Number Story: From Counting to Cryptography

Peter Michael Higgins

Springer | 2008 | 324 páginas | pdf | 1 Mb

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Descrição: Numbers have fascinated people for centuries. They are familiar to everyone, forming a central pillar of our understanding of the world, yet the number system was not presented to us "gift-wrapped" but, rather, was developed over millennia. Today, despite all this development, it remains true that a child may ask a question about numbers that no one can answer. Many unsolved problems surrounding number matters appear as quirky oddities of little account while others are holding up fundamental progress in mainstream mathematics.Peter Higgins distills centuries of work into one delightful narrative that celebrates the mystery of numbers and explains how different kinds of numbers arose and why they are useful. Full of historical snippets and interesting examples, the book ranges from simple number puzzles and magic tricks, to showing how ideas about numbers relate to real-world problems, such as: How are our bank account details kept secure when shopping over the internet? What are the chances of winning at Russian roulette; or of being dealt a flush in a poker hand?This fascinating book will inspire and entertain readers across a range of abilities. Easy material is blended with more challenging ideas about infinity and complex numbers, and a final chapter "For Connoisseurs" works through some of the particular claims and examples in the book in mathematical language for those who appreciate a complete explanation.As our understanding of numbers continues to evolve, this book invites us to rediscover the mystery and beauty of numbers and reminds us that the story of numbers is a tale with a long way to run...

Teaching Number Sense

Julia Anghileri

Continuum | 2006 - 2ª edição | 153 páginas | pdf |  2,43 Mb

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Descrição: What is number sense? How does children's number sense develop? What are the most effective teaching methods and resources? How can research findings inform classroom practice? The fully revised second edition of the best-selling "Teaching Number Sense" is the book to help you answer these questions, and more. This new edition boasts a new chapter on 'The empty number line' as well as a wealth of material on all the latest trends and innovations in mathematics teaching to support children's learning. It is a specialist text that uses a balance of theory and practice to help teachers deal with the problems and issues they will encounter in mathematics teaching, including examples for use specifically in the classroom. This book will prove essential reading for trainee and established mathematics teachers alike.
Outros livros da mesma autora disponível para download:Children's Mathematical Thinking In the Primary Years: Perspectives on Children's Learning (link)
Outros livros da mesma autora não disponíveis para download:

Principles and Practice in Arithmetic Teaching
Buckingham: Open University Press, 2001
ISBN 0335206336, 9780335206339

206 páginas

Developing Number Sense Progression in the Middle YearsContinuum International Publishing Group, 2008
ISBN 1847061265, 9781847061263
176 páginas

The Historical Roots of Elementary Mathematics

(Dover books explaining science)
Lucas N. H. Bunt, Phillip S. Jones, Jack D. Bedient
Dover Publications | 1988 | 320 páginas | djvu | 5 Mb

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Descrição: Exciting, hands-on approach to understanding fundamental underpinnings of modern arithmetic, algebra, geometry and number systems, by examining their origins in early Egyptian, Babylonian and Greek sources. Students can do division like the ancient Egyptians, solve quadratic equations like the Babylonians and more.

Aha! Solutions

(MAA Problem Book Series)

Martin J. Erickson
(página do autor: erickson.sites.truman.edu)

The Mathematical Association of America | 2008 | 207 páginas | rar - PDF |  1,2 Mb

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djvu | 2,09 Mb
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Descrição: Every mathematician (beginner, amateur, and professional alike) thrills to find simple, elegant solutions to seemingly difficult problems. Such happy resolutions are called ``aha! solutions,'' a phrase popularized by mathematics and science writer Martin Gardner. Aha! solutions are surprising, stunning, and scintillating: they reveal the beauty of mathematics.This book is a collection of problems with aha! solutions. The problems are at the level of the college mathematics student, but there should be something of interest for the high school student, the teacher of mathematics, the ``math fan,'' and anyone else who loves mathematical challenges.This collection includes one hundred problems in the areas of arithmetic, geometry, algebra, calculus, probability, number theory, and combinatorics. The problems start out easy and generally get more difficult as you progress through the book. A few solutions require the use of a computer. An important feature of the book is the bonus discussion of related mathematics that follows the solution of each problem. This material is there to entertain and inform you or point you to new questions. If you don't remember a mathematical definition or concept, there is a Toolkit in the back of the book that will help.

Contents

Preface
1 Elementary Problems
2 Intermediate Problems
3 Advanced Problems
A Toolkit
B List of Bonuses
Bibliography
Index

Outros livros do mesmo autor:

Beautiful Mathematics
Principles of Mathematical Problem Solving

Sherlock Holmes in Babylon and Other Tales of Mathematical History

(Spectrum)
Victor Katz, Robin Wilson

The Mathematical Association of America | 2004 | 398 páginas | pdf | 7
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Descrição: This book is a collection of 44 articles on the history of mathematics, published in MAA journals over the past 100 years. Covering a span of almost 4000 years, from the ancient Babylonians to the eighteenth century, it chronicles the enormous changes in mathematical thinking over this time, as viewed by distinguished historians of mathematics from the past (Florian Cajori, Max Dehn, David Eugene Smith, Julian Lowell Coolidge and Carl Boyer) and the present.Each of the four sections of the book (Ancient Mathematics, Medieval and Renaissance Mathematics, The Seventeenth Century, The Eighteenth Century) is preceded by a Foreword, in which the articles are put into historical context, and followed by an Afterword, in which they are reviewed in the light of current historical scholarship. In more than one case, two articles on the same topic are included, to show how knowledge and vies about the topic changed over the years.This book will be enjoyed by anyone interested in mathematics and its history – and in particular by mathematics teachers at secondary, college, and university level.

Teaching Mathematical Reasoning in Secondary School Classrooms

(Mathematics Teacher Education)

Karin Brodie

Springer | 2009 | 225 páginas |  pdf | 2,39 Mb

mediafire.com

 pdf | 3 Mb

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Descrição: For too many students, mathematics consists of facts in a vacuum, to be memorized because the instructor says so, and to be forgotten when the course of study is completed. In this all-too-common scenario, young learners often miss the chance to develop skills—specifically, reasoning skills—that can serve them for a lifetime. The elegant pages of Teaching Mathematical Reasoning in Secondary School Classrooms propose a more positive solution by presenting a reasoning- and discussion-based approach to teaching mathematics, emphasizing the connections between ideas, or why math works. The teachers whose work forms the basis of the book create a powerful record of methods, interactions, and decisions (including dealing with challenges and impasses) involving this elusive topic. And because this approach shifts the locus of authority from the instructor to mathematics itself, students gain a system of knowledge that they can apply not only to discrete tasks relating to numbers, but also to the larger world of people and the humanities.A sampling of the topics covered:Whole-class discussion methods for teaching mathematics reasoning.Learning mathematical reasoning through tasks.Teaching mathematics using the five strands.Classroom strategies for promoting mathematical reasoning.Maximizing student contributions in the classroom.Overcoming student resistance to mathematical conversations.Teaching Mathematical Reasoning in Secondary School Classrooms makes a wealth of cutting-edge strategies available to mathematics teachers and teacher educators. This book is an invaluable resource for researchers in mathematics and curriculum reform and of great interest to teacher educators and teachers.

Brown Paper School book: Math for Smarty Pants

Marilyn Burns

Little, Brown Young Readers | 1982 | 128 páginas | pdf | 5 Mb

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Descrição: Chock full of entertaining mathematical ideas, puzzles, tricks, and word problems, this book proves that everyone can be a math whiz.