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Extending the Challenge in Mathematics

Extending the Challenge in Mathematics
Developing Mathematical Promise in K-8 Students

Other Titles in:
Mathematics | Physical Impairments

July 2014 | 160 pages | Corwin
`Any teacher who uses this book will need to be very much involved in the learning process working through the exercises to fully understand what is required of the students to then be able to (initially) guide the students, particularly the very young students. It is a book that will definitely challenge mathematically promising students…. I recommend this publication' - Catherine Wormald, Gifted

This book is designed to help the general education mathematics teacher challenge his/her student(s) with mathematical promise. By providing math teachers with ready-to-use activities and the tools to create their own activities that will add depth to the standard curriculum, this book will help gifted/talented students in the regular classroom reach their full potential.

This book goes beyond the concept of mathematically gifted students who were traditionally defined as the top three to five percent of students based on one standardized mathematics test or another. Mathematically promising students are defined as those who have the potential to become the leaders and problem solvers of the future. Mathematical promise is described by the National Council of Teachers of Mathematics Task Force on Mathematically Promising Students as a function of ability, motivation, belief, and experience/opportunity. By factoring motivation levels and access to challenging courses in with innate ability, the discovery and talent development of mathematically gifted students is more accurate than before.

List of Reproducible Forms
About the Author
1. Developing Mathematical Promise
What Is Mathematical Promise?

Who Are Mathematically Promising?

What Are the Goals of Mathematics Instructions?

How Might We Find and/or Create Good Problems to Explore?

What Models Might We Use to Increase the Numbers and Levels of Mathematically Promising Students?

How Should We Assess Success?

Structure of the Activities in This Book

2. Number and Operations
Investigation One: How Many Ways?

Investigation Two: Same Sums

Investigation Three: All in a Row

3. Algebra
Investigation One: Where Am I?

Investigation Two: Heads or Tails?

Investigation Three: Field of Dreams

4. Geometry and Measurement
Investigation One: Framed

Investigation Two: Shape Up

Investigation Three: Connect the Dots

5. Data Analysis and Probability
Investigation One: Who's Got the Button?

Investigation Two: On Your Mark

Investigation Three: Bull's-Eye


"The best source I have seen challenging mathematically talented students. The activities are thought provoking and enjoyable. I will recommend this book to parents as well as educators of mathematically talented students!"

Sally Reis, Past President
The National Association for Gifted Children

"This is a distinctive book deserving to be in the vanguard of provision for mathematically promising pupils. Equally accessible to teachers and mathematics educators, this book offers ideas and step-by-step procedures on how to use them. The content is guided by enlightened principles emanating from substantial, well-informed experience of the author. A unique resource indeed."

Valsa Koshy, Reader in Mathematics Education
Brunel University, United Kingdom

"It is an excellent 'how-to' book for teachers that will help them ratchet up a seemingly simple math concept to stimulate critical and creative thinking in talented students. I find this book combines the best of mathematics content as outlined by the National Council of Teachers of Mathematics with the best of gifted education instructional strategies. It should be on the shelf of every elementary math teacher!"

Katherine Gavin, Associate Professor
University of Connecticut

"Sheffield has successfully packaged her exciting, unique vision for teaching all students as if they have the potential to become mathematically gifted.  This easy-to-use resource includes compelling mathematical activities in a simple format for encouraging deep thinking and mathematical creativity.  Extending the Challenge in Mathematics has it all--brain research theory, models for creative thinking, blackline masters with open-ended problems at graduated levels of difficulty for all four mathematical strands, in-depth discussion of solutions and extensions, and a very extensive list of Internet resources.  Finally—a realistic, concrete guide for teaching challenging reform mathematics.  Any math teacher could undoubtedly use it right away!"

Alice Gabbard, 7th Grade Math Teacher
Newport Middle School, Newport, KY

"I would recommend this book highly to anyone working with mathematics instruction for the gifted. It's an outstanding resource."

Joyce VanTassel-Baska, Executive Director
Center for Gifted Children, College of William and Mary

"This book will make a delightful addition to any teacher's classroom tool kit."

Mathematics Teaching in the Middle School, August 2004

Sample Materials & Chapters

Chapter 1: Developing Mathematical Promise

Linda Jensen Sheffield

Dr. Linda Sheffield is a Regents Professor of Mathematics Education at Northern Kentucky University. She received her M. Ed. and Ph.D. in Mathematics Education from the University of Texas at Austin and her bachelor's degree from Iowa State University. She has written numerous books and articles for both teachers and students and has conducted seminars for teachers across the United States and as far away as Spain, Germany, England, Sicily, Japan, Australia, China, and Hungary. Her books include PreK – 2 NCTM Navigations series, a series of math problem solving books for children in third through eighth grade, an integrated math/science... More About Author

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ISBN: 9780761938514