The book synergizes research on number across two disciplines—mathematics education and psychology. The underlying problem the book addresses is how the brain constructs number. The opening chapter frames the problem in terms of children’s activity, including mental and physical actions. Subsequent chapters are organized into sections that address specific domains of number: natural numbers, fractions, and integers. Chapters within each section address ways that children build upon biological primitives (e.g., subitizing) and prior constructs (e.g., counting sequences) to construct number. The book relies on co-authored chapters and commentaries at the end of each section to create dialogue between junior faculty and senior researchers, as well as between psychologists and mathematics educators. The final chapter brings this work together around the framework of children’s activity and additional themes that arise in the collective work. The book is aimed to appeal to mathematics educators, mathematics teacher educators, mathematics education researchers, educational psychologists, cognitive psychologists, and developmental psychologists.

Explains how children between the ages of four and eight construct a deep understanding of numbers and the operations of addition and subtraction.

With this book, children can learn the numbers 1 to 20 while getting "e;in shape"e;! Each page shows children using their bodies to make the shape of numbers, alongside simple printed versions of each number. The book complements the similar Alphabet Fun title.

A concise introduction to personal and professional numeracy skills, helping readers to become more mathematically competent.

Making the transition to student-centered learning begins with finding ways to get students to share their thinking, something that can be particularly challenging for older learners. Authors Ruth Parker and Cathy Humphreys return with Digging Deeper: Making Number Talks Matter Even More, Grades 3-10, taking the readers into classrooms where their Number Talks routines are taught.In this comprehensive sequel to their best-selling book, Making Number Talks Matter, Parker and Humphreys apply their 15 minute lessons to older grade levels to inspire and initiate math talks. Through vignettes in the book, you'll meet other teachers learning how to listen closely to students and how to prompt them into figuring out solutions to problems. You will learn how to make on-the-spot decisions, continually advancing and deepening the conversation. Digging Deeper includes: Sample Problems: Digging Deeper is filled with a range of Number Talks problems, 10-15 minute warm-up routines that lend themselves to mental math and comparison of strategies Navigating Rough Spots: Learn how to create a safe environment for tricky, problematic, or challenging student discussions that can arise when talking through problems and sharing ideas Responding to Mistakes: Ways to handle misconceptions and mathematical errors that come up during the course of Number Talk conversations Digging Deeper is filled with teaching tips for using wait time between problems more efficiently, honoring student contributions while still correcting errors, and teaching concepts while nudging independent thinking. Through daily practice and open conversation, you can make Number Talks matter more.

This is the first book that makes the difficult and important subject of transcendental number theory accessible to undergraduate mathematics students. Edward Burger is one of the authors of The Heart of Mathematics, winner of a 2001 Robert W. Hamilton Book Award. He will also be awarded the 2004 Chauvenet Prize, one of the most prestigious MAA prizes for outstanding exposition.