Learning and Teaching with Maps

Patrick Wiegand

Routledge | 2006 | 153 páginas |  pdf  | 3,5 Mb

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Descrição:
Learning and Teaching with Maps explains how children and young people read, understand, and interpret maps and how teaching with maps can be more effective. Learning abot maps has never been so important for children and young people. The rapid growth of internet mapping, digital atlases and Geographical Information Systems (GIS) demands new skills alongside traditional ones such as locating places and using a map to find the way.

The book describes how children make meaning with maps, including large scale plans, topographic and thematic maps, globes and maps of the world. The book details how teachers can plan a curriculum to ensure balance and progression and suggests workable classroom activities for children from the early years of primary to secondary school. Particular attention is paid to how learning with maps can conribute to children's developing literacy and numercy skills. The book draws on the authors unique experience of teaching primary and secondary schools, teachertraining, and extensive research and development in educational cartography.

This book will be of great use to all primary teachers and subject leaders in primary geography, as well as non-specialist geography teachers.

Proof Theory: History and Philosophical Significance

(Synthese Library)
Vincent F. Hendricks, Stig Andur Pedersen, Klaus Frovin Jørgensen

Springer | 2000 | 256 páginas | djvu | 3,3 Mb

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Descrição: The conference on Proof Theory: History and Philosophical Significance held in 1997 at the University of Roskilde, Denmark, tracked the history of proof theory and its role in the analysis of the philosophical foundations of mathematics since Hilbert's original program to its modern, highly articulated form. This volume is a collection of papers presented at the conference. It can be read with profit and pleasure by philosophers, mathematicians, computer scientists and scholars with no professional training in proof theory, provided they have a general knowledge of foundational issues.

The Self-Made Tapestry: Pattern Formation in Nature

Philip Ball

Oxford University Press, USA | 1999 | 312 páginas |  pdf | 12 Mb

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Descrição: For centuries, scientists have struggled to understand the origins of the patterns and forms found in naturefrom the leopards spots to the graceful spirals of a mollusk shell to the complex designs on a butterflys wing. Now, in this lucid and elegantly written book, Philip Ball applies state-of-the-art scientific understanding from the fields of biology, chemistry, geology, physics, and mathematics to these ancient mysteries, revealing how natures seemingly complex patterns originate in simple physical laws. Ball Traces the history of scientific thought about natural patterns, showing how common presumptionsfor example, that complex form must be guided by some intelligence or that form always follows functionare erroneous and continue to mislead scientists today. He investigates specific patterns in depth, revealing that these designs are self-organized and that simple, local interactions between component parts produce motifs like spots, stripes, branches, and honeycombs. In the process, he examines the mysterious phenomenon of symmetry and why it appearsand breaksin similar ways in different systems. Finally, he attempts to answer this profound questionwhy are some patterns universal? Illustrations throughout the text, many in full color, beautifully illuminate Balls ideas. A fascination with natures patterns is as old as civilization With this spellbinding book, Ball dispels age-old conundrums while increasing the readers wonder and appreciation for the beauty of the natural world. The Self-Made Tapestry will enlighten anyone who has ever marveled at the shape of a seashell or the brilliance of a spiders web.

Shapes: Nature's Patterns: A Tapestry in Three Parts

(Natures Patterns)
Philip Ball

Oxford University Press, USA | 2009 | 320 páginas | pdf | 9,3 Mb

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Descrição: Patterns are everywhere in nature--in the ranks of clouds in the sky, the stripes of an angelfish, the arrangement of petals in flowers. Where does this order and regularity come from? As Philip Ball reveals in Nature's Patterns: A Tapestry in Three Parts, this order creates itself. The patterns we see come from self-organization. Indeed, scientists have found that there is a pattern-forming tendency inherent in the basic structure and processes of nature, whether living or non-living, so that from a few simple themes, and the repetition of simple rules, endless beautiful variations can arise.
Part of a trilogy of books exploring the science of patterns in nature, Shapes looks at how shapes form. From soap bubbles to honeycombs, delicate shell patterns, and even the developing body parts of a complex animal like ourselves, the author uncovers patterns in growth and form in all corners of the natural world, explains how these patterns are self-made, and describes why similar shapes and structures may be found in very different settings, orchestrated by nothing more than simple physical forces. This book will make you look at the world with fresh eyes, seeing order and form in places you'd least expect.

La matematica del Novecento

Dagli insiemi alla complessità
Piergiorgio Odifreddi

Einaudi | 2000 | 193 páginas |  djvu | 46,1 Mb

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Descrição: Il Novecento è stato il secolo della matematica: in soli cento anni si sono dimostrati più teoremi che nell'intero corso della storia, e molti di essi hanno trovato applicazione nei campi più svariati della scienza e perfino della cosiddetta cultura umanistica. Il volume ricostruisce in una forma il più possibile facile e discorsiva la straordinaria vicenda di una disciplina spesso vissuta come astrusa e distante dalla vita quotidiana, descrivendone le idee, i risultati, i principali protagonisti, i problemi ancora irrisolti.