Extending the Challenge in Mathematics

Developing Mathematical Promise in K-8 Students
Linda Jensen Sheffield - Northern Kentucky University, USA
Extending the Challenge in Mathematics
October 2002 | 160 pages | Corwin
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eBook
ISBN: 9781483366098
Available from January 0001
Paperback
ISBN: 9780761938514
Available from January 0001

Description

"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.

Contents

List of Reproducible Forms

List of Reproducible Forms

About the Author

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

Resources

Resources

References

References

Index

Index

Description

"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.

Contents

List of Reproducible Forms

List of Reproducible Forms

About the Author

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

Resources

Resources

References

References

Index

Index

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Extending the Challenge in Mathematics

Developing Mathematical Promise in K-8 Students

Linda Jensen Sheffield
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October 2002 | 160 pages | Corwin

Format Published Date ISBN Price
Paperback 28/04/2023 9780761938514 $39.95
Lifetime 28/04/2023 9781483366098 $36.00

"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.


Table Of Contents:

  • 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
  • Resources
  • References
  • Index

Recent Product Reviews:

"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

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