a good book for elementary school teachers

[Mikayla Beckman · Rating 3 out of 5]

I read this book over the course of the semester for my curriculum class. It was super interesting!

[Kassandra · Rating 3 out of 5]

Not as informative about the CGI process as I had hoped. Great at explaining some of the thoughts students have as they approach problems.

[Mary Beth Revesz · Rating 5 out of 5]

One of the best books about teaching math I have ever read!

[Danielle Cardoza · Rating 4 out of 5]

It was alright and I liked that it used the images to explain concepts. It was just boring but I can’t expect anything else from a book about elementary school math so I’m alright with it.

[Dali Castillo · Rating 5 out of 5]

Great Resource

This is a very good resource for teachers or future teachers. One of the many things I found helpful is the explanation of the different strategies children use to solve problems and how the wording of the problem impacts the strategy used. The reflection questions that some of the chapters included were another thing I found helpful. However, most helpful of all were the many video clips. They really give good insight into the thinking and strategies the students use to solve problems. Listening to them explain their thinking, as well as listening to the instructor ask questions that assists the students in expressing their thought processes, were extremely helpful. It really drives home the importance of observing the student, listening to them express their thinking, and using what you glean from that to impact your instruction.

While I found this to be a very helpful tool for educators, in my humble opinion, I would not recommend it to homeschool parents. The terminology used is very textbookish and could be somewhat daunting for one who is not used to that type of terminology. I would also caution those who work with English Language Learner (ELL) students. While math is a fairly universal language, one must be aware of what country the ELL student is from. This makes a difference when the student is from a country where math procedures are not the same as what most consider the norm. That being said, recommendations in this book are still helpful for ELLs, but with modifications.

Thank you to NetGalley for providing me with a copy of this book. All comments and opinions are voluntary and completely my own.

[Shon · Rating 3 out of 5]

This book is a text book that teaches the reader how to teach math based on children's cognitive development. This book read like a text book; it made use of various math based terminology and examples. The book helped the reader to evaluate the way they view math and how it is taught. Some of the content was hard to understand, and needed a more concrete explanation from someone that had expertise in that field. The book is broken down into addition, subtraction, multiplication, and division which are broken down into sub categories. The book itself is not a difficult read, but some of the concepts are hard to grasp. Overall the book is extremely informative, and if read along with instruction and practice with the various methods, the book becomes easier to understand ad digest. I believe the book achieves what it was set out to do, which is inform reader of cognitively guided math instruction. The book provides information to help you understand what that what exactly cognitively guided instruction (CGI) is and how it benefits students, and it also gives step-by-step instructions on how to implement lessons in the classroom. The book has the feel of a instructional text and a manual. This is not a book I would use to teach a class, simply because I had a lot of difficulty understanding the text myself, and would not feel comfortable using this book as a teaching tool. However this book would be good when talking about the various ways information are presented in a text. This book provides information in a very formal manner, and there is not much that you can glean from the authors except that they are experts in this particular field. There is no since of the authors actual personalities coming through the words in this book; you would not know if their was one author or 5 if they were not listed in the book.

[Katy · Rating 4 out of 5]

Excellent resource for elementary math teachers, even beyond primary years.

[Kelly Sickle · Rating 5 out of 5]

This is a must read for all teachers!!

[Ali Stewart · Rating 4 out of 5]

excellent! easy to read, very important for teacher's to know