Using Math Games and Word Problems to Increase the ...

Using Math Games and Word Problems

to Increase the Math Maturity of K-8 Students

David Moursund

Robert Albrecht

ABOUT THE AUTHORS

Dr. David Moursund

After completing his undergraduate work at the University of Oregon, Dr. Moursund earned his doctorate in

mathematics from the University of Wisconsin-Madison. He taught in the Mathematics Department and

Computing Center at Michigan State University for four years, before joining the faculty at the University of

Oregon. There he had appointments in the Math Department and Computing Center, served six years as the first

head of the Computer Science Department, and spent more than 20 years working in the Teacher Education

component of the College of Education.

A few highlights of his professional career include founding the International Society for Technology in Education

(ISTE), serving as its executive officer for 19 years, establishing ISTE¡¯s flagship publication, Learning and

Leading with Technology, serving as the Editor in Chief for more than 25 years, and working as major professor

or co-major professor for 75 doctoral students. Dr. Moursund has authored or coauthored more than 50 academic

books and hundreds of articles. Many of these materials are now available free on his Website. He has presented

several hundred keynote speeches, talks, and workshops around the world. More recently, he founded Information

Age Education (IAE), a non-profit organization dedicated to improving teaching and learning by people of all ages

and throughout the world. IAE currently provides free educational materials through its Wiki, a free newsletter

published twice a month, and a blog.

Robert Albrecht

A pioneer in the field of computers in education and use of games in education, Robert Albrecht has been a

life-long supporter of computers for everyone. He was instrumental in helping bring about a public-domain

version of BASIC (called Tiny BASIC) for early microcomputers. Joining forces with George Firedrake and

Dennis Allison, he co-founded People¡¯s Computer Company (PCC) in 1972, and also produced and edited

People's Computer Company, a periodical devoted to computer education, computer games, BASIC programming,

and personal use of computers.

Albrecht has authored or coauthored over 30 books and more than 150 articles, including many books about

BASIC and educational games. Along with Dennis Allison, he established Dr. Dobb¡¯s Journal, a professional

journal of software tools for advanced computer programmers. He was involved in establishing organizations,

publications, and events such as Portola Institute, ComputerTown USA, Calculators/Computers Magazine, and

the Learning Fair at Peninsula School in Menlo Park, California (now called the Peninsula School Spring Fair).

Albrecht's current adventures include writing and posting instructional materials on the Internet for free use,

tutoring high school and college students in math and physics, and running HurkleQuest play-by-email games for

Oregon teachers and their students.

This book is available for purchase through the Math Learning Center:

The Math Learning Center

P.O. Box 12929

Salem, OR 97309-0929

Phone: 503-370-8130

Toll Free: 800-575-8130

Fax: 503-370-7961



Copyright ? 2011 David Moursund and Robert Albrecht

Table of Contents

Preface and Introduction ..................................................................... 1

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Chapter 1: WordsWorth Games ......................................................... 7

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Chapter 2: Introduction to Math Maturity ...................................... 17

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Chapter 3: Introduction to Math Intelligence .................................. 35

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Chapter 4: Math Cognitive Development ......................................... 49

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Chapter 5: The Language of Mathematics ....................................... 61

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Chapter 6: Some Learning Theory ................................................... 71

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Chapter 7: Math Word Problems ..................................................... 81

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Chapter 8: Math Games and Puzzles ................................................ 95

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Chapter 9: Dice, Coins, and Chance ............................................... 109

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Chapter 10: Place Value Games ...................................................... 123

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Chapter 11: Word Problems Using Dominoes ............................... 143

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Chapter 12: Factor Monster ............................................................ 155

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Chapter 13: The Game of Pig .......................................................... 165

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Chapter 14: More Games and Puzzles ............................................ 179

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Chapter 15: Final Remarks.............................................................. 193

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Appendix 1: Make It & Take It, and Blackline Masters ............... 197

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Appendix 2: Some Free Resources .................................................. 205

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Appendix 3: Some Not-Free Resources........................................... 209

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Bibliography ...................................................................................... 211

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Index ................................................................................................... 217

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Preface and Introduction

This book is mainly intended for preservice and inservice teachers of math at the PreK-8

levels, and parents and other caregivers of such students. The goal of this book is to help

improve the informal and formal math education of PreK-8 students. The emphasis is on

providing students with learning environments that help to increase their levels of math maturity.

The learning environments stressed in this book include an emphasis on communication in the

language of mathematics, the use of math-oriented games, and the use of math word problems.

The next paragraph is a short definition of a mathematically mature adult. The level of math

maturity described comes from years of appropriate informal and formal education and mathrelated experiences. Later parts of the book will provide a more detailed definition of math

maturity and more detail about possible roads leading to an increased level of math maturity.

Mathematically mature adults have the math knowledge, skills, attitudes, perseverance,

and experience to be responsible adult citizens in dealing with the types of math-related

situations, problems, and tasks that occur in the societies and cultures in which they live. In

addition, a mathematically mature adult knows when and how to ask for and make appropriate

use of help from other people, from books, and from tools such as computer systems and the

Internet.

Scattered throughout this book you will find short Math Maturity Food for Thought

subsections such as the one given below. Each asks you to reflect on a particular idea or presents

you with some problems that you and/or your students might explore. Such reflection,

introspection, and problem-solving challenges are an important aid to learning and to increasing

one¡¯s level of math maturity. If you are using this book in a course, these subsections can be used

in small group and/or large group discussions and sharing. This can be done in a face-to-face

environment or via use of telecommunications systems.

Math Maturity Food for Thought. It¡¯s A-OK to have one¡¯s income taxes prepared by an

expert or for a person to make use of income tax preparation software. The income tax

system and tax law in the United States are frightfully complex and include substantial

changes from year to year.

It is not possible for a person to gain and maintain a high level of personal expertise in every

type of problem area that adults must routinely deal with. Thus, knowing when and how to

ask for math-related help (from a person or from a machine) ¡ªand how to make

effective use of such help¡ªis an important aspect of math maturity.

Think about the math that you do for yourself in your everyday life, and the math that you do

with the help of other people and/or with the help of calculators, computers, GPS, and so on.

Do you consider yourself to be a mathematically mature adult? What could you do to

increase your level of math maturity?

Math is a vast and steadily growing discipline. Moreover, math is an important component of

science, technology, engineering, and many non-science disciplines. As an example, think about

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