A History of Folding in Mathematics

A History of Folding in Mathematics PDF

Author: Michael Friedman

Publisher: Birkhäuser

Published: 2018-05-25

Total Pages: 419

ISBN-13: 3319724878

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While it is well known that the Delian problems are impossible to solve with a straightedge and compass – for example, it is impossible to construct a segment whose length is cube root of 2 with these instruments – the discovery of the Italian mathematician Margherita Beloch Piazzolla in 1934 that one can in fact construct a segment of length cube root of 2 with a single paper fold was completely ignored (till the end of the 1980s). This comes as no surprise, since with few exceptions paper folding was seldom considered as a mathematical practice, let alone as a mathematical procedure of inference or proof that could prompt novel mathematical discoveries. A few questions immediately arise: Why did paper folding become a non-instrument? What caused the marginalisation of this technique? And how was the mathematical knowledge, which was nevertheless transmitted and prompted by paper folding, later treated and conceptualised? Aiming to answer these questions, this volume provides, for the first time, an extensive historical study on the history of folding in mathematics, spanning from the 16th century to the 20th century, and offers a general study on the ways mathematical knowledge is marginalised, disappears, is ignored or becomes obsolete. In doing so, it makes a valuable contribution to the field of history and philosophy of science, particularly the history and philosophy of mathematics and is highly recommended for anyone interested in these topics.

Mathematics at the Margins

Mathematics at the Margins PDF

Author: Elizabeth Warren

Publisher: Springer

Published: 2016-03-17

Total Pages: 120

ISBN-13: 9811007039

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This book reports the impact a four-year longitudinal study (Representations, Oral Language and Engagement in Mathematics (RoleM)) had on teachers and students from 16 schools in disadvantaged contexts. It offers theories with regard to the interplay between teaching and learning mathematics as teachers and students in these contexts implement a mathematics program. The data are longitudinal, drawn from 154 teachers and their students (up to 1738 students) from the first four years of school (Foundation to Year 3). To ascertain the effectiveness of the RoleM Professional Learning model, teachers were interviewed three times a year and pre and post-tests were administered to students at the beginning and end of each year. Students’ results indicated that all students’ understanding of mathematics improved significantly, with the ESL students showing the greatest gains. Their results matched the norm-referenced expectations for all Australian students of this age. This book shares the journey of these teachers, Indigenous teacher aides and students. It outlines the dimensions of the research findings that supported teachers to become effective teachers of mathematics and assisted students in becoming successful learners of mathematics. The book also draws on the expertise of researchers from both Canada and New Zealand. They share the similarities and the differences between RoleM findings and their own contexts, in order to draw general conclusions for the effective teaching and learning of mathematics at the margins of society.

Great Moments in Mathematics Before 1650

Great Moments in Mathematics Before 1650 PDF

Author: Howard Eves

Publisher: American Mathematical Soc.

Published: 1983-12-31

Total Pages: 270

ISBN-13: 1614442142

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Great Moments in Mathematics: Before 1650 is the product of a series of lectures on the history of mathematics given by Howard Eves. He presents here, in chronological order, 20 ``great moments in mathematics before 1650'', which can be appreciated by anyone who enjoys mathematics. These wonderful lectures could be used as the basis of a course on the history of mathematics but can also serve as enrichment to any mathematics course. Included are lectures on the Pythagorean Theorem, Euclid's Elements, Archimedes (on the sphere), Diophantus, Omar Khayyam, and Fibonacci.

What is Mathematics?

What is Mathematics? PDF

Author: Richard Courant

Publisher: Oxford University Press, USA

Published: 1996

Total Pages: 596

ISBN-13: 9780195105193

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The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but not real understanding or greater intellectual independence. The new edition of this classic work seeks to address this problem. Its goal is to put the meaning back into mathematics. "Lucid . . . easily understandable".--Albert Einstein. 301 linecuts.

Oxford Users' Guide to Mathematics

Oxford Users' Guide to Mathematics PDF

Author: Eberhard Zeidler

Publisher: Oxford University Press

Published: 2004-08-19

Total Pages: 1309

ISBN-13: 0198507631

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The Oxford Users' Guide to Mathematics is one of the leading handbooks on mathematics available. It presents a comprehensive modern picture of mathematics and emphasises the relations between the different branches of mathematics, and the applications of mathematics in engineering and the natural sciences. The Oxford User's Guide covers a broad spectrum of mathematics starting with the basic material and progressing on to more advanced topics that have come to the fore in the last few decades. The book is organised into mathematical sub-disciplines including analysis, algebra, geometry, foundations of mathematics, calculus of variations and optimisation, theory of probability and mathematical statistics, numerical mathematics and scientific computing, and history of mathematics. The book is supplemented by numerous tables on infinite series, special functions, integrals, integral transformations, mathematical statistics, and fundamental constants in physics. It also includes a comprehensive bibliography of key contemporary literature as well as an extensive glossary and index. The wealth of material, reaching across all levels and numerous sub-disciplines, makes The Oxford User's Guide to Mathematics an invaluable reference source for students of engineering, mathematics, computer science, and the natural sciences, as well as teachers, practitioners, and researchers in industry and academia.

Critical Issues in Mathematics Education

Critical Issues in Mathematics Education PDF

Author: Bharath Sriraman

Publisher: IAP

Published: 2009-06-01

Total Pages: 503

ISBN-13: 1607522187

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The word "critical" in the title of this collection has three meanings, all of which are relevant. One meaning, as applied to a situation or problem, is "at a point of crisis". A second meaning is "expressing adverse or disapproving comments or judgments". A third is related to the verb "to critique", meaning "to analyze the merits and faults of". The authors contributing to this book pose challenging questions, from multiple perspectives, about the roles of mathematics in society and the implications for education. Traditional reasons for teaching mathematics include: preparing a new generation of mathematics researchers and a cadre of technically competent users of mathematics; training students to think logically; and because mathematics is as much part of cultural heritage as literature or music. These reasons remain valid, though open to critique, but a deeper analysis is required that recognizes the roles of mathematics in framing many aspects of contemporary society, that will connect mathematics education to the lived experiences of students, their communities, and society in general, and that acknowledges the global ethical responsibilities of mathematicians and mathematics educators. The book is organized in four sections (1) Mathematics education: For what and why? (2) Globalization and cultural diversity, (3) Mathematics, education, and society and (4) Social justice in, and through, mathematics education The chapters address fundamental issues such as the relevance of school mathematics in people's lives; creating a sense of agency for the field of mathematics education, and redefining the relationship between mathematics as discipline, mathematics as school subject and mathematics as part of people's lives.

A Wealth of Numbers

A Wealth of Numbers PDF

Author: Benjamin Wardhaugh

Publisher: Princeton University Press

Published: 2012-04-29

Total Pages: 388

ISBN-13: 0691147752

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An entertaining and informative anthology of popular math writing from the Renaissance to cyberspace Despite what we may sometimes imagine, popular mathematics writing didn't begin with Martin Gardner. In fact, it has a rich tradition stretching back hundreds of years. This entertaining and enlightening antholog—the first of its kind—gathers nearly one hundred fascinating selections from the past 500 years of popular math writing, bringing to life a little-known side of math history. Ranging from the late fifteenth to the late twentieth century, and drawing from books, newspapers, magazines, and websites, A Wealth of Numbers includes recreational, classroom, and work mathematics; mathematical histories and biographies; accounts of higher mathematics; explanations of mathematical instruments; discussions of how math should be taught and learned; reflections on the place of math in the world; and math in fiction and humor. Featuring many tricks, games, problems, and puzzles, as well as much history and trivia, the selections include a sixteenth-century guide to making a horizontal sundial; "Newton for the Ladies" (1739); Leonhard Euler on the idea of velocity (1760); "Mathematical Toys" (1785); a poetic version of the rule of three (1792); "Lotteries and Mountebanks" (1801); Lewis Carroll on the game of logic (1887); "Maps and Mazes" (1892); "Einstein's Real Achievement" (1921); "Riddles in Mathematics" (1945); "New Math for Parents" (1966); and "PC Astronomy" (1997). Organized by thematic chapters, each selection is placed in context by a brief introduction. A unique window into the hidden history of popular mathematics, A Wealth of Numbers will provide many hours of fun and learning to anyone who loves popular mathematics and science.

Sociopolitical Dimensions of Mathematics Education

Sociopolitical Dimensions of Mathematics Education PDF

Author: Murad Jurdak

Publisher: Springer

Published: 2018-01-28

Total Pages: 234

ISBN-13: 3319726102

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This book documents and expands on the diverse social and political dimensions of mathematics education issues, concerns, perspectives, contexts, and approaches presented in Topic Study Group 34 of the 13th International Congress on Mathematical Education (ICME-13). The book also argues for and promotes the mainstreaming of the sociopolitical dimensions of mathematics education through an ongoing critique and inquiry into content, policies, practices and theories. Accordingly, the main theme throughout the book is captured and illuminated by bringing voices from the margin to the mainstream. In this respect it is both aspirational and a reality, as evidenced by the increasing references to the sociopolitical dimensions in other areas of mathematics education—for example, in several of the plenary presentations at the ICME-13. The authors have reflected on their ideas with a view to orienting and enhancing research in the sociopolitical dimensions of mathematics education that is grounded in current education systems within their specific sociocultural contexts.

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