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Extending the Challenge in Mathematics

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

October 2002 | 160 pages | Corwin

"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 of The National Association for Gifted Children

Challenge, engage, and inspire your mathematically promising students!

Combining theory and practice, Sheffield expertly guides the reader through the process of mathematical talent development from identifying students with mathematical potential, to finding and creating first-rate problems for exploration and strategies for assessment.

The multi-level investigations in this book are designed to challenge students and inspire deeper and more original mathematical thinking in Number and Operations, Algebra, Geometry and Measurement, and Data Analysis and Probability.

Each investigation is developed in the following easy-to-follow format:

Relate—sets the stage for the investigation by connecting it to prior learning and the NCTM Principles and Standards

Investigate—poses the initial problem to start students thinking about the investigation

Evaluate and Communicate—provides solutions, probing assessment questions, and suggestions for teacher responses

Create—offers ideas for extending and deepening the investigation, allowing even the most accomplished students to add depth and complexity to their reasoning

Discussion—gives teachers hints on what to look for in student solutions, as well as ideas for encouraging students to dig more deeply into the mathematical concepts that are presented

Mathematically promising students have the potential to become the leaders and problem solvers of the future. Extending the Challenge in Mathematics provides the practical tips and tools educators need to help their students develop this potential to the fullest.

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
Key features
  • All material is linked to the NCTM (National Council of Teachers of Mathematics) Principles and Standards
  • Author presents activities that emphasize adding depth and complexity to individual topics within the mathematics curriculum, followed by a section that discusses possible student responses, and finally a section that gives teachers ideas for extending and deepening the investigations even further.
  • Author is an active presenter, writer, and researcher in the field of Mathematics & giftedness/talent development
  • Book contains resource section with curriculum materials, supplemental materials, and on-line resources for further help
  • Book will cluster extremely well with Tomlinson et al., Gregory/Chapman, Sousa (Gifted Brain), Parke, and Smutney and Corwin's other math books


Sample Materials & Chapters

Chapter 1: Developing Mathematical Promise

For instructors

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ISBN: 9781483366098

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