Thinking Mathematically: Integrating Arithmetic & Algebra in Elementary School by Thomas P Carpenter

by Thomas P. Carpenter

In "Children's Cognitively Guided Instruction," Thomas Carpenter, Megan Franke, and Linda Levi helped tens of thousands of teachers understand children's intuitive problem-solving and computational processes. More important, the authors helped teachers figure out how to use that knowledge to enhance students' understanding of arithmetic. In this book the same author team takes teaching and learning mathematics to the next level, revealing how children's developing knowledge of the powerful unifying ideas of mathematics can deepen their understanding of arithmetic and provide a solid foundation for learning algebra. This book also shows how teachers can increase their own knowledge of mathematics in the process of interacting with their children and reflecting about their practice."Thinking Mathematically" provides numerous examples of classroom dialogues that indicate how algebraic ideas emerge in children's thinking and what problems and questions help to elicit them. Special features of the book help teachers develop their own understanding of mathematics along with their students': Teacher Commentaries capture the voices of a number of teachers, providing realistic portrayals of what happens in class. End-of-chapter Challenges offer a variety of problems and activities for teachers to increase their own knowledge of mathematics and to help their students develop algebraic thinking. An accompanying CD provides rich illustrations of ideas in the book-extended interactions with individual children or classroom episodes-all clearly linked to the text.

Genres: Teaching, Professional Development

Paperback

First published January 15, 2003

Reviews

[Adam · Rating 5 out of 5]

This is relevant for middle school teachers! It's the best resource out there that connects arithmetic and algebra that I've read. With two very simple tools--true/false and open number sentences--the authors have created a path to understanding the big ideas of algebra. They've also centered everything around conjecture; they describe classrooms where kids always ask themselves "Does this always work? Why or why not?" Students get conjectures on the wall and question them all year. How cool! The accompanying videos show that this is more than fantasy.

A bunch of books compliment this one well.

For middle-school teachers, pair this with Cathy Humphrey's current "Making Number Talks Matter."

For teachers grappling with problem-based math teaching, pair this with James Hiebert's "Making Sense," a book cowritten by one of these authors.

This is the second book in the Cognitively Guided Instruction series. Check out "Children's Mathematics" and "Extending Children's Mathematics," books one and three respectfully.

[Andrea · Rating 4 out of 5]

This book gave me so much to think about when teaching math. I really want to encourage algebraic thinking in my elementary students, and this book gave lots of good ways to do that, including lots of examples. I have already tried some out on my students and they really got them thinking.

[Anna · Rating 5 out of 5]

A great resource for any elementary school teacher that wants to prepare students for algebra. The book offers great ideas on how to incorporate algebraic thinking into elementary mathematics instruction. The CD will inspire you!

[Joe · Rating 4 out of 5]

Fantastic resource for introducing fundamentals of algebra in early elementary math education. The book is very accessible and informative. Appreciated the emphasis on teacher/student interactions through transcripts of conversation (there's a DVD, as well).

[Brenda · Rating 4 out of 5]

This book, along with Jo Boaler's number talks and Week of Inspirational Maths have given me a fresh outlook on my math teaching. Feeling inspired and interested to see how the kids feel about understanding and problem/puzzling solving.

[Courtney Lofgren · Rating 4 out of 5]

I do not think I would have gotten as much value from this book if I did not have a chance to apply what I learned. Thanks Maggie!

[Charla Cosgray · Rating 4 out of 5]

This book, along with our book study, helped to change the way I think about and teach math.

[Lauren Flower · Rating 5 out of 5]

Practical and useful. Provided many resources and support in engaging students in all modalities. I use this book as a resource and often refer to it when lesson planning.