Math through the Ages: A Gentle History for Teachers and Others Expanded Second Edition PDF Download
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Author: William P. Berlinghoff
Publisher: American Mathematical Soc.
ISBN: 147046456X
Category : Education
Languages : en
Pages : 331
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Book Description
Where did math come from? Who thought up all those algebra symbols, and why? What is the story behind π π? … negative numbers? … the metric system? … quadratic equations? … sine and cosine? … logs? The 30 independent historical sketches in Math through the Ages answer these questions and many others in an informal, easygoing style that is accessible to teachers, students, and anyone who is curious about the history of mathematical ideas. Each sketch includes Questions and Projects to help you learn more about its topic and to see how the main ideas fit into the bigger picture of history. The 30 short stories are preceded by a 58-page bird's-eye overview of the entire panorama of mathematical history, a whirlwind tour of the most important people, events, and trends that shaped the mathematics we know today. “What to Read Next” and reading suggestions after each sketch provide starting points for readers who want to learn more. This book is ideal for a broad spectrum of audiences, including students in history of mathematics courses at the late high school or early college level, pre-service and in-service teachers, and anyone who just wants to know a little more about the origins of mathematics.
Author: William P. Berlinghoff
Publisher: American Mathematical Soc.
ISBN: 147046456X
Category : Education
Languages : en
Pages : 331
Get Book Here
Book Description
Where did math come from? Who thought up all those algebra symbols, and why? What is the story behind π π? … negative numbers? … the metric system? … quadratic equations? … sine and cosine? … logs? The 30 independent historical sketches in Math through the Ages answer these questions and many others in an informal, easygoing style that is accessible to teachers, students, and anyone who is curious about the history of mathematical ideas. Each sketch includes Questions and Projects to help you learn more about its topic and to see how the main ideas fit into the bigger picture of history. The 30 short stories are preceded by a 58-page bird's-eye overview of the entire panorama of mathematical history, a whirlwind tour of the most important people, events, and trends that shaped the mathematics we know today. “What to Read Next” and reading suggestions after each sketch provide starting points for readers who want to learn more. This book is ideal for a broad spectrum of audiences, including students in history of mathematics courses at the late high school or early college level, pre-service and in-service teachers, and anyone who just wants to know a little more about the origins of mathematics.
Author: Alan Sultan
Publisher: Routledge
ISBN: 1315391899
Category : Education
Languages : en
Pages : 789
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Book Description
Designed to help pre-service and in-service teachers gain the knowledge they need to facilitate students' understanding, competency, and interest in mathematics, the revised and updated Second Edition of this popular text and resource bridges the gap between the mathematics learned in college and the mathematics taught in secondary schools. Highlighting multiple types of mathematical understanding to deepen insight into the secondary school mathematics curriculum, it addresses typical areas of difficulty and common student misconceptions so teachers can involve their students in learning mathematics in a way that is interesting, interconnected, understandable, and often surprising and entertaining. Six content strands are discussed—Numbers and Operations; Algebra; Geometry; Measurement; Data Analysis and Probability; and Proof, Functions, and Mathematical Modeling. The informal, clear style supports an interactive learner-centered approach through engaging pedagogical features: Launch Questions at the beginning of each section capture interest and involve readers in learning the mathematical concepts. Practice Problems provide opportunities to apply what has been learned and complete proofs. Questions from the Classroom bring the content to life by addressing the deep "why" conceptual questions that middle or secondary school students are curious about, and questions that require analysis and correction of typical student errors and misconceptions; focus on counter intuitive results; and contain activities and/or tasks suitable for use with students. Changes in the Second Edition New sections on Robotics, Calculators, Matrix Operations, Cryptography, and the Coefficient of Determination New problems, simpler proofs, and more illustrative examples Answers and hints for selected problems provided
Author: William P. Berlinghoff
Publisher: American Mathematical Soc.
ISBN: 1939512123
Category : Education
Languages : en
Pages : 349
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Book Description
`Math through the Ages' is a treasure, one of the best history of math books at its level ever written. Somehow, it manages to stay true to a surprisingly sophisticated story, while respecting the needs of its audience. Its overview of the subject captures most of what one needs to know, and the 30 sketches are small gems of exposition that stimulate further exploration. --Glen van Brummelen, Quest University, President (2012-14) of the Canadian Society for History and Philosophy of Mathematics Where did math come from? Who thought up all those algebra symbols, and why? What is the story behind $pi$? ... negative numbers? ... the metric system? ... quadratic equations? ... sine and cosine? ... logs? The 30 independent historical sketches in Math through the Ages answer these questions and many others in an informal, easygoing style that is accessible to teachers, students, and anyone who is curious about the history of mathematical ideas. Each sketch includes Questions and Projects to help you learn more about its topic and to see how the main ideas fit into the bigger picture of history. The 30 short stories are preceded by a 58-page bird's-eye overview of the entire panorama of mathematical history, a whirlwind tour of the most important people, events, and trends that shaped the mathematics we know today. ``What to Read Next'' and reading suggestions after each sketch provide starting points for readers who want to learn more. This book is ideal for a broad spectrum of audiences, including students in history of mathematics courses at the late high school or early college level, pre-service and in-service teachers, and anyone who just wants to know a little more about the origins of mathematics.
Author: Phyllis Haddox
Publisher: Simon and Schuster
ISBN: 0671631985
Category : Education
Languages : en
Pages : 416
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Book Description
A step-by-step program that shows parents, simply and clearly, how to teach their child to read in just 20 minutes a day.
Author: National Research Council
Publisher: National Academies Press
ISBN: 0309324882
Category : Social Science
Languages : en
Pages : 587
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Book Description
Children are already learning at birth, and they develop and learn at a rapid pace in their early years. This provides a critical foundation for lifelong progress, and the adults who provide for the care and the education of young children bear a great responsibility for their health, development, and learning. Despite the fact that they share the same objective - to nurture young children and secure their future success - the various practitioners who contribute to the care and the education of children from birth through age 8 are not acknowledged as a workforce unified by the common knowledge and competencies needed to do their jobs well. Transforming the Workforce for Children Birth Through Age 8 explores the science of child development, particularly looking at implications for the professionals who work with children. This report examines the current capacities and practices of the workforce, the settings in which they work, the policies and infrastructure that set qualifications and provide professional learning, and the government agencies and other funders who support and oversee these systems. This book then makes recommendations to improve the quality of professional practice and the practice environment for care and education professionals. These detailed recommendations create a blueprint for action that builds on a unifying foundation of child development and early learning, shared knowledge and competencies for care and education professionals, and principles for effective professional learning. Young children thrive and learn best when they have secure, positive relationships with adults who are knowledgeable about how to support their development and learning and are responsive to their individual progress. Transforming the Workforce for Children Birth Through Age 8 offers guidance on system changes to improve the quality of professional practice, specific actions to improve professional learning systems and workforce development, and research to continue to build the knowledge base in ways that will directly advance and inform future actions. The recommendations of this book provide an opportunity to improve the quality of the care and the education that children receive, and ultimately improve outcomes for children.
Author: E. H. Gombrich
Publisher: Yale University Press
ISBN: 0300213972
Category : History
Languages : en
Pages : 401
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Book Description
E. H. Gombrich's Little History of the World, though written in 1935, has become one of the treasures of historical writing since its first publication in English in 2005. The Yale edition alone has now sold over half a million copies, and the book is available worldwide in almost thirty languages. Gombrich was of course the best-known art historian of his time, and his text suggests illustrations on every page. This illustrated edition of the Little History brings together the pellucid humanity of his narrative with the images that may well have been in his mind's eye as he wrote the book. The two hundred illustrations—most of them in full color—are not simple embellishments, though they are beautiful. They emerge from the text, enrich the author's intention, and deepen the pleasure of reading this remarkable work. For this edition the text is reset in a spacious format, flowing around illustrations that range from paintings to line drawings, emblems, motifs, and symbols. The book incorporates freshly drawn maps, a revised preface, and a new index. Blending high-grade design, fine paper, and classic binding, this is both a sumptuous gift book and an enhanced edition of a timeless account of human history.
Author: Allison K. Henrich
Publisher:
ISBN: 9781470452810
Category : Academic achievement
Languages : en
Pages : 136
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Book Description
Wow! This is a powerful book that addresses a long-standing elephant in the mathematics room. Many people learning math ask ``Why is math so hard for me while everyone else understands it?'' and ``Am I good enough to succeed in math?'' In answering these questions the book shares personal stories from many now-accomplished mathematicians affirming that ``You are not alone; math is hard for everyone'' and ``Yes; you are good enough.'' Along the way the book addresses other issues such as biases and prejudices that mathematicians encounter, and it provides inspiration and emotional support for mathematicians ranging from the experienced professor to the struggling mathematics student. --Michael Dorff, MAA President This book is a remarkable collection of personal reflections on what it means to be, and to become, a mathematician. Each story reveals a unique and refreshing understanding of the barriers erected by our cultural focus on ``math is hard.'' Indeed, mathematics is hard, and so are many other things--as Stephen Kennedy points out in his cogent introduction. This collection of essays offers inspiration to students of mathematics and to mathematicians at every career stage. --Jill Pipher, AMS President This book is published in cooperation with the Mathematical Association of America.
Author: Ekkehard Kopp
Publisher: Open Book Publishers
ISBN: 1800640978
Category : Mathematics
Languages : en
Pages : 282
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Book Description
Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research. The book explains how conceptual hurdles in the development of numbers and number systems were overcome in the course of history, from Babylon to Classical Greece, from the Middle Ages to the Renaissance, and so to the nineteenth and twentieth centuries. The narrative moves from the Pythagorean insistence on positive multiples to the gradual acceptance of negative numbers, irrationals and complex numbers as essential tools in quantitative analysis. Within this chronological framework, chapters are organised thematically, covering a variety of topics and contexts: writing and solving equations, geometric construction, coordinates and complex numbers, perceptions of ‘infinity’ and its permissible uses in mathematics, number systems, and evolving views of the role of axioms. Through this approach, the author demonstrates that changes in our understanding of numbers have often relied on the breaking of long-held conventions to make way for new inventions at once providing greater clarity and widening mathematical horizons. Viewed from this historical perspective, mathematical abstraction emerges as neither mysterious nor immutable, but as a contingent, developing human activity. Making up Numbers will be of great interest to undergraduate and A-level students of mathematics, as well as secondary school teachers of the subject. In virtue of its detailed treatment of mathematical ideas, it will be of value to anyone seeking to learn more about the development of the subject.
Author: Fernando Q. Gouvea
Publisher: Springer Science & Business Media
ISBN: 3662222787
Category : Mathematics
Languages : en
Pages : 285
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Book Description
p-adic numbers are of great theoretical importance in number theory, since they allow the use of the language of analysis to study problems relating toprime numbers and diophantine equations. Further, they offer a realm where one can do things that are very similar to classical analysis, but with results that are quite unusual. The book should be of use to students interested in number theory, but at the same time offers an interesting example of the many connections between different parts of mathematics. The book strives to be understandable to an undergraduate audience. Very little background has been assumed, and the presentation is leisurely. There are many problems, which should help readers who are working on their own (a large appendix with hints on the problem is included). Most of all, the book should offer undergraduates exposure to some interesting mathematics which is off the beaten track. Those who will later specialize in number theory, algebraic geometry, and related subjects will benefit more directly, but all mathematics students can enjoy the book.
Author: Leonard Sax, M.D., Ph.D.
Publisher: Harmony
ISBN: 0307419584
Category : Family & Relationships
Languages : en
Pages : 338
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Book Description
Are boys and girls really that different? Twenty years ago, doctors and researchers didn’t think so. Back then, most experts believed that differences in how girls and boys behave are mainly due to differences in how they were treated by their parents, teachers, and friends. It's hard to cling to that belief today. An avalanche of research over the past twenty years has shown that sex differences are more significant and profound than anybody guessed. Sex differences are real, biologically programmed, and important to how children are raised, disciplined, and educated. In Why Gender Matters, psychologist and family physician Dr. Leonard Sax leads parents through the mystifying world of gender differences by explaining the biologically different ways in which children think, feel, and act. He addresses a host of issues, including discipline, learning, risk taking, aggression, sex, and drugs, and shows how boys and girls react in predictable ways to different situations. For example, girls are born with more sensitive hearing than boys, and those differences increase as kids grow up. So when a grown man speaks to a girl in what he thinks is a normal voice, she may hear it as yelling. Conversely, boys who appear to be inattentive in class may just be sitting too far away to hear the teacher—especially if the teacher is female. Likewise, negative emotions are seated in an ancient structure of the brain called the amygdala. Girls develop an early connection between this area and the cerebral cortex, enabling them to talk about their feelings. In boys these links develop later. So if you ask a troubled adolescent boy to tell you what his feelings are, he often literally cannot say. Dr. Sax offers fresh approaches to disciplining children, as well as gender-specific ways to help girls and boys avoid drugs and early sexual activity. He wants parents to understand and work with hardwired differences in children, but he also encourages them to push beyond gender-based stereotypes. A leading proponent of single-sex education, Dr. Sax points out specific instances where keeping boys and girls separate in the classroom has yielded striking educational, social, and interpersonal benefits. Despite the view of many educators and experts on child-rearing that sex differences should be ignored or overcome, parents and teachers would do better to recognize, understand, and make use of the biological differences that make a girl a girl, and a boy a boy.
