Constructing Number

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.

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

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.

"Sense-making makes mathematics personal, and when it's personal, it comes to life. And that's how Number Talks can really make a difference."--Ruth Parker and Cathy Humphreys How teachers react to wrong answers and mistakes makes all the difference in mathematics class. The response can determine whether a student tunes out or delves in. In this comprehensive sequel to Making Number Talks Matter, Ruth Parker and Cathy Humphreys explore more deeply the ways Number Talks can transform student understanding of mathematics. Through vignettes and videos, you'll meet teachers who are learning to listen closely to students and prompting them to figure things out for themselves. You'll learn how they make on-the-spot decisions, continually advancing and deepening the conversation. Personal and accessible, this book highlights: The kinds of questions that elicit deeper thinking Ways to navigate tricky, problematic, or just plain hard exchanges in the classroom How to more effectively use wait time during Number Talks The importance of creating a safe learning environment How to nudge students to think more flexibly without directing their thinking This book offers a rich assortment of ideas to help make Number Talks even more vibrant and meaningful for you and your students.

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

Making Numbers shares exemplars of good practice drawing on the latest research on using manipulatives to develop understanding of arithmetic. Focusing initially on the teaching of numbers from 1-12, Making Numbers progresses to 200 and beyond, including ideas for teaching partitioning, arrays, and times tables.

"A multimedia professional learning resource"--Cover.

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.

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 math class. Authors Ruth Parker and Cathy Humphreys introduce. Making Number Talks Matter: Developing Mathematical Practices and Deepening Understanding, Grades 3-10, taking the readers into classrooms where their Number Talks routines are taught. Parker and Humphreys apply their 15 minute lessons 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. Making Number Talks Matter includes: Sample Problems: 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 fortrickyor 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 Making Number Talks Matter is filled with teaching tips for honoring student contributions while still correcting errors, and teaching concepts while nudging independent thinking. Whether you are an elementary, middle school, or high school teacher, through daily practice and open conversation, you can build a solid foundation for the study of mathematics and Make Number Talks Matter.