e-livros - matemática

Origami Design Secrets: Mathematical Methods for an Ancient Art

2011-11-01T03:20:00.002+01:00

Robert J. Lang

AK Peters | 2003 | 594 páginas | djvu | 24 Mb

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Link sobre o livro: web.mit.edu

Robert J. Lang, one of the world's foremost origami artists and scientists, presents the never-before-described mathematical and geometric principles that allow anyone to design original origami, something once restricted to an elite few. From the theoretical underpinnings to detailed step-by-step folding sequences, this book takes a modern look at the heart of the centuries-old art of origami.

Origami novices will appreciate the organization of the book, which begins with easy techniques and progresses to deep and powerful tools for design, all based on simple, intuitive concepts like grafting, circle packing, and assembly of tiles.

Both novices and aficionados will find detailed, step-by-step instructions for previously unpublished models, including the famous "Black Forest Cuckoo Clock."

Learning to Teach Mathematics in the Secondary School: A Companion to School Experience

2011-11-01T01:49:00.003+01:00

(Learning to Teach Subjects in the Secondary School Series)

Sue Johnston-Wilder, Peter Johnston-Wilder, David Pimm, Clare Lee

Routledge | 2010 | 3.ª edição | 348 páginas | pdf | 3 Mb

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What is the role of mathematics in the secondary classroom? What is expected of a would-be maths teacher? How is mathematics best taught and learnt? Learning to Teach Mathematics in the Secondary School combines theory and practice to present a broad introduction to the opportunities and challenges of teaching mathematics in the modern secondary school classroom. Written specifically with the new and student teacher in mind, the book covers a wide range of issues related to the teaching of mathematics, including: The role of ICT Assessment for Learning NEW Using mathematics in context NEW Communicating mathematically Planning mathematics lessons Including special-needs pupils Teaching mathematics post-16 Professional Development Already a major text for many university teaching courses, this fully revised third edition takes into account new developments in the National Curriculum as well as recent changes to the standards for Qualified Teacher Status. Featuring two brand new chapters, a glossary of useful terms, addresses for resources and organisations, and tasks designed to prompt critical reflection and support thinking and writing at Masters level, this book will help you make the most of school experience, during your training and beyond. Designed for use as a core textbook, this new edition of Learning to Teach Mathematics in the Secondary School provides essential guidance and advice for all trainee and practising teachers of secondary mathematics.

Table of Contents

CONTENTS

INTRODUCTION TO THE SERIES

ILLUSTRATIONS

FIGURES
TABLES

TASKS

NOTES ON CONTRIBUTORS

ACKNOWLEDGEMENTS

INTRODUCTION

MAKING THE MOST OF YOUR SCHOOL EXPERIENCE
HOW TO USE THIS BOOK

INTRODUCTION TO THE THIRD EDITION

1 MATHEMATICS EDUCATION: WHO DECIDES?

INTRODUCTION
MATHEMATICS AND YOU
MATHEMATICS AND EDUCATION
COMPETING INFLUENCES ON THE MATHEMATICS CURRICULUM
AGENCIES FOR CHANGE
FURTHER READING

2 MATHEMATICS IN THE NATIONAL CURRICULUM

INTRODUCTION
THE SCOPE, PRESCRIPTION AND PRESENTATION OF THE CURRICULUM
THE DEVELOPMENT AND REVISION OF THE CURRICULUM
PERFORMANCE STANDARDS AND ASSESSMENT WITHIN THE CURRICULUM
PROGRAMMES OF STUDY FOR THE CURRICULUM
FURTHER READING

3 PUPILS LEARNING MATHEMATICS

INTRODUCTION
THE SOCIAL CONTEXT OF LEARNING
THEORIES OF LEARNING AND KNOWLEDGE
FEELINGS AND MOTIVATION
THE COGNITIVE DIMENSION
FURTHER READING

4 DIFFERENT TEACHING APPROACHES

INTRODUCTION
TEACHING AS LISTENING, ASKING AND TELLING
FORMS OF CLASSROOM ORGANISATION
RESOURCES AND IDEAS FOR ENHANCING YOUR TEACHING
FURTHER READING

5 PLANNING FOR MATHEMATICS LEARNING

INTRODUCTION
LEARNING FROM TEACHERS PLANNING MATHEMATICS LESSONS
PLANNING A LESSON, PLANNING COLLABORATIVELY
PLANNING SEQUENCES OF LESSONS
PLANNING FOR OUT-OF-SCHOOL LEARNING
ESSENTIAL DOCUMENTS
FURTHER READING

6 ASSESSMENT FOR LEARNING

INTRODUCTION
LEARNING INTENTIONS AND SUCCESS CRITERIA (LISC)
FEEDBACK
QUESTIONING
PEER AND SELF-ASSESSMENT
FURTHER READING

7 ASSESSMENT AND PUBLIC EXAMINATIONS

INTRODUCTION
IN-CLASS ASSESSMENT
OTHER ASPECTS OF IN-CLASS ASSESSMENT
PUBLIC ASSESSMENTS AND EXAMINATIONS
GCSE ASSESSMENT
FURTHER READING

8 COMMUNICATING MATHEMATICALLY

INTRODUCTION
THE NATURE OF MATHEMATICAL LANGUAGE
WRITING MATHEMATICALLY
FURTHER READING

9 USING INFORMATION AND COMMUNICATION TECHNOLOGY (ICT)

INTRODUCTION
SOME BACKGROUND
CALCULATING DEVICES
SPREADSHEETS
GRAPH PLOTTERS
GRAPHIC CALCULATORS
DYNAMIC GEOMETRY PACKAGES
PROGRAMMING LANGUAGES – LOGO
SMALL TEACHING PROGRAMS
THE INTERNET AND CD-ROMS
FURTHER READING

10 INCLUSION IN PRACTICE: SPECIAL NEEDS PUPILS IN MAINSTREAM MATHEMATICS

INTRODUCTION
INCLUSION AND DIVERSITY, DISABILITY AND SPECIAL NEEDS
ORIENTING TO SPECIAL NEEDS
CLASSIFICATION AND CHARACTERISATION OF SPECIAL EDUCATIONAL NEEDS
PARTICULAR SPECIAL NEEDS AND LEARNING DISABILITIES
SPEECH, LANGUAGE AND COMMUNICATION AND EAL
SENSORY/PHYSICAL IMPAIRMENTS
RESOURCES FOR LEARNING
ONE OF A TEAM
ACKNOWLEDGEMENT
FURTHER READING

11 MATHEMATICS IN CONTEXT

INTRODUCTION
WHY DO PEOPLE DO MATHEMATICS?
SKILLS FOR LEARNING MATHEMATICS IN CONTEXT
STRENGTHS AND WEAKNESSES OF DIFFERENT CONTEXTS
PROBLEMS WITH USING CONTEXTS IN TEACHING
TEACHING MATHEMATICS IN CONTEXT
FURTHER READING

12 GETTING THE WHOLE PICTURE

INTRODUCTION
THE WHOLE CURRICULUM
THE WHOLE PERSON
FURTHER READING

13 TEACHING MATHEMATICS POST-16

INTRODUCTION
BACKGROUND: 14–19 PATHWAYS
KNOWLEDGE FOR TEACHING
QUALIFICATIONS: TYPES AND LEVELS
MATHEMATICS AND QUALIFICATIONS POST-16
INSTITUTIONS CATERING FOR POST-16 STUDENTS
THE NATURE OF STUDENTS POST-16
TEACHING STYLES
PREPARING TO TEACH A TOPIC
THE USE OF ICT IN POST-16 MATHEMATICS
REFLECTING ON THE PAST: LOOKING TO THE FUTURE?
FURTHER READING

14 PROFESSIONAL DEVELOPMENT

INTRODUCTION
FINDING THE RIGHT POST
THE FIRST YEAR OF TEACHING
DEVELOPING AS A TEACHER
DEVELOPING AS A MATHEMATICIAN
CAREER DEVELOPMENT
FURTHER READING

APPENDIX 1 GLOSSARY OF TERMS

APPENDIX 2 SOURCES AND RESOURCES

APPENDIX 3 MAKING CLOSED TASKS OPEN

APPENDIX 4 STARTING WITH ICT: PRACTICALITIES FOR BEGINNERS

APPENDIX 5 PRACTICAL TASK: ROLLING BALLS

APPENDIX 6 GROUP ACTIVITY

REFERENCES

NAME AND AUTHOR INDEX

SUBJECT INDEX

Developing Thinking in Statistics

2011-11-01T01:40:00.002+01:00

Alan Graham

Paul Chapman Educational Publishing | 2006| 288 páginas | PDF | 3 MB

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This book should prove to be an important addition to the relatively few publications that exist on statistical thinking. It very nicely encourages the reader to take an active learning approach through simultaneously promoting pedagogy with knowledge and skills enhancement in statistics. Understanding what the subject is for and what it can do are crucial in statistical education - by getting the reader to think statistically Mr Graham has provided us with a very readable book that helps to dispel the poor reputation that statistics has acquired over many years' - Professor Neville Davies, Director, Royal Statistical Society Centre for Statistical Education, Nottingham Trent University

Secondary Algebra Education

2011-10-30T12:15:00.003+01:00

Paul Drijvers

1.º capítulo, online: sensepublishers.com

Página de Paul Drijvers:

fi.uu.nl

Sense Publishers | 2010 | 234 páginas | pdf | 5,6 Mb

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Nowadays, algebra education is subject to worldwide scrutiny. Different opinions on its goals, approaches and achievements are at the heart of debates among teachers, educators, researchers and decision makers. What should the teaching of algebra in secondary school mathematics look like? Should it focus on procedural skills or on algebraic insight? Should it stress practice or integrate technology? Do we require formal proofs and notations, or do informal representations suffice? Is algebra in school an abstract subject, or does it take its relevance from application in (daily life) contexts? What should secondary school algebra education that prepares for higher education and professional practice in the twenty-first century look like?

This book addresses these questions, and aims to inform in-service and future teachers, mathematics educators and researchers on recent insights in the domain, and on specific topics and themes such as the historical development of algebra, the role of productive practice, and algebra in science and engineering in particular. The authors, all affiliated with the Freudenthal Institute for Science and Mathematics Education in the Netherlands, share a common philosophy, which acts as a – sometimes nearly invisible – backbone for the overall view on algebra education: the theory of realistic mathematics education. From this point of departure, different perspectives are chosen to describe the opportunities and pitfalls of today’s and tomorrow’s algebra education. Inspiring examples and reflections illustrate current practice and explore the unknown future of algebra education to appropriately meet students’ needs.

CONTENTS PREFACE 1. ALGEBRA EDUCATION: EXPLORING 2. ALGEBRA FROM AHMES TO APPLET 3. FROM ARITHMETIC TO ALGEBRA 4. PATTERNS AND FORMULAS 5. RESTRICTIONS IN ALGEBRA 6. ALGEBRA IN FUNCTION 7. PRINCIPLES OF PRACTICE 8. ALGEBRA AND TECHNOLOGY 9. ALGEBRA IN SCIENCE AND ENGINEERING INDEX

Pi: A Biography of the World's Most Mysterious Number

2011-10-30T11:37:00.001+01:00

Alfred S. Posamentier, Ingmar Lehmann

Prometheus Books | 2004 | 324 páginas | Djvu | 3,4 MB

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Comentário em: MAA

In this delightful layperson's introduction to one of math's most interesting phenomena, Drs Posamentier and Lehmann review p's history from pre-biblical times to the 21st century, the many amusing and mind-boggling ways of estimating p over the centuries, quirky examples of obsessing about p (including an attempt to legislate its exact value), and useful applications of p in everyday life, including statistics.

Reading, Writing, and Proving: A Closer Look at Mathematics

2011-10-28T17:05:00.001+02:00

2nd Edition (Undergraduate Texts in Mathematics)

Ulrich Daepp, Pamela Gorkin

Springer | 2011 | 391 páginas | pdf | 5,7 Mb

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This book, which is based on Polya's method of problem solving, aids students in their transition from calculus (or precalculus) to higher-level mathematics. The book begins by providing a great deal of guidance on how to approach definitions, examples, and theorems in mathematics and ends with suggested projects for independent study. Students will follow Polya's four step approach: analyzing the problem, devising a plan to solve the problem, carrying out that plan, and then determining the implication of the result. In addition to the Polya approach to proofs, this book places special emphasis on reading proofs carefully and writing them well. The authors have included a wide variety of problems, examples, illustrations and exercises, some with hints and solutions, designed specifically to improve the student's ability to read and write proofs. Historical connections are made throughout the text, and students are encouraged to use the rather extensive bibliography to begin making connections of their own. While standard texts in this area prepare students for future courses in algebra, this book also includes chapters on sequences, convergence, and metric spaces for those wanting to bridge the gap between the standard course in calculus and one in analysis.

Contents

Chapter 1: The How, When, and Why of Mathematics

Solutions to Exercises

Spotlight: George Pólya

Problems

Tips on Doing Homework

Chapter 2: Logically Speaking

Solutions to Exercises

Problems

Chapter 3: Introducing the Contrapositive and Converse

Definitions

Solutions to Exercises

Problems

Chapter 4: Set Notation and Quantifiers

Solutions to Exercises

Problems

Tips on Quantification

Chapter 5: Proof Techniques

Definitions

Problems

Tips on Definitions

Chapter 6: Sets

Definitions

Solutions to Exercises

Spotlight: Paradoxes

Problems

Chapter 7: Operations on Sets

Definition

Solutions to Exercises

Problems

Chapter 8: More on Operations on Sets

Definitions

Solutions to Exercises

Problems

Chapter 9: The Power Set and the Cartesian Product

Definitions

Solutions to Exercises

Problems

Tips on Writing Mathematics

Chapter 10: Relations

Definitions

Solutions to Exercises

Problems

Tips on Reading Mathematics

Chapter 11: Partitions

Definition

Solutions to Exercises

Problems

Tips on Putting It All Together

Chapter 12: Order in the Reals

Definitions

Solutions to Exercises

Problems

Chapter 13: Consequences of the Completeness of R

Definitions

Solutions to Exercises

Problems

Tips: You Solved It. Now What?

Chapter 14: Functions, Domain, and Range

Definitions

Solutions to Exercises

Spotlight: The Definition of Function

Problems

Chapter 15: Functions, One-to-One, and Onto

Definitions

Solutions to Exercises

Problems

Chapter 16: Inverses

Definitions

Solutions to Exercises

Problems

Chapter 17: Images and Inverse Images

Definitions

Solutions to Exercises

Spotlight: Minimum or Infimum?

Problems

Chapter 18: Mathematical Induction

Definitions

Solutions to Exercises

Problems

Chapter 19: Sequences

Definitions

Solutions to Exercises

Problems

Chapter 20: Convergence of Sequences of Real Numbers

Definitions

Solutions to Exercises

Problems

Chapter 21: Equivalent Sets

Definitions

Solutions to Exercises

Problems

Chapter 22: Finite Sets and an Infinite Set

Definition

Solutions to Exercises

Problems

Chapter 23:Countable and Uncountable Sets

Definitions

Solutions to Exercises

Problems

Chapter 24: The Cantor–Schröder–Bernstein Theorem

Definitions

Solutions to Exercises

Spotlight: The Continuum Hypothesis

Problems

Chapter 25:Metric Spaces

Definitions

Solutions to Exercises

Problems

Chapter 26: Getting to Know Open and Closed Sets

Definitions

Solutions to Exercises

Problems

Chapter 27: Modular Arithmetic

Definitions

Solutions to Exercises

Problems

Chapter 28: Fermat’s Little Theorem

Definition

Solutions to Exercises

Spotlight: Public and Secret Research

Problems

Chapter 29: Projects

Tips on Talking about Mathematics

29.1 Picture Proofs

Introduction

Prerequisites

Guided Project

Open-Ended Project

Notes and Sources

29.2 The Best Number of All (and Some Other Pretty Good Ones)

Introduction

Prerequisites

Guided Project

Open-Ended Project

Notes and Sources

29.3 Set Constructions

Introduction

Prerequisites

Guided Project

Open-Ended Project

Notes and Sources

29.4 Rational and Irrational Numbers

Introduction

Prerequisites

Guided Project

Open-Ended Project

Notes and Sources

29.5 Irrationality of e and p

Introduction

Prerequisites

Guided Project

Open-Ended Project

Notes and Sources

29.6 A Complex Project

Introduction

Prerequisites

Guided Project

Open-Ended Project

Notes and Sources

29.7 When Does f-1 = 1/f ?

Introduction

Prerequisites

Guided Project

Open-Ended Project

Notes and Sources

29.8 Pascal’s Triangle

Introduction

Prerequisites

Guided Project

Open-Ended Project

Notes and Sources

29.9 The Cantor Set

Introduction

Prerequisites

Guided Project

Open-Ended Project

Notes and Sources

29.10 The Cauchy–Bunyakovsky–Schwarz Inequality

Introduction

Prerequisites

Guided Project

Open-Ended Project

Notes and Sources

29.11 Algebraic Numbers

Introduction

Prerequisites

Guided Project

Open-Ended Project

Notes and Sources

29.12 The Axiom of Choice

Introduction

Prerequisites

Guided Project

Open-Ended Project

Notes and Sources

29.13 The RSA Code

Introduction

Prerequisites

Guided Project

Open-Ended Project

Notes and Sources

Spotlight: Hilbert’s Seventh Problem

Appendix

Algebraic Properties of R

Order Properties of R

Axioms of Set Theory

Pólya’s List

References

Index

Matematica e cultura 2011

2011-10-28T16:26:00.001+02:00

Michele Emmer

Springer | 2011 | 249 páginas | pdf | 10 Mb

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Raccoglie gli articoli presentati al convegno di Matematica e cultura del marzo 2010.Picasso che dialoga con Luciano Emmer è l’immagine simbolo di Matematica e cultura 2011. Un omaggio al grande artista spagnolo e un ricordo del regista italiano che ha partecipato diverse volte agli incontri veneziani. E quelle immagini indimenticabili di Picasso a torso nudo che affresca una grande parete, e i suoi segni cancellati per un banale errore umano e rimasti solo sulla pellicola. Di arte, di arte contemporanea, di arte antica si parla. Di Venezia, di quel grande capolavoro che è la basilica di San Marco, e dei mosaici dimenticati del suo pavimento. Ne scrivono Ettore Vio che della basilica è il Proto, e Luigi Fregonese che ne ha portato a termine, con altri, il rilievo tridimensionale. Un lavoro di 20 anni! E di teatro, di matematica e cucina, non tralasciando le tante applicazioni della matematica. Con un occhio particolare alla letteratura di Neal Stephenson e al suono delle maree. Non potevano mancare le bolle di sapone e i fantastici progetti architettonici basati su lamine di sapone computerizzate di Tobias Walliser. Né manca la geometria delle gondole e i rapporti tra spazio matematico e teologia. Matematica, Venezia, cultura, un incontro che continua a stupire, anno dopo anno, rinnovandosi sempre. Pur restando in continuità con gli eventi passati.Matematica e cultura 2011. Un omaggio al grande artista spagnolo e un ricordo del regista italiano che ha partecipato diverse volte agli incontri veneziani. E quelle immagini indimenticabili di Picasso a torso nudo che affresca una grande parete, e i suoi segni cancellati per un banale errore umano e rimasti solo sulla pellicola. Di arte, di arte contemporanea, di arte antica si parla. Di Venezia, di quel grande capolavoro che è la basilica di San Marco, e dei mosaici dimenticati del suo pavimento. Ne scrivono Ettore Vio che della basilica è il Proto, e Luigi Fregonese che ne ha portato a termine, con altri, il rilievo tridimensionale. Un lavoro di 20 anni! E di teatro, di matematica e cucina, non tralasciando le tante applicazioni della matematica. Con un occhio particolare alla letteratura di Neal Stephenson e al suono delle maree. Non potevano mancare le bolle di sapone e i fantastici progetti architettonici basati su lamine di sapone computerizzate di Tobias Walliser. Né manca la geometria delle gondole e i rapporti tra spazio matematico e teologia. Matematica, Venezia, cultura, un incontro che continua a stupire, anno dopo anno, rinnovandosi sempre. Pur restando in continuità con gli eventi passati.

Indice
Parole dipinte. Omaggio a Luciano Emmer
La basilica di San Marco da cappella ducale a cattedrale della città: storia, procuratori, proti e restauri
Tutta la storia di Venezia è legata alla basilica
La presenza della signoria
Gli studi sull’acustica
Jacopo Sansovino
Le modifiche al presbiterio
I grandi lavori della piazza
La struttura e gli interventi
Il crollo di Venezia
L’Austria
Napoleone
L’epoca moderna
Le trasformazioni
Venezia all’Austria
Pietro Saccardo
I calchi a Parigi
Ferdinando Ongania
Saccardo proto
La caduta del campanile
Manfredo Manfredi
Luigi Marangoni
Le due guerre
La fabbriceria ritorna procuratoria
Il dopoguerra
L’alluvione del 1966
Gli studi e i restauri contemporanei
Bibliografia
Simmetria a San Marco
La basilica di San Marco
Bibliografia
Il pavimento tessulare di San Marco
La conoscenza del Bene Culturale e la sua documentazione
Metodi di rilievo
L’ortofoto digitale delle superfici complesse
La valorizzazione del pavimento tessulare attraverso la consultazione definitiva dell’ortofoto
Bibliografia
Gondole e traghetti
Traghetti e gondole da guadagno
I traghetti
La gondola
Bibliografia
Il design digitale nell’architettura – oltre la geometria classica
Idee matematiche come riferimento per progetti e design architettonici
Un hotel acquatico realizzato sulla base della superficie di Costa-Hoffman-Meeks
Bibliografia
Un piccolo libro sulle bolle di sapone
Un piccolo libro sulle bolle
Descrizione delle osservazioni fatte dai riferenti
Bibliografia
Quando il cielo ci cade sulla testa
Tolomeo
Kepler
Newton
Laplace
Le Verrier
Poincaré
Kolmogorov, Arnold, Moser e Nekhoroshev
Laskar
Bibliografia
Google, come cercare (e trovare) un ago in un pagliaio
Quando la matematica domina il mondo
Il web; cos’è e, soprattutto, quanto è grande?
La rivoluzione Google
Entra in gioco la matematica
Non solo ricerche
Non è tutto oro
Privacy
Censura
Diritto d’autore
Matematica e Cultura
Bibliografia
Ottimizzazione su reti
Introduzione
La teoria dei grafi
Il problema del percorso ottimo
Un problema ancora aperto
Bibliografia
Recenti sviluppi nella Teoria dei Giochi: l’ingegneria strategica
Introduzione
Ingegneria dei mercati
Ingegneria dei contratti
Ingegneria dei conflitti
Ingegneria delle istituzioni
Bibliografia
Affascinanti forme per oggetti topologici
Introduzione
Raggruppamenti di bolle e schiume
Eversioni di sfere con l’energia di Willmore
Nodi stretti
Visualizzare matematica e arte
Bibliografia
La matematica in cucina, un’introduzione allo spettacolo
La matematica in cucina
Da dove vengono gli oggetti matematici?
Ma che c’entra la cucina?
Bibliografia
Amleto e il teatro nell’era scientifica
Coincidenze e corrispondenze
Il teorema di Amleto
Bibliografia
La canzone delle maree
L’analisi armonica delle maree
Forme e formule
Matematica e architettura
Costruzione di nuovi strumenti
La formazione
Tante lingue in continua evoluzione
Rappresentazione implicita delle superfici
Rappresentazione parametrica delle superfici
La paura della matematica
Sintetizzatore di forme
SurfaceSynthetizer
Conclusioni
Bibliografia
Genesi. 1,1 2,4
L’origine dell’idea moderna dello spazio tra matematica, fisica e teologia
Bibliografia
Estratto da Anathem di Neal Stephenson
Dal Glossario di Anathem
Autori
Collana Matematica e cultura

Matematica e cultura 2010

2011-10-28T16:19:00.003+02:00

Michele Emmer

Springer | 2010 | 323 páginas | pdf | 9 Mb

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Il colonnello Yorke (John Wayne) torna da una missione contro gli Apache (alla frontiera tra USA e Messico) e incontra il generale inviato a parlare con lui. "Mi dispiace Kirby, vostro figlio bocciato in matematica a West Point, lo hanno allontanato dall.Accademia Militare". Dialogo delle scene iniziali del film "Rio Grande" di John Ford, 1950. Morale: neppure nei territori di frontiera in lotta con gli Apache si possono trascurare gli studi di matematica! Di cinema, ma anche di letteratura, del grande amore di Stendhal per la matematica, si parla. E della geometria visionaria dei vestiti di Capucci, dei legami con l'arte contemporanea e i numeri. Con un omaggio a quella singolare figura di intellettuale che fu Pavel Florenskij, prete ortodosso, matematico, fondatore della scuola di Design di Mosca con Kandinsky. Riflessioni sul tema di matematica e religione, di cui molto si parla a sproposito. E poi di musica e di danza, delle dune del deserto e della ricostruzione virtuale degli affreschi del Mantegna distrutti durante la seconda guerra mondiale a Padova. Per finire con i grandi effetti speciale del cinema, da "King Kong" al "Signore degli anelli", fino al recentissimo "Avatar". Tanti temi, un grande legame culturale: la matematica. Perché della matematica non si può fare a meno!

Title Page
Copyright Page
Nel lontano West
Indice
Matematica e religione. Omaggio a Florenskij
Spazio iconico, geometria non e uclideae cultura nella visione del mondo di Pavel Florenskij
La geometria non euclidea in Russia: dalla scienza alla metafora
Lo spazio curvo delle icone
Conclusioni
Bibliografia
Pavel Florenskij,tra matematica e religione
L’interesse per la matematica
L’insegnamento ai Laboratori e le ricerche scientifiche sulla geometria e sulle teorie dello spazio
Florenskij tra matematica e religione nella Russia Sovietica [10]
Bibliografia
Curve di riempimento dello spazio nella new media art ispirata a Pavel Florenskij
Introduzione
L’interesse di Pavel Florenskij per le curve di riempimento dello spazio
La costruzione delle curve di riempimento dello spazio e la loro scoperta
Kazimir Malevich sulle forme spezzate
Italo Calvino e i meandri della narrazione
Opere più recenti
Conclusioni
Ringraziamenti
Bibliografia
Florenskij, l’infinito, la teologia
Bibliografia
Matematica e arte
Superfici di seta: la geometria negli abiti di Capucci
Dal Teorema Egregium al pallone da calcio
Curvature in alcuni abiti di Capucci
Le superfici algebriche
I fibrati
Le foliazioni
Conclusioni
Bibliografia
Pop Numbers
Nota
Bibliografia
Forme matematiche: dalla formula alla forma nello spazio La matematica nell’opera di Donald Judd e Ruth Vollmer
Introduzione – la matematica nel Circolo di New York
Specific Objects
Spherical Objects
La conquista dello spazio
Dalla formula alla forma I
Forme spaziali
Dalla formula alla forma II
Le forme dello spazio
Bibliografia
Matematica e immagini
Da King Kong a Ratatouille: nuove sfide matematiche per i personaggi digitali
Effetti speciali
Computer Graphics
Il Digital Character
Maturità
Le dimensioni contano
Interazione di luce e materia
Bibliografia
Filmografia*
_zur form Un progetto di Florian Grond, Thomas Kienzl e Gabriele Engelhardt
Cenni storici sui modelli matematici
L’origine delle forme scelte
Brevi cenni storici sulle dinamiche non lineari e sugli attrattori strani
Il ruolo della visualizzazione nella comunicazione dei risultati delle ricerche
Il progetto _zur form, forme, foto, installazione
Conclusioni
Ringraziamenti
Bibliografia
M.C. Escher e il piano iperbolico
Coxeter e Escher
Il piano iperbolico
In superficie
Cristalli iperbolici
Bibliografia*
Matematica e cinema: novità
Bibliografia
Matematica e applicazioni
Pile di sabbia e dune del deserto: materia granulare e matematica
La materia granulare: interesse e applicazioni
L’effetto “noci del Brasile”
La crescita di una pila di sabbia su di una tavola
I modelli matematici
La dinamica delle dune
Le dune “cantano”!
Conclusioni
Bibliografia
La matematica dentro l’immagine*
Introduzione
Ricomporre Mantegna
Immagini digitali e rotazioni
Complessità e tempo di calcolo
Una soluzione ingegnosa: le espansioni in armoniche circolari
Ricolorazione dell’immagine
Ringraziamenti
Bibliografia
La fisica degli stormi di storni in volo
L’analisi di un fenomeno biologico
Un sistema di ripresa metrico
Analisi statica del fenomeno biologico
Ricostruzione tridimensionale
Analisi statica
Ricostruzione tridimensionale delle singole traiettorie
Definizione di energia di una traiettoria
Analisi dinamica
Conclusioni
Bibliografia
Matematica e…
Prezzi nel caos
Adam Smith e la dottrina della mano invisibile
Un modello semplice: economia di scambio
Generalizzazioni
Conclusioni
Bibliografia
Matematica e sincerità
Paradossi e puzzle logici
Sincerità e interazioni economiche
La scoperta delle bugie
La prevenzione delle bugie
Postilla
Bibliografia
Matematica e letteratura
Percorsi
Bibliografia
Matematica: passione giovanile di Stendhal
Bibliografia
Conti e racconti: la scienza come laboratorio creativo
Bibliografia
Matematica e musica
Dianaballo1
Lirica Numerica
Dai numeri alle parole
Dai numeri alle note
La messa in scena
Il testo recitato
La scenografia
Bibliografia
Matematica e danza
Incontrare la scienza a passo di danza: flamenco
Conclusioni
Ringraziamenti
Bibliografia
Venezia
Le perle veneziane: un tesoro da scoprire
Le perle di Venezia
Le “margarite”, ossia le perle di canna di vetro
Le perle “a lume”
Bibliografia
Autori
Collana Matematica e cultura
Matematica e applicazioni

The Stanford Mathematics Problem Book

2011-10-28T15:07:00.007+02:00

George Polya, Jeremy Kilpatrick

Dover | 2009 | 73 páginas

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Teachers College Press | 1973 | 73 páginas

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This volume features a complete set of problems, hints, and solutions based on Stanford University's well-known competitive examination in mathematics. It offers stude

nts at both high school and college levels an excellent mathematics workbook. Filled with rigorous problems, it assists students in developing and cultivating their logic and probability skills.

A short account of the history of mathematics

2011-10-28T14:27:00.002+02:00

W. W. Rouse Ball

The Macmillan Company | 1901

online: archive.org

online: gutenberg.org

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This is the classic resource on the history of mathematics providing a deeper understanding of the subject and how it has impacted our culture, all in one essential volume. From the early Greek influences to the middle ages and the renaissance to the end of the 19th-century, trace the fascinating foundation of mathematics as it developed through the ages.

Geometry Revisited

2011-10-28T13:58:00.002+02:00

H.S.M. Coxeter e S. L. Greitzer

The Mathematical Association of America |1967 | 207 páginas| DjVu | 1,5 M

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Among the many beautiful and nontrivial theorems in geometry found in Geometry Revisited are the theorems of Ceva, Menelaus, Pappus, Desargues, Pascal, and Brianchon. A nice proof is given of Morley's remarkable theorem on angle trisectors. The transformational point of view is emphasized: reflections, rotations, translations, similarities, inversions, and affine and projective transformations. Many fascinating properties of circles, triangles, quadrilaterals, and conics are developed.

The Number Sense: How the Mind Creates Mathematics

2011-10-28T13:47:00.001+02:00

Stanislas Dehaene

Oxford University Press, USA | 2011 | 339 páginas

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Our understanding of how the human brain performs mathematical calculations is far from complete, but in recent years there have been many exciting breakthroughs by scientists all over the world. Now, in The Number Sense, Stanislas Dehaene offers a fascinating look at this recent research, in an enlightening exploration of the mathematical mind. Dehaene begins with the eye-opening discovery that animals--including rats, pigeons, raccoons, and chimpanzees--can perform simple mathematical calculations, and that human infants also have a rudimentary number sense. Dehaene suggests that this rudimentary number sense is as basic to the way the brain understands the world as our perception of color or of objects in space, and, like these other abilities, our number sense is wired into the brain. These are but a few of the wealth of fascinating observations contained here. We also discover, for example, that because Chinese names for numbers are so short, Chinese people can remember up to nine or ten digits at a time--English-speaking people can only remember seven. The book also explores the unique abilities of idiot savants and mathematical geniuses, and we meet people whose minute brain lesions render their mathematical ability useless. This new and completely updated edition includes all of the most recent scientific data on how numbers are encoded by single neurons, and which brain areas activate when we perform calculations. Perhaps most important, The Number Sense reaches many provocative conclusions that will intrigue anyone interested in learning, mathematics, or the mind. "A delight." --Ian Stewart, New Scientist"Read The Number Sense for its rich insights into matters as varying as the cuneiform depiction of numbers, why Jean Piaget's theory of stages in infant learning is wrong, and to discover the brain regions involved in the number sense." --The New York Times Book Review"Dehaene weaves the latest technical research into a remarkably lucid and engrossing investigation. Even readers normally indifferent to mathematics will find themselves marveling at the wonder of minds making numbers." --Booklist

Contents

Preface to the Second Edition ix

Preface to the First Edition xiii

Introduction xvii

part one | our numerical heritage

1. Talented and Git ed Animals 3

2. Babies Who Count 30

3 . The Adult Number Line 53

part two | beyond approximation

4 . Th e Language of Numbers 79

5. Small Heads for Big Calculations 104

6. Geniuses and Prodigies 129

part three | of neurons and numbers

7. Losing Number Sense 161

8 . Th e Computing Brain 191

9. What is a Number? 214

part four | the contemporary science of number and brain

10. The Number Sense, Fit een Years Later 237

appendix A 279

appendix B 281

bibliography 283

index 3 0 7

Mathematics for the Nonmathematician

2011-10-27T20:30:00.002+02:00

Morris Kline

Courier Dover Publications | 1985 | 658 páginas

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Erudite and entertaining overview follows development of mathematics from ancient Greeks, through Middle Ages and Renaissance to the present. Chapters focus on logic and mathematics, the number, the fundamental concept, differential calculus, the theory of probability, and much more. Exercises and problems.

Mathematics and the Physical World

2011-10-27T20:25:00.002+02:00

Morris Kline

Dover Publications | 1981 | 496 páginas

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Stimulating account of development of basic mathematics from arithmetic, algebra, geometry and trigonometry, to calculus, differential equations and non-Euclidean geometries. Also describes how math is used in optics, astronomy, motion under the law of gravitation, acoustics, electromagnetism, other phenomena.

Mathematics : A Cultural Approach

2011-10-27T20:11:00.002+02:00

Morris Kline

Addison-Wesley | 1963 | 701 páginas

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Mathematics in Aristotle

2011-10-27T19:42:00.001+02:00

Thomas Heath

Clarendon Press | 1949 | 303 páginas |

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Mathematics in Aristotle is the result of work done during the last years of my husband's life, which he devoted to reading all that had been written on the subject and to making his own translations from the Greek.

His eagerness to return to this work too soon after a serious illness in 1939 was probably instrumental in hastening his end.

After his death in 1940 I found the manuscript (which I took to be unfinished) and consulted Sir David Ross as to the possibility of getting it completed. He most kindly read it through and, to my immense satisfaction, reported that the rough copy was, in fact, complete and advised that the fair copy, much of which was already done, should be finished in typescript.

This I undertook to do myself, and it proved not only a welcome distraction from the more disturbing elements of' total war', but, in addition, an unexpectedly enjoyable introduction to the fascinating world of Aristotle, which I had hitherto regarded as far above the head of one not a classical scholar. I had, however, not failed to remark the concomitance of Aristotelian learning with a love of music. During a short visit to Corpus Christi College during the presidency of Thomas Case, I had the unforgettable experience, having returned somewhat early from a Balliol Sunday concert, of discovering the President and my husband playing, by candle-light on the Broadwood grand piano, with unrestrained fortissimo, the four-hand arrangements of Haydn Symphonies. The conventional fiction obtained that my being a professional pianist precluded such indulgence within my hearing!

My very grateful thanks are due to Sir David Ross for his invaluable help and encouragement. For the reading of the proofs I am indebted to him and to Mr. Ivor Thomas, M.P., whose knowledge of Greek mathematics has been of the greatest assistance. Having no Greek myself, I have to thank Mr. Kerry Downes and Mr. P. R. W. Holmes for their assistance in transcribing the Greek quotations, and also my son Geoffrey T. Heath who, since his demobilization, has helped me in reading proofs and revising Greek quotations, mathematical figures, and formulae.

I regret the absence of a bibliography, as my husband left no note of authorities consulted, though some indications are given in footnotes as well as in the text.

The Copernicus of Antiquity - Aristarchus of Samos

2011-10-27T19:39:00.001+02:00

Thomas L. Heath

online: archive.org

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Apollonius of Perga Treatise on Conic Sections 1896

2011-10-27T19:36:00.001+02:00

Thomas L. Heath

online: archive.org

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Índice

Introduction: pt. I. The earlier history of conic sections among the Greeks. 1. The discovery of conic sections; Menaechmus. 2. Aristaeus and Euclid. 3. Archimedes. pt. II. Introduction to the conics of Apollonius. 1. The author and his own account of the conics. 2. General characteristics. 3. The methods of Apollonius. 4. The construction of a conic by means of tangents. 5. The three-line and four-line locus. 6. The construction of a conic through five points.-Appendix: Notes on the terminology of Greek geometry.--The conics of Apollonius

The Works of Archimedes

2011-10-27T19:32:00.000+02:00

Thomas L. Heath

PDF| 18,45 MB
on-line: archive.org

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Diophantus of Alexandria: A Study in the History of Greek Algebra

2011-10-27T19:28:00.002+02:00

Second Edition.
Thomas L. Heath
Cambridge, University Press | 1910| 387 páginas | PDF| 39,47 MB

online: archive.org

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More Mathematical Activities: A Resource Book for Teachers

2011-10-26T21:35:00.002+02:00

Brian Bolt

Cambridge University Press | 1985 | 112 páginas | PDF | 4 MB

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This book follows the successful Mathematical Activities by the same author and has been written to provide teachers with further ideas to enrich their teaching of mathematics. It contains 127 investigations, puzzles, games and practical activities together with a commentary which provides solutions and additional ideas. These activities are suitable for use with children from age nine upwards to stimulate their interest and encourage mathematical thinking.

A Mathematical Jamboree

2011-10-26T21:25:00.002+02:00

Brian Bolt

Cambridge University Press | 1995 | 112 páginas | PDF | 2,32 MB

online: mathhome.ir

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A Mathematical Jamboree follows the very successful puzzle books by the same author. It contains 114 puzzles and activities to challenge people of all ages. There is a detailed commentary at the end of the book, giving solutions and explanations, together with the occasional follow-up problem

Mathematical Cavalcade

2011-10-26T21:22:00.002+02:00

Brian Bolt

Cambridge University Press | 1992 |124 páginas | PDF | 2,2 MB

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Mathematical Cavalcade follows the very successful Amazing Mathematical Amusement Arcade and The Mathematical Funfair by the same author. It contains a further 131 puzzles to challenge people of all ages. Hints and solutions are given in a commentary at the back of the book.

The Mathematical Funfair

2011-10-26T21:15:00.002+02:00

Brian Bolt

Cambridge University Press | 1989 |128 páginas | PDF | 2,6 MB

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This book follows the successful Amazing Mathematical Amusement Arcade by the same author. It contains a further 128 puzzles and games designed to challenge people of all ages. The subjects range from matchsticks and coins to chocolate manufacture and expeditions across Dartmoor. The second part of the book contains a commentary giving hints and solutions.

A Mathematical Pandora's Box

2011-10-26T21:11:00.002+02:00

Brian Bolt

Cambridge University Press | 1993 | 126 páginas | PDF | 2,4 MB

online:

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A Mathematical Pandora's Box has been written in response to the success of Brian Bolt's earlier mathematical puzzle books. Through his own experience, the author has discovered a worldwide interest in these and similar puzzles. Not only do they stimulate creative thinking but they can also open up new areas of mathematics to the reader. This book contains 142 activities: in addition to puzzles, there are games, tricks, models and explanations of various phenomena. They range from number manipulation, through happy and amicable numbers, coin puzzles, picnicking bears and pentominoes, to building shapes with cubes. Some of the puzzles date from hundreds of years ago while many others are original, giving everyone something to think about. There is a detailed commentary at the end of the book, giving solutions and explanations, together with the occasional follow-up problem.

Even More Mathematical Activities

2011-10-26T21:07:00.002+02:00

Brian Bolt

Cambridge University Press | 1987| 224 Páginas | 4 MB

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This book follows the tradition of the highly successful books, Mathematical Activities and More Mathematical Activities by the same author. It contains a further 133 puzzles, investigations, games, projects and applications of mathematics, together with a commentary which provides solutions and additional ideas. These activities are suitable for use with children from age nine upwards to stimulate their interest and encourage mathematical thinking.

Mathematical Activities: A Resource Book for Teachers

2011-10-26T21:02:00.002+02:00

Brian Bolt

Cambridge University Press | 1982 | 224 Páginas | PDF | 4,51 MB

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This book contains more than 150 games, puzzles and investigations designed to motivate everyone interested in mathematics. Many of the activities encourage creative thinking and practical work. The book provides a resource of ideas for all those concerned with mathematical education.

Issues in Teaching Numeracy in Primary Schools

2011-10-25T17:30:00.002+02:00

Ian Thompson

Open University Press | 2010 | 2.ª Edição | 270 páginas | PDF

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"For more than a decade, the 'Thompson Trilogy' has chronicled the ebb and flow of primary mathematics in England, to the benefit of anyone with an interest in children's learning. The first edition anticipated the National Numeracy Strategy, helping teachers to understand and to implement the new pedagogies. Ian Thompson devotees, past and present, will be delighted with this new edition, which maps the territory in the post-strategy era. Although set in the contemporary context of the most recent Reports and Reviews, many of the issues addressed in this edition are timeless, This is an important book - for the present, and for posterity." Tim Rowland, University of Cambridge, UK The new edition of this bestselling book provides an accessible guide to a wide range of research evidence about teaching and learning mathematics. Major changes in the primary mathematics curriculum in recent years – such as those recommended in the National Numeracy Strategy, the Primary National Strategy, the Early Years Foundation Stage, the Williams, Rose and Alexander Reviews – are reflected throughout the book. The new edition comprises fourteen new chapters, including a section devoted to post-Williams issues and four popular chapters that have been retained and updated in light of the vast changes in the field. Key topics include: Using resources, ICT, AfL and problem solving approaches effectively Learning from errors and misconceptions Developing mental and written calculation The 'gifted and talented' Transition from EYFS into Key Stage 1 Intervention and the Every Child Counts programme This popular book is essential reading for all trainee and practising primary school teachers, classroom assistants and mathematics specialist teachers. Contributors: Mike Askew, Patrick Barmby, Meindert Beishuizen, Margaret Brown, Kev Delaney, Nick Dowrick, Sylvia Dunn, Richard English, Sue Gifford, Tony Harries, Steve Higgins, Jeremy Hodgen, Louise Matthews, Frank Monaghan, Mike Ollerton, Julie Ryan, Ian Thompson, John Threlfall, Julian Williams, Jan Winter

Contents

Notes on contributors ix

Editor’s preface xv

SECTION 1

Setting the context 1

1 Swings and roundabouts 3

Margaret Brown

SECTION 2

Post-Williams issues 27

2 It ain’t (just) what you do: effective teachers of numeracy 31

Mike Askew

3 Teaching for understanding/understanding for teaching 45

Patrick Barmby, Tony Harries and Steve Higgins

4 Thinking aloud means talking allowed: group work in the primary school mathematics classroom 58

Frank Monaghan

5 Making connections: teachers and children usingresources effectively 72

Kev Delaney

6 Using problem-solving approaches to learn mathematics 84

Mike Ollerton

7 The role of ICT 97

Richard English

8 Shaking the foundations: does the Early Years Foundation Stage provide a secure basis for early mathematics? 108

Sue Gifford

9 Home–school knowledge exchange 118

Jan Winter

SECTION 3

Assessment issues 131

10 Assessment for learning: what is all the fuss about? 133

Jeremy Hodgen and Mike Askew

11 Children’s mathematical understanding as a work in progress: learning from errors and misconceptions 146

Julie Ryan and Julian Williams

SECTION 4

Calculation issues 159

12 Getting your head around mental calculation 161

Ian Thompson

13 The empty number line 174

Meindert Beishuizen (1935–2009)

14 Written calculation: addition and subtraction 188

Ian Thompson

15 Progression in the teaching of multiplication 199

Ian Thompson

16 Progression in the teaching of division 210

Ian Thompson

SECTION 5

Special needs issues 221

17 Numbers Count: developing a national approach to early intervention 223

Sylvia Dunn, Louise Matthews and Nick Dowrick

18 The ‘gifted and talented’ 235

John Threlfall

Index 249

The Open-Ended Approach: A New Proposal for Teaching Mathematics

2011-10-25T17:14:00.001+02:00

Jerry P. Becker

National Council of Teachers of Mathematics | 1997 | 92 páginas | Djvu | 3 Mb

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This book is an English translation from the Japanese book Open-Ended Approach in Arithmetic and Mathematics: A New Proposal for the Improvement of Teaching. It substantiates the effectiveness of open-ended problems as a method to evaluate higher-order-thinking skills, as well as its rich potential for improving teaching and learning.

Mathematical Misconceptions: A Guide for Primary Teachers

2011-10-25T16:56:00.003+02:00

Anne Cockburn, Paul Littler

Sage Publications | 2008 | 177 páginas | PDF | 2 MB

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With contributors comprised of teachers, teacher educators, mathematicians, and psychologists, Mathematical Misconceptions brings together information about pupils’ work from four different countries, and looks at how children, from the ages of 3 - 11, think about numbers and use them. It explores the reasons for their successes, misunderstandings, and misconceptions, while also broadening the reader’s own mathematical knowledge.

Contents

List of figures vi

List of pictures ix

List of tables x

Introduction 1

0 Zero: understanding an apparently paradoxical number 7

Anne D. Cockburn and Paul Parslow-Williams

1 Equality: getting the right balance 23

Paul Parslow-Williams and Anne D. Cockburn

2 Beginning to unravel misconceptions 39

Sara Hershkovitz, Dina Tirosh and Pessia Tsamir

3 Insights into children’s intuitions of addition, subtraction, multiplication and division 54

Dina Tirosh, Pessia Tsamir and Sara Hershkovitz

4 Right or wrong? Exploring misconceptions in division 71

Pessia Tsamir, Sarah Hershkovitz and Dina Tirosh

5 Developing an understanding of children’s acquisition of number concepts 86

Anne D. Cockburn

6 Highlighting the learning processes 101

Graham Littler and Darina Jirotková

7 Everyday numbers under a mathematical magnifying glass 123

Carlo Marchini and Paola Vighi

Appendix 152

Index 159

Trends in Teaching and Learning of Mathematical Modelling

2011-10-25T16:43:00.002+02:00

ICTMA14

Gabriele Kaiser, Werner Blum, Rita Borromeo Ferri, Gloria Stillman

Springer | 2011 | 747 páginas | PDF | 15,5 MB

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Applications and modelling and their learning and teaching in school and university have become a prominent topic in the last decades in view of the world-wide importance of the usage of mathematics in science, technology and everyday life. "Trends in Teaching and Learning of Mathematical Modelling "provides the reader ship with an overview on the newest international trends and developments on the teaching and learning of modelling from various theoretical and practical perspectives. The comprehensive overview on the most recent empirical research reflecting the development and promotion of modelling competencies at various age levels allows insight into possible affective and cognitive blockages and barriers for students modelling processes and its teaching. The papers on the usage of technology describe new possibilities, how the usage of technology can inspire the teaching and learning of modelling. International modelling projects offer chances and possibilities to enrich the teaching and learning of mathematical modelling at secondary and tertiary level and describe challenging modelling examples and their possible usage in school and university. The necessary change of teacher education towards an inclusion of mathematical modelling is reflected from different perspectives and challenging examples are given. The contributing authors are influential members of the group International Community of Teachers of Modelling and Applications and important researchers in mathematics and mathematics education. The book will be of interest to mathematics educators, teacher educators, researchers, education administrators, curriculum developers, teachers and student teachers.

Common terms and phrases:
mathematical modelling mathematics education metacognitive praxeologies Springer Science+Business Media

Cover

International Perspectives on the Teaching and Learning of Mathematical Modelling 1

Trends in Teaching and Learning of Mathematical Modelling

ISBN 9789400709096

Series Preface

Contents

Chapter 1: Trends in Teaching and Learning of Mathematical Modelling – Preface

References

Part I: Modelling from Primary to Upper Secondary School: Findings of Empirical Research

Chapter 2: Modelling from Primary to Upper Secondary School: Findings of Empirical Research – Overview

Chapter 3: Can Modelling Be Taught and Learnt? Some Answers from Empirical Research

1 A Cognitive View on Mathematical Modelling

2 How Do Students Deal with Modelling Tasks?

3 How Do Teachers Treat Modelling in the Classroom?

4 Some Ideas for Teaching Modelling

References

Chapter 4: “Can Modelling Be Taught and Learnt?” – A Commentary

1 Introduction

2 View of Modelling

3 Technology and Modelling

4 Critical Perspective and Cognition

5 Teachers and Modelling

6 Final Considerations

References

Chapter 5: Upper Secondary Students’ Handling of Real-World Contexts.*

1 Introduction

2 Some Aspects of the Current Discussion and Research Question

3 Methodology and Methods

3.1 Methodological Remarks

3.2 Methods

3.3 Tasks

4 Results

4.1 General Results

4.2 Ideal Types

4.3 Case Synopsis

5 Final Remarks

References

Chapter 6: Word Problem Classification: A Promising Modelling Task at the Elementary Level

1 Theoretical and Empirical Background

2 Method

2.1 Subjects, Tasks and Procedure

2.2 Analysis

3 Results

3.1 Solution Task

3.2 Classification Task

4 Conclusions and Discussion

References

Chapter 7: Understanding and Promoting Mathematical Modelling Competencies: An Applied Perspective

1 Introduction

2 Methodology

3 Results

3.1 Finding Similar Examples or Phenomena

3.2 Connecting Physical Phenomena with Abstract Concepts

3.3 Building Modelling from the Ground up

3.4 Communicating Broader Context of a Modelling Solution

4 Discussion and Summary

References

Chapter 8: Secondary Teachers’ Beliefs About Teaching Applications – Design and Selected Results of a Qualitative Case Study

1 The Call for Applications in Mathematics Curriculum is Quite Old!

2 A First Root Cause Analysis: Focusing on Teachers

3 Why a Qualitative Case Study?: Methodology and Methods

3.1 Theoretical Constructs

3.2 Study Design

4 Discussion and Some Selected Results

5 Conclusion

References

Chapter 9: Secondary Teachers’ Beliefs on Modelling in Geometry and Stochastics

1 Teachers’ Beliefs and Individual Curricula

2 Theoretical Background, Data, and Evaluation

3 Applications and Model Building

4 Geometry

4.1 Elementary Geometry

4.2 Analytical Geometry

5 Stochastics

6 Conclusions

References

Chapter 10: Examining Mathematising Activities in Modelling Tasks with a Hidden Mathematical Character

1 Introduction

2 Framework

2.1 ATD and Modelling

2.2 Structural Analysis

3 Empirical Design

4 A Priori Analysis

5 Findings

6 Summary and Conclusions

References

Chapter 11: The Sun Hour Project

1 Introduction

2 Classroom Circumstances

2.1 Classroom Experiences in Sweden

2.2 Classroom Experiences in Germany

3 Researchers’ View of the Project

3.1 Theoretical Frameworks

3.2 Analyzing the Work in the Swedish Classroom

3.3 Analyzing the Work in the German Classroom

4 Conclusions

References

Chapter 12: Mathematical Knowledge Application and Student Difficulties in a Design-Based Interdisciplinary Project

1 Background of Research

2 Rationale for Research

3 Research Design

3.1 Research Task

3.2 Setting and Sample

3.3 Data Collection Methods

3.4 Analysis Procedures

4 Findings

4.1 Coverage of Mathematical Knowledge and Skills

4.2 Mathematical Difficulties

5 Discussion and Conclusion

References

Chapter 13: Evaluation of Teaching Activities with Multi-Variable Functions in Context

1 The Background of the Research

2 The Educational Course Content

2.1 Two-Variable Functions – Analytic Geometry Approach

2.2 Mathematical Modelling

2.2.1 The Vehicle Stopping Distance Example

2.2.2 The Sound Propagation Example

3 Results from an Evaluation Questionnaire

3.1 Content of Investigation

3.2 Results from the Evaluation Questionnaire and Discussion

4 Conclusion

Reference

Chapter 14: Mathematical Modelling in Secondary Education: A Case Study

1 Introduction

2 Methodology

3 Results and Discussion

4 Conclusions and Recommendations

References

Chapter 15: Students Overcoming Blockages While Building a Mathematical Model: Exploring a Framework

1 Introduction

2 Theoretical Framework

2.1 Modelling

2.2 Mathematising

2.3 Opportunities and Blockages

3 Method

4 Results

4.1 The Swimming Pool Task

4.2 The Horizon Task

4.3 Additional Results

5 Conclusion and Discussion

References

Chapter 16: What Did Taiwan Mathematics Teachers Think of Model-Eliciting Activities and Modelling Teaching?

1 Background

2 Theoretical Frame

3 Methodological Approach

3.1 Samples

3.2 Research Process

3.3 Data Collection

3.4 Data Analysis

3.4.1 Positive Thinking about MEAs and Modelling Teaching

Close-in Real Life Situation

Enhancement of Mathematical Competencies

Advantages of Modelling Teaching

MEAs as Supplementary Materials

3.4.2 Negative Thinking about Modelling Teaching

Out of School Curriculum

Out of Entrance Examinations

Other Obstacles of Modelling Teaching

3.4.3 Weaknesses of Designing MEAs

4 Conclusions and Implications

References

Part II: Looking Deeper into Modelling Processes: Studies with a Cognitive Perspective

Chapter 17: Looking Deeper into Modelling Processes: Studies with a Cognitive Perspective – Overview

References

Chapter 18: Applying Metacognitive Knowledge and Strategies in Applications and Modelling Tasks at Secondary School

1 Introduction

2 Modelling and Metacognition

2.1 The Modelling Process and Reflection

2.2 Meta-Metacognition and Modelling

2.3 Productive Metacognitive Acts and Modelling

2.3.1 Routine Metacognitive Activity

2.3.2 Responses to Red Flag Situations

3 Development of Modellers’ Reflective Metacognitive Activity Through Meta-Metacognition

4 Conclusions

References

Chapter 19: Effective Mathematical Modelling without Blockages – A Commentary

1 Meta-Cognition – A Fuzzy Word?

2 Effective Modelling Without Blockages: But How?

3 Connecting and Acting

References

Chapter 20: Modelling Tasks: Insight into Mathematical Understanding

1 Prior Knowledge of Task Context

2 Ways of Dealing with the Context

3 Higher Order Thinking

4 Methods

4.1 The Tasks

5 Findings

5.1 Evidence of Prior Knowledge of Task Context

5.2 Busse’s Ideal Types

5.3 Modelling and Higher Order Thinking

6 Discussion and Conclusion

References

Chapter 21: Mathematical Modelling of Daily Life in Adult Education: Focusing on the Notion of Knowledge

1 Introduction

2 Theoretical Framework

2.1 A Discussion on the Real World

2.2 Knowledge, Practice and Context

2.3 A Connection with Modelling and Competence

3 Methodology and Data Analysis

4 Results

4.1 Students’ First Chains of Meanings

4.2 Responses to Question 1 – Number Magnitude

4.3 A “Different” Answer in the Group

4.4 Responses to Question 2 – The Best Flavour

4.5 Explaining to the Group – The Medium Flavour

4.6 Responses to Question 3 – The Size of the Glass

4.7 Responses to Question 4 – Part/Whole Relation Versus a Total of 120

5 Discussion and Final Comments

References

Chapter 22: Students’ Modelling Routes in the Context of Object Manipulation and Experimentation in Mathematics

1 Introduction

2 Connecting Modelling to Experimentation in Mathematics Classroom

2.1 From the Point of View of Mathematics Education

2.2 From the Point of View of Learning by Doing

3 Theoretical Perspectives on Applications and Modelling

4 The Research Empirical Work

5 Description and Data Analysis

6 Synthesis of Findings

References

Chapter 23: Engineering Model Eliciting Activities for Elementary School Students

1 Introduction

2 Theoretical Framework

3 The Present Study

3.1 Participants and Procedures

3.2 Data Sources and Analysis

4 Results

4.1 Model A

4.2 Model B

4.3 Model C

4.4 Model D

5 Conclusions

References

Chapter 24: Project Modelling Routes in 12–16-Year-Old Pupils*

1 Context and Aims

2 Theoretical Background

3 Study Methodology

4 From Analysis to Results

5 Results

6 Conclusions

References

Part III: Mathematical Modelling in Teacher Education

Chapter 25: Mathematical Modelling in Teacher Education – Overview

1 Introduction

2 Research Using Different Perspectives of Modelling

3 Reflections

References

Chapter 26: Models and Modelling Perspectives on Teaching and Learning Mathematics in the Twenty-First Century

1 Introduction

2 MMP Research Investigates What It Means to “Understand” Important Concepts and Abilities

3 Do Model-Eliciting Activities (MEAs) Work?

4 In What Ways Do MEAs (and MMP in General) Provide Alternatives to Traditional Research?

4.1 MEAs Provide Alternatives to Naturalistic Observations

4.2 MEAs Provide Alternatives to Expert-Novice Studies

5 Teaching from a Models and Modelling Perspective

5.1 The Nature of Teachers’ Knowledge

5.1.1 Engaging Students with Modelling Tasks

5.1.2 Recognizing and Responding to Students’ Thinking

5.2 The Development of Teachers’ Knowledge

5.2.1 The Collaborative Design of Sequences of Modelling Tasks

5.3 Principles for the Design of Model Development Experiences for Teachers

6 Concluding Remarks

References

Chapter 27: Mathematical Modelling in a Distance Course for Teachers

1 Introduction

2 MM Course: Main and Common Events

2.1 Modelling in the Classroom: Possibilities and Challenges

3 Conclusion

References

Chapter 28: In-Service and Prospective Teachers’ Views About Modelling Tasks in the Mathematics Classroom – Results of a Quantitative Empirical Study

1 Introduction

2 Theoretical Background

3 Research Questions

4 Design and Sample

5 Results

6 Discussion and Conclusions

References

Chapter 29: Pre-service Secondary Mathematics Teachers’ Affinity with Using Modelling Tasks in Teaching Years 8–10

1 Introduction

2 Background

3 Theoretical Framework

4 The Study

5 Findings

5.1 Diagnostic Competencies with Respect to Modelling

5.2 Competencies in Didactical Reflections About Modelling – Appropriateness of Task

5.3 Affinity with Modelling in Teaching in Years 8–10

5.4 Affinity with Modelling Related to Beliefs About the Nature of Mathematics

6 Discussion and Conclusion

References

Part IV: Using Technologies: New Possibilities of Teaching and Learning Modelling

Chapter 30: Using Technologies: New Possibilities of Teaching and Learning Modelling – Overview

1 Modelling Using Digital Tools

2 Empirical Studies and Experiences on Modelling Using Digital Tools

References

Chapter 31: Factors Affecting Teachers’ Adoption of Innovative Practices with Technology and Mathematical Modelling

1 Introduction

2 The Use of CAS in Mathematical Modelling

3 Models of the Use of Technology in Mathematical Modelling

4 Context of the Study

4.1 Curriculum Contexts

4.2 Teachers’ Backgrounds

5 Method and Approach to Data Collection

6 A Tale of Two Cities and Two Teachers

6.1 Teacher 1

6.2 Teacher 2

7 Discussion and Conclusions

References

Chapter 32: Modelling Considering the Influence of Technology

1 Introduction

2 Alcohol in Blood – A Prospective Example for Modelling with Technology

2.1 Modelling a Theoretical Concentration

2.2 Absorption and Reduction Shown as a Mathematical Process

2.2.1 First Model – Linear Approach

2.2.2 Second Model – Semi-linear Approach

2.3 The Role of Technology in the Modelling Cycle

2.4 An Example Where Technology Is Helpful to Get an Idea

2.5 The Fuel Tank – An Example for Using Technology to Validate

3 Examination Tasks – With Modelling Problems and Use of Technology?

4 Conclusion

References

Chapter 33: Improving Learning in Science and Mathematics with Exploratory and Interactive Computational Modelling

1 Introduction

2 Course Organisation, Methodology and Student Evaluation Procedures

3 Computational Modelling Activities with Modellus

4 Conclusions

References

Part V: Modelling Competency: Teaching, Learning and Assessing Competencies

Chapter 34: Modelling Competency: Teaching, Learning and Assessing Competencies – Overview

1 Presentation of the Papers

References

Chapter 35: Drivers for Mathematical Modelling: Pragmatism in Practice

1 Being in Touch with the Real World

2 How Well Do Students Link Mathematical Knowledge to the Task at Hand?

3 How Far Away Is the Real World?

3.1 Kidney Dialysis

3.2 Rocket Satellite Systems

3.3 Aggregation of Slime Mould Amoebae

3.4 Road Traffic Flows

3.5 Local Models

4 Is Mathematical Modelling a Driver for Mathematical Modelling?

References

Chapter 36: Identifying Drivers for Mathematical Modelling – A Commentary

1 How Well Do Students Link Mathematical Knowledge to the Task at Hand?

2 How Far Away Is the Real World?

3 Is Mathematical Modelling a Driver for Mathematical Modelling?

4 What the Title Made Me Think of…

References

Chapter 37: Documenting the Development of Modelling Competencies of Grade 7 Mathematics Students

1 Introduction

2 A Perspective for Modelling

3 What Is Competence and What Are Modelling Competencies?

4 Methodology

5 Results

References

Chapter 38: Students’ Reflections in Mathematical Modelling Projects

1 Introduction

2 Internal and External Reflections in Mathematical Modelling Competency

3 Students’ Reflections in Modelling Projects

3.1 The Institutional Context of the Project Work at Roskilde University

3.2 The Use of a Traffic Model in the City of Roskilde – The Case of ‘Ny Østergade’

3.3 Modelling in Scientific Investigations: The Project of the HPA-Axis

4 Concluding Remarks

References

Chapter 39: From Data to Functions: Connecting Modelling Competencies and Statistical Literacy

1 Introduction

2 Modelling Competencies and Statistical Literacy

3 Empirical Evidence on Modelling Competencies and Statistical Thinking

4 Results

4.1 Discussion and Outlook on Further Results

5 Conclusions

References

Chapter 40: First Results from a Study Investigating Swedish Upper Secondary Students’ Mathematical Modelling Competencies

1 Introduction and Purpose

2 Methodology, Theoretical Considerations and Method

2.1 Mathematical Modelling and Modelling Competencies

2.2 Developing an Instrument

2.3 Statistical Analysis

3 Results

4 Discussion

5 Conclusions

References

Chapter 41: Why Cats Happen to Fall from the Sky or on Good and Bad Models

1 The Operation ‘Cat Airdrop’

2 Modelling in School: Chances and Obstacles

3 The Problem Field ‘Central Examinations

4 The Use of Computers

5 The Professional Development and Motivation of Teachers

6 Conclusion

References

Chapter 42: Assessing Modelling Competencies Using a Multidimensional IRT Approach

1 Introduction

2 Modelling Competency

3 Test Instrument

4 Data Scaling

5 Results of the Evaluation

6 Discussion

References

Part VI: Modelling in Tertiary Education

Chapter 43: Modelling in Tertiary Education – Overview

References

Chapter 44: The Mathematical Expertise of Mechanical Engineers: Taking and Processing Measurements

1 Introduction

2 Method of Investigation and Task

3 Approach of Students

4 Findings and Discussion

4.1 Benefits and Problems of the Method

4.2 Modelling Qualifications

4.3 Data Interpretation and Model Validation Qualifications

4.4 Comparison with Other Research

5 Conclusions for Education

References

Chapter 45: Mathematical Modelling Skills and Creative Thinking Levels: An Experimental Study

1 Introduction

2 Mathematical Modelling Skills

2.1 Test Questions

2.2 Implementation

2.3 Results

3 Creative Thinking Levels

3.1 Test Questions

3.2 Implementation

3.3 Results

3.4 Relationship with Mathematical Modelling Skills

4 Knowledge in Basic Mathematics

4.1 Score in Basic Mathematical Courses

4.2 Relationship with Mathematical Modelling Skills

5 Summary

References

Chapter 46: Modelling the Evolution of the Belgian Population Using Matrices, Eigenvalues and Eigenvectors

1 Introduction

2 The Teaching Sequence

2.1 Calculations with Authentic Data

2.2 The Matrix Model

2.3 Two Observations Concerning the Long Term Evolution of the Population

2.4 Mathematical Treatment of the Observations

2.5 Eigenvalues and Eigenvectors

3 Experiences

3.1 During the ‘Science Week’

3.2 In Mathematics Teacher Education

3.3 In an Introductory Mathematics Course for Bachelor Students in Applied Economics

4 Conclusion

References

Chapter 47: Modelling and the Educational Challenge in Industrial Mathematics

1 Computational Technology

2 Educational Challenge

3 Sphere of Applications

4 Modelling as a Course Subject

5 Modelling Problems to Challenge Undergraduates

6 Modelling Education: How Much and When?

References

Chapter 48: Modelling of Infectious Disease with Biomathematics: Implications for Teaching and Research

1 Introduction and Framework

2 The Study

2.1 The Models

2.2 The Questionnaire

3 The Responses

3.1 Students

3.2 Lecturers

3.3 Analysis of the Responses

4 Conclusions

References

Chapter 49: Using Response Analysis Mapping to Display Modellers’ Mathematical Modelling Progress

1 Introduction

2 Components Based on Experiences

3 Applied Response Analysis Mapping as an Analysis Method

4 Research Setting

5 Modelling Progress Using Applied Response Analysis Mapping

5.1 The Case of a Graduate School Student

5.2 The Case of an Electronics Expert

6 Discussion

6.1 Focus on CRE

6.2 Focus on CME

7 Conclusion

Appendix 1: Mathematical Modelling Progress of NT

Appendix 2: Mathematical Modelling Progress of KN

References

Part VII: Modelling Examples and Modelling Projects: Concrete Cases

Chapter 50: Modelling Examples and Modelling Projects – Overview

1 The Challenge

1.1 Analysis of the Challenge

1.2 Helping Teachers

1.3 Situations for Modelling

Chapter 51: Modelling Chemical Equilibrium in School Mathematics with Technology

1 Introduction

2 The Case

3 Models of Chemical Equilibria

3.1 Chemical Equilibria in Our Case

4 Aims of the Students’ Work

5 Methods for Examination of Data

6 Results

6.1 Students’ Perception of Modelling in Mathematics and in Chemistry

6.2 The Students’ Understanding of the System of Chemical Equilibrium

6.3 Students’ Understanding of Connections Between Theory and Practice

6.4 Technology as a Means to Make the Modelling Process More Explicit

7 Conclusion

7.1 Technical Obstacles

7.2 Few Students’ Reflections

7.3 Little Focus on Modelling

8 Perspectives

References

Chapter 52: Real-World Modelling in Regular Lessons: A Long-Term Experiment

1 Idea of the Experiment

2 Design of the Experiment

3 Choice of Five Real-World Modelling Tasks

3.1 First Task: A Guided Modelling as an Introduction

3.2 Second Task: Is the Olympic Medals Table Fair?

3.3 Third Task: How to Type on a Container?

3.4 Fourth Task: Building of an ICE-Track 9

3.5 Fifth Task: How to Do an Optimal Free Throw in Basketball 11 ?

3.6 Difficulty and Attractiveness of the Projects

4 Detailed Discussion of Task Number 4: ICE-Track

5 Evaluation

5.1 Concept of Questionnaires

5.2 Development from Second to Fourth Task and Final Judgements

6 Comparison Project: Setting and Results

7 Summary and Conclusion

References

Chapter 53: Modelling Tasks at the Internet Portal “Program for Gifted”

1 Fostering of Gifted Students

2 The Interests of Gifted Students: A Bottom-up Approach

3 Examples Containing Modelling Components

3.1 From Cones to Higher Algebraic Curves and Back

3.2 From the Lottery to the Pascal Triangle

4 Summary

References

Chapter 54: Modelling at Primary School Through a French–German Comparison of Curricula and Textbooks

1 Origin, Method and Theoretical Framework of the Study

2 Comparison of Curricula: Is Modelling a Knowledge to Be Taught?

3 Articulation Between Real and Mathematical World in Textbooks

3.1 Real World Knowledge

3.2 Mathematical World Knowledge

3.3 Representation Involved in the Tasks

3.4 Whole Competencies and Partial Competencies: Didactical Functions of Tasks

4 Conclusion: Challenges for Modelling Resources and Teacher Training

References

Chapter 55: Modifying Teachers’ Practices: The Case of a European Training Course on Modelling and Applications

1 Introduction

2 Teacher Education on Modelling and Applications: From a Teachers’ Problem to a Professional Problem

3 A Theoretical Framework to Describe Teaching Actions

3.1 Modelling the Teaching Activity

4 LEMA Professional Development: Changing Teachers’ Practices

5 Conclusions and Implications

References

Chapter 56: Google’s PageRank: A Present-Day Application of Mathematics in the Classroom *

1 Introduction

2 The a Directed Graph and the Description by Transition Matrices

2.1 How Can We Measure the Relevance of a Site?

2.2 Now to an Example Slightly More Complicated

2.3 The Crucial Attribute of U

2.4 Explicit Solution (Formula)

3 Summary and Reflections

References

Chapter 57: Authentic Modelling Problems in Mathematics Education

1 Theoretical Framework for Modelling in Mathematics Education

2 Framework and Structure of the Modelling Week

3 Students Modelling the Spread of Disease in a Population of Ladybirds

4 Evaluation of the Modelling Week

References

Chapter 58: Using Modelling Experiences to Develop Japanese Senior High School Students’ Awareness of the Interrelations between Mathematics and Science

1 Introduction

2 An Example Using Modelling: Teaching Materials for Kepler’s Law for High School Students Becoming Scientists

2.1 Premodel

2.2 Mathematical Development Model

3 Students’ Evaluation and Impressions

3.1 The Class Treated the Premodel

3.2 The Class Treated the Mathematical Development Model

4 Conclusion and Future Subjects

References

Chapter 59: Stochastic Case Problems for the Secondary Classroom with Reliability Theory

1 Introduction

2 Reliability Theory

2.1 Brief History

2.2 A Summary of the Reliabilities of Simple Fundamental Systems

2.2.1 Series Systems

2.2.2 Parallel Systems

2.2.3 Combined Systems

3 Reliability Theory Problems for the Secondary Classroom

3.1 Prerequisites for Reliability Theory

3.2 Examples of Problems for Secondary School

3.2.1 Level I Problems

3.2.2 Level II Problems

3.2.3 Sample Project

4 Conclusion: The Mathematical Residue of Reliability Tasks (RT)

References

Chapter 60: LEMA – Professional Development of Teachers in Relation to Mathematical Modelling*

1 Theoretical Background

2 Design of the Course of Professional Development

3 Design of the Evaluation

4 Results and Discussion

References

Chapter 61: Modelling in the Classroom: Obstacles from the Teacher’s Perspective

1 Basic Theory

1.1 Mathematical Modelling

1.2 Obstacles to the Integration of Modelling

1.3 Research Questions

2 Methodology

2.1 Instruments for the Study

2.2 Study Design

2.3 Sample

3 Questionnaire Development

3.1 Questionnaire Development

3.2 Format of Questionnaire

4 Results

4.1 I Have Too Little Material

4.2 Performance Assessment is Too Complex

4.3 I Don’t Have Enough Time for Modelling

5 Discussion

References

Chapter 62: Teachers’ Professional Learning: Modelling at the Boundaries

1 Introduction

2 Classroom Practice and Its Transformation

3 Knowledge for Teaching and Learning in Modelling Classrooms

4 Further Theoretical Reflections

References

Part VIII: Theoretical and Curricular Ref lections on Mathematical Modelling

Chapter 63: Theoretical and Curricular Reflections on Mathematical Modelling – Overview

1 Paper Summaries

References

Chapter 64: Making Connections Between Modelling and Constructing Mathematics Knowledge: An Historical Perspective

1 Aims in This Study

2 Mathematics Textbooks Before World War II in Japan

3 Roles of Real World Situations

4 Repeated Instances of the Same Contexts

5 Making Connections Between Real World Problems

6 Implications for Teaching of Mathematics Today Including Modelling

7 Conclusion

References

Chapter 65: Practical Knowledge of Research Mathematicians, Scientists, and Engineers About the Teaching of Modelling

1 Introduction

2 The Case Study

2.1 Theoretical Framework

2.2 Design of the Case Study

3 Summary of Interview Findings

3.1 Teaching Goals of Modelling in Tertiary Education

3.2 Modelling Courses in Tertiary Education

3.3 Students’ Modelling Competencies

3.4 Opinions about Modelling in Secondary Education

4 Discussion and Conclusions

4.1 Similarities Between Interviewees and Education Researchers

4.2 Differences Between Interviewees and Education Researchers

4.3 Differences Among Interviewees

4.4 Possible Implications for Secondary Education

References

Chapter 66: Evolution of Applications and Modelling in a Senior Secondary Curriculum

1 Introduction

2 Mathematical Modelling and Applications in Queensland

2.1 Syllabus Objectives

2.2 Implementation in Schools

3 Research Methods

4 Findings

4.1 Reasons Applications and Modelling Valuable Initiative at Senior Secondary

4.2 Distinction Between Applications and Modelling

4.3 Embedding Applications and Modelling in Current Practice

4.4 Designing Tasks

5 Discussion and Conclusion

References

Chapter 67: Sense of Reality Through Mathematical Modelling.*

1 Introduction

2 Brief Description of Modelling in Colombian Educational Regulations

3 The Project

3.1 The Context

3.2 Methodological Approach

4 Results

4.1 What is Sense of Reality ?

4.2 What is Reality for Alberto and Alexander?

4.3 Sense of Reality in School Mathematics

4.4 A First Approach

5 Discussion

6 Conclusions

References

Chapter 68: What Is ‘Authentic’ in the Teaching and Learning of Mathematical Modelling?

1 Introduction

2 Variations of Tasks in Mathematics Education

3 Definitions of ‘Authenticity’ in Mathematics Education

4 Problems with Defining ‘Authenticity’

5 Pragmatically Constructing Authenticity in Mathematical Modelling

References

Thinking Mathematically

2011-10-25T16:32:00.002+02:00

J. Mason, L. Burton, K. Stacey

Addison Wesley | 2nd Edition | 265 páginas | PDF

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Thinking Mathematically is invaluable for anyone who wishes to promote mathematical thinking in others or for anyone who has always wondered what lies at the core of mathematics.

New in the Second Edition:
· The text has been updated with 77 fresh problems matched to curriculum topics together with links between those topics and the original problems.
· There is a new preface describing the origins and uses of the first edition
· New chapter correlates mathematical processes with the natural powers that every learner has already demonstrated in learning to speak.ng to speak.

The Elements of Creativity and Giftedness in Mathematics

2011-10-25T16:16:00.003+02:00

Bharath Sriraman, Kyeong Hwa Lee

Sense Publishers | 2010 | 240 páginas | PDF | 9 MB

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depositfiles

The Elements of Creativity and Giftedness in Mathematics edited by Bharath Sriraman and KyeongHwa Lee covers recent advances in mathematics education pertaining to the development of creativity and giftedness. The book is international in scope in the "sense" that it includes numerous studies on mathematical creativity and giftedness conducted in the U.S.A, China, Korea, Turkey, Israel, Sweden, and Norway in addition to cross-national perspectives from Canada and Russia. The topics include problem -posing, problem-solving and mathematical creativity; the development of mathematical creativity with students, pre and in-service teachers; cross-cultural views of creativity and giftedness; the unpacking of notions and labels such as high achieving, inclusion, and potential; as well as the theoretical state of the art on the constructs of mathematical creativity and giftedness. The book also includes some contributions from the first joint meeting of the American Mathematical Society and the Korean Mathematical Society in Seoul, 2009. Topics covered in the book are essential reading for graduate students and researchers interested in researching issues and topics within the domain of mathematical creativity and mathematical giftedness. It is also accessible to pre-service and practicing teachers interested in developing creativity in their classrooms, in addition to professional development specialists, mathematics educators, gifted educators, and psychologists.

Contents

AIMS AND SCOPE

1. WHAT ARE THE ELEMENTS OF GIFTEDNESS AND CREATIVITY IN MATHEMATICS?: An Overview of the KMS-AMS Symposium and the Book

INTRODUCTION

ACKNOWLEDGEMENT

2. AN EXPLORATORY STUDY OF RELATIONSHIPS BETWEEN STUDENTS’ CREATIVITY AND MATHEMATICAL PROBLEM-POSING ABILITIES: Comparing Chinese and U.S Students

INTRODUCTION

CONCEPTUAL FRAMEWORK

Guilford’s Structure of Intellect Model

Mathematical Problem-posing Framework

STUDY VARIABLES AND DEFINITION OF STUDY TERMS

Definition of Creativity

Definition of Mathematical Problem Posing

RESEARCH DESIGN

PARTICIPANTS

Participants from China

Participants from the United States

MEASURES AND INSTRUMENTATION

The Mathematics Content Test

The Torrance Tests of Creative Thinking

The Mathematical Problem-Posing Test

The Translation of the Tests from English to Chinese

DATA ANALYSIS

The Scoring of the Mathematics Content Test

The Scoring of the TTCT Tests

The Scoring of the Mathematical Problem-posing Test

RESULTS

Comparison of the Mathematics Content Test Scores

Comparison of TTCT Scores

Comparison of the Mathematical Problem-posing Test Scores

Correlations between TTCT and the Mathematical Problem-posing Test

DISCUSSION

LIMITATIONS OF THIS STUDY

The Participants

The Translation of the Instruments

The Time and Distance Restrictions

CONCLUSIONS AND IMPLICATIONS

REFERENCES

3. ARE MATHEMATICALLY TALENTED ELEMENTARY STUDENTS ALSO TALENTED IN STATISTICS?

INTRODUCTION

CONCEPTUAL ANALYSIS OF AVERAGE

METHOD

Participants

Tasks

Administration and Analysis

RESPONSES AND FINDINGS

Average as Being Representative

Mathematical Abstract Construction

Treatment of Variation

SUMMARY AND DISCUSSION

REFERENCES

4. DOES HIGH ACHIEVING IN MATHEMATICS = GIFTED AND/OR CREATIVE IN MATHEMATICS

INTRODUCTION

CREATIVITY AND MATHEMATICAL CREATIVITY

The Gestalt principle:

The Aesthetic principle:

The Scholarly principle:

The Free market principle:

The Uncertainty principle:

INTELLIGENCE AND MATHEMATICAL INTELLIGENCE

GIFTEDNESS AND MATHEMATICAL PRECOCIOUSNESS

Exceptional Abilities from a Young Age

Late Development of Mathematical Giftedness

Identifying Precociuosness

Programmes for the Highly Gifted Youth

SEVEN CASES OF VARIOUS LEVELS OF GIFTEDNESS AND ACHIEVEMENT

John, Gifted but not High Achieving in Mathematics

Lisa, High Achieving Merely through Hard Work

Steve, Late Discovery of Mathematical Precociousness

Annie, Initially a High Achiever by Strategic Social and Mathematical Behaviour

Chris, from Above Average to Low Achieving

Mary, High Achieving, Gifted and Creative

Nelly, Gifted but not Creative

DISCUSSION

The Labels High Achiever, Gifted and Creative in Mathematics

Social Impact and Changed Development

Assessment and School Practice

REFERENCES

5. DEVELOPING MATHEMATICAL POTENTIAL IN UNDERREPRESENTED POPULATIONS THROUGH PROBLEM SOLVING, MATHEMATICAL DISCOURSE AND ALGEBRA

INTRODUCTION

THEORETICAL FRAMEWORK

Participation Gap among Diverse Learners in Accessing Rigorous Mathematics

METHODOLOGY

Participants

Design Features of the Project

Focusing on the Core Traits of Mathematically Proficient Students

Procedures

RESULTS

Selecting Tasks and Sequences of Related Problems

Integrating Pedagogical Content Tools to Extend Students’ Reasoning

Orchestrating Classroom Discourse through Pedagogical Moves and Questioning

CONCLUSIONS

REFERENCES

6. ON TRACK TO GIFTED EDUCATION IN MATHEMATICS IN SWEDEN

INTRODUCTION

A HISTORICAL REVIEW – DEVELOPMENT OF THE SCHOOL SYSTEM AND THE CURRICULUM

NATIONAL POLICIES

ADVOCACY

GIFTED EDUCATION RESEARCH RELEVANT FOR MATHEMATICS EDUCATION

GIFTED EDUCATION IN THE SWEDISH TEACHER EDUCATION

IMPLEMENTATION OF GIFTED EDUCATION IN SCHOOLS

CHALLENGES FACING SWEDISH GIFTED EDUCATION IN MATHEMATICS

Legal Recognition of Gifted Students

Strengthening the Connection between Research and Implementation of Gifted Education

Identification of Gifted Students

Gifted Educa tion in the Swedish Teacher Education

Coordinating Measures for Gifted Students

Social Dimensions of Giftedness

CONCLUDING REMARK

REFERENCES

7. TEACHERS’ IMAGES OF GIFTED STUDENTS AND THE ROLES ASSIGNED TO THEM IN HETEROGENEOUS MATHEMATICS CLASSES

INTRODUCTION

THEORETICAL BACKGROUND

Mathematically able Students

Teachers of MAS

THE STUDY

Participating Teachers

Procedure

Data Analysis

FINDINGS

Teachers’ Images of Gifted Students

High abilities as a gift of god.

A gift is like a jug with a narrow opening.

A gifted student is a cyclamen with a lowered head.

Students’ Roles in the Classroom

MAS as a catalyst for class discussion.

MAS as a scaffold for class discussion.

MAS as a springboard for class discussion.

CONCLUDING REMARKS

NOTES

REFERENCES

8. MATHEMATICAL CREATIVITY AND MATHEMATICS EDUCATION: A Derivative of Existing Research

INTRODUCTION

IDENTIFICATION AND DEVELOPMENT OF MATHEMATICAL CREATIVITY

THE PROCESS OF CREATIVE MATHEMATICAL ACTIVITY

THE WALLAS MODEL OF PROBLEM SOLVING

MORE REMARKS ON INCUBATION

FALLIBILITY AND CRATIVE MATHEMATICAL ACTIVITY

THINKING AS MATHEMATICIANS

CONCLUSION

NOTES

REFERENCES

9. GIFTED EDUCATION IN RUSSIA AND THE UNITED STATES: Personal Notes

ABOUT MY EXPERIENCE

ON TECHNOLOGY IN MATHEMATICS GIFTED EDUCATION

ON THE PLACE OF TEACHING THE MATHEMATICALLY GIFTED IN THE EDUCATION SYSTEM

SOME PRACTICAL OBSERVATIONS

Public Opinion

Opportunities for Children

On Teachers

CONCLUSION: SO WHAT SHOULD WE DO?

REFERENCES

10. SEMIOTIC MICROWORLD FOR MATHEMATICAL VISUALIZATION

INTRODUCTION

MICROWORLD TOOLS FOR MATHEMATICAL VISUALIZATION

SEMIOTIC TOOLS FOR MATHEMATICAL VISUALIZATION

MATHEMATICAL VISUALIZATION WITH TURTLE BLOCKS

CLOSING REMARKS

REFERENCES

11. MATHEMATICALLY GIFTED STUDENTS IN INCLUSIVE SETTINGS: The Example of New Brunswick, Canada

INTRODUCTION: CONTEXT AND ISSUES

GIFTED EDUCATION IN CANADA: A BRIEF PORTRAYAL

NEW TRENDS IN MATHEMATICS EDUCATION: WHAT DOES IT BRING TO GIFTED STUDENTS?

INNOVATIVE PROJECTS AND NEW OPPORTUNITIES FOR GIFTED

EXAMPLES OF EXTRACURRICULAR INITIATIVES

CONCLUSIVE REMARKS ON UNSOLVED ISSUES

REFERENCES

12. PROSPECTIVE SECONDARY MATHEMATICS TEACHERS’ MATHEMATICAL CREATIVITY IN PROBLEM SOLVING: A Turkish Study

CONCEPTUAL FRAMEWORK

THE STUDY

THE PROBLEMS

DATA SOURCES

A SAMPLE PROBLEM AND SOLUTIONS

Problem

S9’s Solution for the Problem

S5’s Solution to the Problem

S4’s Solution for the Problem

Excerpt from S4’s Journal [solution has been translated/described above]

DATA ANALYSIS AND RESULTS

FINDINGS AND DISCUSSION

Logical Thinking

DISCUSSION

Difficulties

Creative Thinking Skills

Personal Choices

Logical and Intuitive Thinking

Other Affective Factors

Differences between Uses of Strategies

CONCLUSIONS

NOTES

REFERENCES

13. WHAT CHARACTERISES HIGH ACHIEVING STUDENTS’ MATHEMATICAL REASONING?

INTRODUCTION

Research Question

Literature Review

CONCEPTUAL FRAMEWORK

CREATIVE REASONING

IMITATIVE REASONING

Memorized Reasoning

Algorithmic Reasoning

METHODS

Procedures

Participants

Tasks

ANALYSIS

METHODOLOGICAL ISSUES

Validity

Reliability

RESULTS

Attacking the Problem

– Alf Description

Interpretation

– Anna Description

Interpretation

– Hege Description

Interpretation

The Prompt and Solution

– Alf Description

Interpretation

– Anna Description

Interpretation

– Hege Description

Interpretation

DISCUSSION

REFERENCES

14. FOSTERING CREATIVITY THROUGH GEOMETRICAL AND CULTURAL INQUIRY INTO ORNAMENTS

INTRODUCTION

CREATIVITY PATHWAYS

MATHEMATICS EDUCATION IN CULTURAL CONTEXT

EDUCATIONAL FRAMEWORK

EXAMPLES OF CREATIVE ACTIVITIES

Example 1

Example 2

Example 3

Experience of Learning Mathematics with Applications

Experience of Learning Geometry in Cultural Context

Experience of Connecting Geometry with Culture and Art

Geometrical View of Visual Patterns

Curiosity and Pride in Own Cultural Heritage

Interest, Motivation and Readiness to Teach Geometry in Cultural Context

Self-directed Inquiry

The Impact of the Technion Seminar

DISCUSSION AND CONCLUSION

ACKNOWLEDGEMENT

REFERENCES

Geometry as Objective Science in Elementary School Classrooms: Mathematics in the Flesh

2011-10-25T16:11:00.003+02:00

Wolff-Michael Roth

Routledge International Studies in the Philosophy of Education

Routledge | 2011 | 312 páginas | PDF | 3,70 MB

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his study examines the origins of geometry in and out of the intuitively given everyday lifeworlds of children in a second-grade mathematics class. These lifeworlds, though pre-geometric, are not without model objects that denote and come to anchor geometric idealities that they will understand at later points in their lives. Roth's analyses explain how geometry, an objective science, arises anew from the pre-scientific but nevertheless methodic actions of children in a structured world always already shot through with significations. He presents a way of understanding knowing and learning in mathematics that differs from other current approaches, using case studies to demonstrate contradictions and incongruences of other theories – Immanuel Kant, Jean Piaget, and more recent forms of (radical, social) constructivism, embodiment theories, and enactivism – and to show how material phenomenology fused with phenomenological sociology provides answers to the problems that these other paradigms do not answer.

Contents

List of Figures ix

Preface xiii

Introduction: Of Hands, Flesh, and Mind 1

PART A

Toward a Theory of Mathematics in the Flesh

Introduction to Part A 15

1 What Makes a Cube a Cube? A Phenomenological Overture 19

2 From Intellectualist Metaphysics to Embodiment Epistemologies 35

3 Material Life as the Organizing Principle of Knowing 60

PART B

Stories of Mathematics in the Flesh

Introduction to Part B 83

4 The Flesh, Distractions, and Mathematics 87

5 Coordinating Touch and Gaze: Re/Constructing a Mystery Object 111

6 Emergence of Measurement as the Realization of Geometry 138

7 Doing Time in Mathematical Praxis 157

PART C

Emergence of Geometry—An Objective Science

Introduction to Part C 197

8 Ethno-methods of Sorting Geometrically 201

9 Reproducing Geometry as Objective Science 231

10 Rethinking Mathematical Conceptions 243

Epilogue: From the Flesh to Society in the Mind 260

Appendix: Transcription Conventions 267

Notes 269

References 279

Index 287

Unexpected Links Between Egyptian and Babylonian Mathematics

2011-10-25T15:04:00.001+02:00

Joran Friberg

World Scientific Publishing Company | 2005 | 307 páginas | DjVu | 6 MB

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Comentário em: MAA

Mesopotamian mathematics is known from a great number of cuneiform texts, most of them Old Babylonian, some Late Babylonian or pre-Old-Babylonian, and has been intensively studied during the last couple of decades. In contrast to this Egyptian mathematics is known from only a small number of papyrus texts, and the few books and papers that have been written about Egyptian mathematical papyri have mostly reiterated the same old presentations and interpretations of the texts. In this book, it is shown that the methods developed by the author for the close study of mathematical cuneiform texts can also be successfully applied to all kinds of Egyptian mathematical texts, hieratic, demotic, or Greek-Egyptian. At the same time, comparisons of a large number of individual Egyptian mathematical exercises with Babylonian parallels yield many new insights into the nature of Egyptian mathematics and show that Egyptian and Babylonian mathematics display greater similarities than expected.

Amazing Traces of a Babylonian Origin in Greek Mathematics

2011-10-25T14:59:00.003+02:00

Amazing Traces of a Babylonian Origin in Greek Mathematics
Joran Friberg

World Scientific Publishing Company 2007 | 498 páginas | PDF | 2 MB

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Comentário em: MAA

A sequel to Unexpected Links Between Egyptian and Babylonian Mathematics (World Scientific, 2005), this book is based on the author s intensive and ground breaking studies of the long history of Mesopotamian mathematics, from the late 4th to the late 1st millennium BC. It is argued in the book that several of the most famous Greek mathematicians appear to have been familiar with various aspects of Babylonian metric algebra, a convenient name for an elaborate combination of geometry, metrology, and quadratic equations that is known from both Babylonian and pre-Babylonian mathematical clay tablets. The book s use of metric algebra diagrams in the Babylonian style, where the side lengths and areas of geometric figures are explicitly indicated, instead of wholly abstract lettered diagrams in the Greek style, is essential for an improved understanding of many interesting propositions and constructions in Greek mathematical works. The author s comparisons with Babylonian mathematics also lead to new answers to some important open questions in the history of Greek mathematics.

What Counts in Teaching Mathematics: Adding Value to Self and Content

2011-04-11T18:56:00.002+02:00

Sandy Schuck, Peter Pereira

Springer | 2011 | 208 páginas

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In this book, internationally recognised scholars and practitioners synthesise current practice and research developments in the area of mathematics teacher education and mathematics education. The book "s two sections examine the role and significance of collaborations and critical friends in the self-study of mathematics teaching and teacher education; and the emerging conflicts, dilemmas and incongruities arising from the study of mathematics education practices. The book considers the insights gained from self-analysis regarding the practitioner themselves, as well as their pedagogical content, students and approaches. The contributions highlight the complexity, characteristics and features of mathematics education.The chapters reveal nuances in teaching and learning that are of particular relevance in mathematics education. In addition, the book contains ideas and suggestions on how to enhance the teaching of mathematical content to pre-service teachers. Accordingly, the book appeals to a wide audience of educators including education academics, teachers, student teachers and researchers. As teacher educators involved in mathematics education, reflection on practice and engagement in practitioner research is becoming increasingly important in our efforts to enhance our teaching. Teachers and student teachers also gain from the insights arising from such reflection. The knowledge and experience encapsulated in this book provides much for the mathematics education community to build on.

Series Editor’s Foreword.- List of Contributors.- What counts in mathematics education? Sandy Schuck and Peter Pereira.- Part 1 Collaborations and Critical Friends.- 1. Tensions of Mentoring Mathematics Teachers: Translating Theory into Practice, Paul Betts.- 2. Team Teaching about Mathematics for All Collaborative Self-Study, Hafdís Guðjónsdóttir and Jónína Vala Kristinsdóttir.- 3. Growing Possibilities: Designing mathematical and pedagogical problems using variation, Cynthia Nicol.- 4. Resisting complacency: my teaching through an outsider’s eyes, Sandy Schuck.- Part 2 Examining our practice: Conflicts, dilemmas and incongruities.- 5. How students teach you to learn: Using Roundtable Reflective Inquiry to enhance a mathematics teacher educator’s teaching and learning, Robyn Brandenburg.- 6. Making sense of students’ fractional representations using critical incidents, Nell B.Cobb.- 7. Reforming Mathematics Teacher Education Through Self Study, Joanne E. Goodell.- 8. Opportunities for Learning: A Self-Study Of Teaching Statistics in a Mathematics Learning Centre, Sue Gordon.- 9. Reconstructing Teachers of Mathematics, Peter Pereira.- 10. Are we singing from the same songbook? Anne Prescott.- Adding value to self and content in mathematics education: Working in a third space, Peter Pereira and Sandy Schuck.

Early Algebraization: A Global Dialogue from Multiple Perspectives

2011-04-11T13:28:00.003+02:00

Jinfa Cai, Eric Knuth

Springer | 2011 |647 páginas | PDF - 7,7 Mb

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In recent years there has been increased interest in the development of students’ algebraic thinking in the elementary and middle school grades. This important and timely new volume contains the most comprehensive collection of research focused on early algebraization. The volume’s authors—leading international mathematics education scholars—present perspectives on early algebraization that promote a global dialogue on the topic. Research is presented from many parts of the world, including Asia, Australasia, Western and Eastern Europe, and North America. The volume authors consider issues concerning early algebraization from three fundamental perspectives—curricular, cognitive, and instructional. The chapters in this volume not only represent the state of the art about research on early algebraization, but also provide suggestions for future research.

“This volume on early algebraization reveals the rich diversity that characterizes the rapidly evolving field of early algebra .… this volume offers to researchers, teachers, curriculum developers, professional development educators, and policy makers alike some of the most recent thinking in the field.” (Carolyn Kieran)

Learning and Teaching Number Theory

2010-10-04T18:36:00.004+02:00

Learning and Teaching Number Theory: Research in Cognition and Instruction
(Mathematics, Learning, and Cognition: Monograph Series of the Journal of Mathematical Behavior)
Stephen R. Campbell, Rina Zazkis

Ablex Publishing | 2001 | 206 páginas | ZIP - html | 1 MB

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Number theory has been a perennial topic of inspiration and importance throughout the history of philosophy and mathematics. Despite this fact, surprisingly little attention has been given to research in learning and teaching number theory per se. This volume is an attempt to redress this matter and to serve as a launch point for further research in this area. Drawing on work from an international group of researchers in mathematics education, this volume is a collection of clinical and classroom-based studies in cognition and instruction on learning and teaching number theory. Although there are differences in emphases in theory, method, and focus area, these studies are bound through similar constructivist orientations and qualitative approaches toward research into undergraduate students' and preservice teachers' subject content and pedagogical content knowledge.

Teaching Number Sense: Grade 2

2010-09-17T20:03:00.003+02:00

Teaching Number Sense: Grade 2
Susan Scharton

Math Solutions | 2005 | 200 páginas | PDF | 2,262 MB

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Lessons in this book are organized in an accessible, easy-to-read format that includes an overview, a materials list, the lesson duration, step-by-step teaching directions, and vignettes of how the lesson actually unfolded in a classroom. Each lesson concludes with a list of assessment questions to help guide teacher observations. In this book, children learn to compose and decompose larger numbers, develop their computation strategies, strengthen their sense of place value, and sharpen their estimation skills.

Teaching Number Sense, Grade 1

2010-09-17T19:57:00.001+02:00

Teaching Number Sense, Grade 1
Chris Confer

Math Solutions | 2005 | 160 páginas | PDF | 1,345 MB

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This title is part of a three-book Teaching Number Sense series that focuses on the critical role that number sense plays in developing mathematical understanding. Number sense encompasses a wide range of abilities, including being able to make reasonable estimates and to think and reason flexibly. These lessons help students develop good number intuition and the ability to see numbers as tools, not barriers. By encouraging young children to reason their way to solutions, teachers help students form a solid foundation upon which all of their later mathematical understanding will be built.Lessons in this book are organized in an accessible, easy-to-read format that includes an overview, a materials list, the lesson duration, step-by-step teaching directions, and vignettes of how the lesson actually unfolded in a classroom. Each lesson concludes with a list of assessment questions to help guide teacher observations. In this book, children build their understanding of counting, number relationships, and landmark numbers. They also develop computation strategies, further their understanding of composing and decomposing numbers, and develop a beginning sense of place value.

Teaching Number Sense: Kindergarten

2010-09-17T19:52:00.002+02:00

Teaching Number Sense: Kindergarten
Chris Confer

Math Solutions | 2005 | 152 páginas | PDF | 3,2 MB

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This title is part of a three-book Teaching Number Sense series that focuses on the critical role that number sense plays in developing mathematical understanding. Number sense encompasses a wide range of abilities, including being able to make reasonable estimates and to think and reason flexibly. These lessons help students develop good number intuition and the ability to see numbers as tools, not barriers. By encouraging young children to reason their way to solutions, teachers help students form a solid foundation upon which all of their later mathematical understanding will be built.Lessons in this book are organized in an accessible, easy-to-read format that includes an overview, a materials list, the lesson duration, step-by-step teaching directions, and vignettes of how the lesson actually unfolded in a classroom. Each lesson concludes with a list of assessment questions to help guide teacher observations. In this book, children investigate number relationships, practice problem solving using landmark numbers, and explore ways to count, compose, and decompose numbers.

The Grammar of Graphics

2010-09-17T15:05:00.002+02:00

The Grammar of Graphics (Statistics and Computing)
Leland Wilkinson

Springer | 2005 | 694 páginas | RAR - PDF | 12 MB

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This book was written for statisticians, computer scientists, geographers, researchers, and others interested in visualizing data. It presents a unique foundation for producing almost every quantitative graphic found in scientific journals, newspapers, statistical packages, and data visualization systems. While the tangible results of this work have been several visualization software libraries, this book focuses on the deep structures involved in producing quantitative graphics from data. What are the rules that underlie the production of pie charts, bar charts, scatterplots, function plots, maps, mosaics, and radar charts? Those less interested in the theoretical and mathematical foundations can still get a sense of the richness and structure of the system by examining the numerous and often unique color graphics it can produce. The second edition is almost twice the size of the original, with six new chapters and substantial revision. Much of the added material makes this book suitable for survey courses in visualization and statistical graphics."This fascinating book deconstructs the process of producing graphics and in doing so raises many fascinating questions on the nature and representation of information...This second edition is almost twice the size of the original, with six new chapters and substantial revisions." Short Book Reviews of the International Statistical Institute, December 2005"When the first edidtion of this book appeared in 2000 it was much praised. I called it a tour de force of the highest order. (Wainer, 2001), Edward Wegman (2000) argued that it was destined to become a classic. Now, six years later this very fine book has been much improved." Howard Wainer for Psychometrika"...The second edition is an impressive expansion beyond a quite remarkable first edition. The text remains dense and even more encyclopedic, but it is a pleasure to read, whether a novice or an expert in graphics...this book is a bargain...The second edition is a must-have volume for anyone interested in graphics." Thomas E. Bradstreet for the Journal of the American Statistical Association, December 2006"I find myself still thinking about the book and its ideas, several weeks after I finished reading it. I love that kind of book." Mark Bailey for Techometrics, Vol. 49, No. 1, February 2007"Warts and all, The Grammar of Graphics is a richly rewarding work, an outstanding achievement by one of the leaders of statistical graphics. Seek it out." Nicholas J. Cox for the Journal of Statistical Software, January 2007.

Origami Tessellations: Awe-Inspiring Geometric Designs

2010-09-17T14:59:00.002+02:00

Origami Tessellations: Awe-Inspiring Geometric Designs
Eric Gjerde

AK Peters | 2008 | 128 páginas

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Paper artist Eric Gjerde demonstrates 25 of his favorite tessellations and turns them into folding projects for newcomers as well as experienced origamists. With step-by-step instructions, illustrated crease patterns, and how-to photos, you'll learn to create these wonderful designs yourself.

Enriching Early Mathematical Learning

2010-09-17T14:49:00.002+02:00

Enriching Early Mathematical Learning
Grace Cook, Lesley Jones, Cathy Murphy, Gillian Thumpston

Open University Press | 1997 | 96 páginas | RAR - PDF | 3,489 MB

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This book is a rich resource intended to support teachers and teachers in training with their teaching of mathematics in the early years. It comprises twenty activities which can be used as starting points. For each activity there are suggestions about how children might respond and guidance as to how the children may be further developed as learners. Support is also given to enable the teacher to embed the learning in a theoretical framework and make links with the National Curriculum.

All of the activities have been tried and tested in school and suggestions are made about the way in which these might be fitted into general classroom topics. There is a strong focus on formative assessment and how this can inform future planning.

Special features include:

* Very accessible to teachers

* Attractive and user friendly format

* Detailed support for introducing and extending activities which cover each area
of the National Curriculum

* Focus on using and applying maths at the early stages of Key Stage 1.

Math Matters: Understanding the Math You Teach Grades K-8

2010-09-17T14:25:00.002+02:00

Math Matters: Understanding the Math You Teach Grades K-8
Suzanne H. Chapin, Art Johnson

Math Solutions | 2006 | 376 páginas

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Math Matters, first published in 2000, quickly became an invaluable resource for math educators nationwide, helping them clarify their own understanding of the math concepts they are required to teach. This important book contains activities and discussions on key elementary topics such as whole number computation, fractions, algebra, geometry, and measurement. The scope in this second edition has now been expanded to address key topics in the middle school math curriculum as well, including sections on integers, exponents, similarity, the Pythagorean Theorem, and more.

Math For All: Differentiating Instruction, Grades K-2

2010-09-17T14:20:00.002+02:00

Math For All: Differentiating Instruction, Grades K-2
Linda Dacey, Rebeka Eston Salemi

Math Solutions | 2007 | 248 páginas | PDF | 2,082 MB

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In this two-book series, teachers will find powerful strategies for adapting mathematical lessons and tasks to address the wide range of abilities, interests, and learning styles of the students in their classrooms. Each book in this research-based series contains a wealth of activities tailored to its particular K-2 or 3-5 grade span. The authors provide numerous differentiated tasks ready for classroom implementation, as well as guidance in managing differentiated lessons and strategies for providing and structuring choice with the classroom. This series is a must-read for teachers, administrators, math coaches, special education staff, and any other educator who wishes to ensure that all children are successful learners of mathematics.

Math For All: Differentiating Instruction, Grades 3-5

2010-09-17T14:11:00.003+02:00

Math For All: Differentiating Instruction, Grades 3-5
Linda Dacey, Jayne Bamford Lynch

Math Solutions Publications | 2007 | 265 páginas

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In this two-book series, teachers will find powerful strategies for adapting mathematical lessons and tasks to address the wide range of abilities, interests, and learning styles of the students in their classrooms. Each book in this research-based series contains a wealth of activities tailored to its particular K-2 or 3-5 grade span. The authors provide numerous differentiated tasks ready for classroom implementation, as well as guidance in managing differentiated lessons and strategies for providing and structuring choice with the classroom. This series is a must-read for teachers, administrators, math coaches, special education staff, and any other educator who wishes to ensure that all children are successful learners of mathematics.

The Sea Island Mathematical Manual: Surveying and Mathematics in Ancient China

2010-09-17T13:51:00.002+02:00

The Sea Island Mathematical Manual: Surveying and Mathematics in Ancient China
Frank Swetz

Pennsylvania State University Press | 1992 | 73 páginas

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The Haidao Suanjing or Sea Island Mathematical Manual, is one of the "Ten Classics" of traditional Chinese mathematics, and its contents demonstrate the high standards of theoretical and mathematical sophistication present in early Chinese surveying theory. The Haidao composed in A.D. 263 by Liu Hui, established the mathematical procedures for much of East Asian surveying activity for the next one thousand years. The contents of the Haidao also testify to the ability of the Chinese to systematize mathematics and hint at the use of proof in Chinese mathematics, a concept usually associated with Greek mathematical thought.Frank Swetz provides an annotated translation of the Haidao and an analysis of its surveying problems. In particular, he details surveying techniques and undertakes a mathematical exposition of the Chinese chong cha solution procedures. The Haidao is a testimony to the ingenuity and skill of China's early surveyors and its author, Liu Hui. This study complements and extends the findings of Swetz's previous book, Was Pythagoras Chinese? An Examination of Right Triangle Theory in Ancient China.

Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity

2010-09-17T13:42:00.003+02:00

Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity
Committee on Early Childhood Mathematics, National Research Council

National Academies Press | 2009 | 398 páginas

on-line: nap.edu

23,6 MB | PDF

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Early childhood mathematics is vitally important for young children's present and future educational success. Research has demonstrated that virtually all young children have the capability to learn and become competent in mathematics. Furthermore, young children enjoy their early informal experiences with mathematics. Unfortunately, many children's potential in mathematics is not fully realized, especially those children who are economically disadvantaged. This is due, in part, to a lack of opportunities to learn mathematics in early childhood settings or through everyday experiences in the home and in their communities. Improvements in early childhood mathematics education can provide young children with the foundation for school success.
Relying on a comprehensive review of the research, Mathematics Learning in Early Childhood lays out the critical areas that should be the focus of young children's early mathematics education, explores the extent to which they are currently being incorporated in early childhood settings, and identifies the changes needed to improve the quality of mathematics experiences for young children. This book serves as a call to action to improve the state of early childhood mathematics. It will be especially useful for policy makers and practitioners-those who work directly with children and their families in shaping the policies that affect the education of young children.

The Cambridge Dictionary of Statistics

2010-09-17T13:37:00.002+02:00

The Cambridge Dictionary of Statistics
B. S. Everitt, A. Skrondal

Cambridge University Press | 2010 | 478 páginas

4,177 MB | PDF

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If you work with data and need easy access to clear, reliable definitions and explanations of modern statistical and statistics-related concepts, then look no further than this dictionary. Nearly 4000 terms are defined, covering medical, survey, theoretical, and applied statistics, including computational and graphical aspects. Entries are provided for standard and specialized statistical software. In addition, short biographies of over 100 important statisticians are given. Definitions provide enough mathematical detail to clarify concepts and give standard formula when these are helpful. The majority of definitions then give a reference to a book or article where the user can seek further or more specialized information, and many are accompanied by graphical material to aid understanding.

Mathematics and Humor: A Study of the Logic of Humor

2010-09-17T13:30:00.002+02:00

Mathematics and Humor: A Study of the Logic of Humor
John Allen Paulos

University Of Chicago Press | 1982 | 124 páginas

PDF | 1,45 MB

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"Jokes, paradoxes, riddles, and the art of non-sequitur are revealed with great perception and insight in this illuminating account of the relationship between humor and mathematics."--Joseph Williams, New York Times"'Leave your mind alone,' said a Thurber cartoon, and a really complete and convincing analysis of what humour is might spoil all jokes forever. This book avoids that danger. What it does. . .is describe broadly several kinds of mathematical theory and apply them to throw sidelights on how many kinds of jokes work."--New Scientist"Many scholars nowadays write seriously about the ludicrous. Some merely manage to be dull. A few--like Paulos--are brilliant in an odd endeavor."--Los Angeles Times Book Review

A Mathematical Tapestry: Demonstrating the Beautiful Unity of Mathematics

2010-09-17T13:18:00.003+02:00

A Mathematical Tapestry: Demonstrating the Beautiful Unity of Mathematics
Peter Hilton, Jean Pedersen

Cambridge University Press | 2010 | 306 páginas

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This easy-to-read book demonstrates how a simple geometric idea reveals fascinating connections and results in number theory, the mathematics of polyhedra, combinatorial geometry, and group theory. Using a systematic paper-folding procedure it is possible to construct a regular polygon with any number of sides. This remarkable algorithm has led to interesting proofs of certain results in number theory, has been used to answer combinatorial questions involving partitions of space, and has enabled the authors to obtain the formula for the volume of a regular tetrahedron in around three steps, using nothing more complicated than basic arithmetic and the most elementary plane geometry. All of these ideas, and more, reveal the beauty of mathematics and the interconnectedness of its various branches. Detailed instructions, including clear illustrations, enable the reader to gain hands-on experience constructing these models and to discover for themselves the patterns and relationships they unearth.

Understanding and Teaching Primary Mathematics

2010-08-05T22:12:00.003+02:00

Understanding and Teaching Primary Mathematics
Tony Cotton

Longman | 2010 | 272 páginas | rar - pdf | 4,8 Mb

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Understanding and Teaching Primary Mathematics is a full colour, core textbook for anyone training to teach Maths at primary level. A self-audit is provided at the outset to assess your prior knowledge and highlight areas for your personal development. The book will then help you to develop your mathematical understanding by encouraging you to think mathematically. You will be asked to create an action plan to aid your development and this will also allow you to build up a portfolio of evidence to help you achieve QTS (Qualified Teacher Status). Rather than treating subject knowledge and pedagogy as two separate entities, the book sets maths subject knowledge in context, showing you how to apply it in the classroom, through models and cases of best practice. Misconception boxes appear throughout each chapter to highlight common misconceptions children have in maths and help you to make connections between different areas of mathematics so that your pupils will see mathematics as a whole rather than a series of separate and often disparate ideas. Case studies in each chapter also provide you with an exemplar lesson plan annotated by a new teacher which shows you how to deal with a common misconception. This book will help you to deliver Maths at primary level in a clear and confident manner.

Contents

Teaching and Learning Primary Mathematics

What Should I Know? What Do I Know?

Using and Applying Mathematics

Counting and Understanding Number

Knowing and Using Number Facts

Calculating

Understanding Shape

Measuring

Handling Data

Teaching and Learning Mathematics in the Early Years

Issues of Inclusion

ICT and Teaching and Learning Mathematics

The QTS Skills Test

Defending Hypatia: Ramus, Savile, and the Renaissance Rediscovery of Mathematical History

2010-08-05T22:07:00.002+02:00

Defending Hypatia: Ramus, Savile, and the Renaissance Rediscovery of Mathematical History (Archimedes)
Robert Goulding

Springer | 2010 | 201 páginas | rar - pdf | 1,6 Mb

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Why should mathematics, the purest of sciences, have a history? Medieval mathematicians took little interest in the history of their discipline. Yet in the Renaissance the history of mathematics flourished. This book explores how Renaissance scholars recovered and reconstructed the origins of mathematics by tracing its invention in prehistoric Antiquity, its development by the Greeks, and its transmission to modern Europe via the works of Euclid, Theon and Proclus. The principal architects of this story -- the French philosopher and University of Paris reformer Peter Ramus, and his critic, the young Oxford astronomy lecturer Henry Savile – worked out diametrically opposed models for the development of the mathematical arts, models of historical progress and decline which mirrored each scholar’s larger convictions about the nature of mathematical thinking, the purpose of the modern university, and the potential of the human mind. In their hands, the obscure story of mathematical history became a site of contention over some of the most pressing philosophical and pedagogical debates of the sixteenth century.

Improving Mathematics at Work: The Need for Techno-Mathematical Literacies

2010-08-05T22:01:00.002+02:00

Improving Mathematics at Work: The Need for Techno-Mathematical Literacies
(Improving Learning)
Celia Hoyles, Richard Noss, Phillip Kent, Arthur Bakker

Routledge | 2010 | 224 páginas | RAR - PDF | 1,76 MB

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Improving Mathematics at Work questions the mathematical knowledge and skills that matter in the 21st century world of work, and studies how the use of mathematics in the workplace is evolving in the rapidly-changing context of new technologies and globalisation. Through a series of case studies from the manufacturing and financial service sectors, the authors argue that there has been a radical shift in the type mathematical skills required for work – a shift not yet fully recognised by the formal education system, or by employers and managers.Examining how information technology has changed mathematical requirements, the idea of Techno-mathematical Literacies (TmL) is introduced to describe the emerging need to be fluent in the language of mathematical inputs and outputs to technologies and to interpret and communicate with these, rather than merely to be procedurally competent with calculations. The authors argue for careful analyses of workplace activities, looking beyond the conventional thinking about numeracy, which still dominates policy arguments about workplace mathematics. Throughout their study, the authors answer the following fundamental questions:What mathematical knowledge and skills matter for the world of work today?How does information technology change the necessary knowledge and the ways in which it is encountered?How can we develop these essential new skills in the workforce?With evidence of successful opportunities to learn with TmL that were co-designed and evaluated with employers and employees, this book provides suggestions for the development of TmL through the use of authentic learning activities, and interactive software design. Essential reading for trainers and managers in industry, teachers, researchers and lecturers of mathematics education, and stakeholders implementing evidence-based policy, this book maps the fundamental changes taking place in workplace mathematics

Test Your Logic

2010-08-05T21:55:00.002+02:00

Test Your Logic
George J. Summers

Dover Publications | 1972 | 100 páginas | RAR-DJVU |530 kb

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George J. Summers creates 50 new puzzles for fans eager to test their logic. The puzzles range in difficulty from the relatively simple examples at the beginning of the book to others that are tricky, complex and subtle enough to the test the expert.

Essays on the Foundations of Mathematics by Moritz Pasch

2010-08-05T21:45:00.002+02:00

Essays on the Foundations of Mathematics by Moritz Pasch
(The Western Ontario Series in Philosophy of Science)
Stephen Pollard

Springer | 2010 | 245 páginas | PDF | 2,15 Mb

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Moritz Pasch (1843-1930) is justly celebrated as a key figure in the history of axiomatic geometry. Less well known are his contributions to other areas of foundational research. This volume features English translations of 14 papers Pasch published in the decade 1917-1926. In them, Pasch argues that geometry and, more surprisingly, number theory are branches of empirical science; he provides axioms for the combinatorial reasoning essential to Hilbert’s program of consistency proofs; he explores "implicit definition" (a generalization of definition by abstraction) and indicates how this technique yields an "empiricist" reconstruction of set theory; he argues that we cannot fully understand the logical structure of mathematics without clearly distinguishing between decidable and undecidable properties; he offers a rare glimpse into the mind of a master of axiomatics, surveying in detail the thought experiments he employed as he struggled to identify fundamental mathematical principles; and much more. This volume will: Give English speakers access to an important body of work from a turbulent and pivotal period in the history of mathematics, help us look beyond the familiar triad of formalism, intuitionism, and logicism, show how deeply we can see with the help of a guide determined to present fundamental mathematical ideas in ways that match our human capacities, will be of interest to graduate students and researchers in logic and the foundations of mathematics.

Math and Nonfiction, Grades 6-8

2010-08-05T21:35:00.002+02:00

Math and Nonfiction, Grades 6-8
Jennifer M. Bay-Williams, Sherri L. Martinie

Math Solutions | 2008 | 224 páginas | PDF | 1,9 MB

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This new addition to the Math, Literature, and Nonfiction series helps teachers build on their students' natural passion for knowledge as they engage in real-world mathematical problem solving. The lessons in this book use nonfiction as a springboard to explore mathematical concepts key to the middle school curriculum. The lessons inspire students to collect and analyze data, use proportional reasoning, and explore probability, relationships between two-and three-dimensional objects, pi, and more. Each lesson includes an overview of the nonfiction title; a discussion of the lesson s mathematical focus; and a detailed narrative description of how the activity unfolds.

Adventures with Impossible Figures

2010-07-13T01:37:00.001+02:00

Adventures with Impossible Figures
Bruno Ernst (J.A.F de Rijk)

Tarquin | 1986 | 96 páginas | djvu | 1,9Mb

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Descrição: Describes the methods which are used to construct intriguing impossible figures which can tease the eye and baffle the imagination. Copious examples are drawn from the author's own work and the fertile imagination of Escher and Oscar Reutersvärd.

Combinatorics and Reasoning: Representing, Justifying and Building Isomorphisms

2010-07-13T01:23:00.002+02:00

Combinatorics and Reasoning: Representing, Justifying and Building Isomorphisms
(Mathematics Education Library)
Carolyn A. Maher, Arthur B. Powell, Elizabeth B. Uptegrove

Springer | 2010 | 224 páginas | RAR - PDF | 3,35 MB

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Descrição: Combinatorics and Reasoning: Representing, Justifying and Building Isomorphisms is based on the accomplishments of a cohort group of learners from first grade through high school and beyond, concentrating on their work on a set of combinatorics tasks. By studying these students, the editors gain insight into the foundations of proof building, the tools and environments necessary to make connections, activities to extend and generalize combinatoric learning, and even explore implications of this learning on the undergraduate level.

This volume underscores the power of attending to basic ideas in building arguments; it shows the importance of providing opportunities for the co-construction of knowledge by groups of learners; and it demonstrates the value of careful construction of appropriate tasks. Moreover, it documents how reasoning that takes the form of proof evolves with young children and discusses the conditions for supporting student reasoning.

Conteúdos:
Introduction.- The Longitudinal Study.- Methodology.- Representations as a Tool for Building Arguments.- Building Towers: Justifications Leading to Proof Making.- Making Pizzas: Reasoning by Cases and recursion.- Responding to Ankur's Challenge: Co-construction of Argument Leading to Proof.- Co-construction of Proof.- The Case of Stephanie.- Representations and Connections.- Pizzas, Block Towers, and Binomials.- Generalizing from Pizzas, Towers, Binomial Expansion, and Pascal's Triangle.- Extending and Generalizing the Isomorphism: Towers, Pizzas, Pascal's Triangle, and the Taxicab Problem.- College Students Building Towers and Making Pizzas.- Comparing the Problem Solving of College Students with Longitudinal Study Students.- Conclusions and Suggestions for Practice.

A Focus on Fractions: Bringing Research to the Classroom

2010-07-02T01:57:00.002+02:00

A Focus on Fractions: Bringing Research to the Classroom
(Studies in Mathematical Thinking and Learning Series)
Marjorie M. Petit, Robert E. Laird, Edwin L. Marsden

Routledge | 2010 | 208 páginas | RAR -PDF | 6,778 MB

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A Focus on Fractions is the first book to make cognitive research on how students develop their understanding of fraction concepts readily accessible and understandable to pre- and in-service K– 8 mathematics educators. This important resource assists teachers in translating research findings into their classroom practice by conveying detailed information about how students develop fraction understandings as well as common student misconceptions, errors, preconceptions, and partial understandings that may interfere with students learning.　 Using extensive annotated samples of student work, as well as vignettes characteristic of classroom teachers’ experiences, this book equips educators with knowledge and tools to reveal students’ thinking so that they can modify their teaching to improve student learning of fractions concepts.　

Special Features:

End of Chapter Questions provide teachers the opportunity to analyze student thinking and consider instructional strategies for their own students. Instructional Links help teachers relate concepts from the chapter to their own instructional materials and programs. Big Ideas and Research Reviews frame the chapters and provide a platform for meaningful exploration of the teaching of fractions. Answer Key posted online offers extensive explanations of in-chapter questions.

A Focus on Fractions bridges the gap between what mathematics education researchers have discovered about the learning of fraction concepts and what teachers need to know to make effective instructional decisions.

Fractions in Realistic Mathematics Education: A Paradigm of Developmental Research

2010-07-02T01:45:00.003+02:00

Fractions in Realistic Mathematics Education: A Paradigm of Developmental Research
(Mathematics Education Library)
Leen Streefland

Springer | 1991 | 368 páginas | RAR - PDF | 27,505 MB

(Falta página 121)

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This book has a two-fold purpose. First, it was intended as a description of the development and testing of a primary school fraction program, presently in practice. This project seeks to develop a realistic alternative to the teaching and learning of fractions. The second purpose was to produce a theory on the teaching and learning of fractions that could be an example for a theory of realistic mathematics education.

The introduction gives an overview of the research and the sequential development of the course.

Chapter 1, "Description of the Fraction Problem," describes an historical background of the problem created by fractions in mathematics education.

Chapter 2, "Currents-Standpoint-Proposal," regards fractions from a variety of viewpoints from the background of the historical learning process.

Chapter 3, "The Context of the Research," offers a framework of the circumstances and conditions of the research.

Chapter 4, "The "Course in Theory and Practice", contains a general outline of the new course.

Chapter 5, "Individual Portraits of the Fraction Researchers," draws portions of the individual learning processes of those 13 students who participated throughout the entire research period.

Chapter 6, "Internal Evaluation of the Learning Process," illuminates the individual learning processes against the background of the type of instruction given.

Chapter 7, "External or Summative Evaluation", contains the research group's results on a "cross-section test" compared to a control group.

Chapter 8, "Theoretical Review", is a theoretical reflection that establishes certain links with the more general frameworks of cognitive psychology and educational psychology.

Jeux Mathematiques du Monde

2010-07-01T23:25:00.002+02:00

Jeux Mathematiques du Monde
Berloquin Pierre

Flammarion | 1978 | 162 páginas | djvu | 2,8 MB

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Les récréations de ce livre ont d’abord été publiées dans le journal Le Monde. Contient 75 problèmes. Les problèmes vont de la formule du calendrier à une fraude sur le rectangle en passant par les carrés magiques et la flèche de Zénon.

The Legacy of Leonhard Euler: A Tricentennial Tribute

2010-07-01T23:05:00.002+02:00

The Legacy of Leonhard Euler: A Tricentennial Tribute
Lokenath Debnath

Imperial College Press | 2009 | 420 páginas | PDF | 6,728 MB

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This book primarily serves as a historical research monograph on the biographical sketch and career of Leonhard Euler and his major contributions to numerous areas in the mathematical and physical sciences. It contains fourteen chapters describing Euler's works on number theory, algebra, geometry, trigonometry, differential and integral calculus, analysis, infinite series and infinite products, ordinary and elliptic integrals and special functions, ordinary and partial differential equations, calculus of variations, graph theory and topology, mechanics and ballistic research, elasticity and fluid mechanics, physics and astronomy, probability and statistics. The book is written to provide a definitive impression of Euler's personal and professional life as well as of the range, power, and depth of his unique contributions. This tricentennial tribute commemorates Euler the great man and Euler the universal mathematician of all time. Based on the author's historically motivated method of teaching, special attention is given to demonstrate that Euler's work had served as the basis of research and developments of mathematical and physical sciences for the last 300 years. An attempt is also made to examine his research and its relation to current mathematics and science. Based on a series of Euler's extraordinary contributions, the historical development of many different subjects of mathematical sciences is traced with a linking commentary so that it puts the reader at the forefront of current research.

Problems in Elementary Mathematics

2010-07-01T22:59:00.002+02:00

Problems in Elementary Mathematics
Victor Lidsky, L. Ovsyannikov, A. Tulaikov, M. Shabunin

MIR Publishers, Moscow | 1973 | 376 páginas | PDF | 22,5 Mb

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Translated from the Russian by V. Volosov.

First Published 1973, Revised from the 1970 Russian Edition.

This book is written by a group of Soviet mathematicians under the guidance of Professor Victor Lidsky, D.Sc. (Phys. & Math.). It includes advanced problems in elementary mathematics with hints and solutions. In each section – Algebra, Geometry and Trigonometry – The problems are arranged in the order of increasing difficulty. There are 658 problems in all.

Algebra: 291 Questions

Plane Geometry: 139 Questions

Solid Geometry: 102 Questions

Tirgonometry: 126 Questions

The text can be used in mathematical schools and school mathematics societies.

Victor LIDSKY, D. Sc., teaches at the Moscow Physico-Technical Institute. He has published about sixty scientific works on spectral theory of differential equations, matrix algebra, functional analysis, and mechanics.

Many of his books are used as manuals in mathematics departments of higher educational institutions.

...

This is the famous out of print and impossible to find “Lidsky Book.”

If you have time for only one book to prepare for mathematics contests such as the AMC, the AIME, and the USAMO, this is the ONE. It actually covers 6 of the key areas – Algebra (including Inequalities and Combinatorics,) Plane Geometry, Solid Geometry and Trigonometry. You will not need much more than this book and proof techniques for success. - DP.

Mathematical Quickies: 270 Stimulating Problems with Solutions

2010-07-01T22:43:00.002+02:00

Mathematical Quickies: 270 Stimulating Problems with Solutions
(Dover Books on Mathematical and Word Recreations)
Charles W. Trigg

Dover Publications | 1985 | 210 páginas | PDF | 3,8 MB

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Nearly 300 mathematical brain-teasers from the fields of arithmetic, algebra, plane and solid geometry, trigonometry, number theory, and general recreational mathematics. From simple to complex; all challenge the reader to devise solutions more elegant than the ones provided. Offers hours of brain-bending amusement. 270 problems. 121 illustrations. Solutions. List of Sources

MATHKNOW

2010-07-01T22:28:00.003+02:00

MATHKNOW: Mathematics, Applied Science and Real Life (MS&A)
Michele Emmer, Alfio Quarteroni

Springer | 2009 | 263 páginas | PDF | 36 MB

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Mathematics forms bridges between knowledge, tradition, and contemporary life.
The continuous development and growth of its many branches, both classical and modern, permeates and fertilizes all aspects of applied science and technology, and so has a vital impact on our modern society. The book will focus on these aspects and will benefit from the contribution of several world-famous scientists from mathematics and related sciences, such as: Ralph Abraham, Andrew Crumey, Peter Markowich, Claudio Procesi, Clive Ruggles, Ismail Serageldin, Amin Shokrollahi, Tobias Wallisser

Math Wise!

2010-07-01T22:10:00.003+02:00

Math Wise! Over 100 Hands-On Activities that Promote Real Math Understanding, Grades K-8
(Jossey-Bass Teacher)
James L. Overholt, Laurie Kincheloe

Jossey-Bass | 2010 | 448 páginas | RAR - PDF | 4,5 MB

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A fun, easy-to-implement collection of activities that give elementary and middle-school students a real understanding of key math concepts

Math is a difficult and abstract subject for many students, yet teachers need to make sure their students comprehend basic math concepts. This engaging activity book is a resource teachers can use to give students concrete understanding of the math behind the questions on most standardized tests, and includes information that will give students a firm grounding to work with more advanced math concepts.

Contains over 100 activities that address topics like number sense, geometry, computation, problem solving, and logical thinking.
Includes projects and activities that are correlated to National Math Education Standards
Activities are presented in order of difficulty and address different learning styles

Math Wise! is a key resource for teachers who want to teach their students the fundamentals that drive math problems.

Learning Through Teaching Mathematics: Development of Teachers' Knowledge and Expertise in Practice

2010-07-01T21:49:00.002+02:00

Learning Through Teaching Mathematics: Development of Teachers' Knowledge and Expertise in Practice
(Mathematics Teacher Education)
Roza Leikin, Rina Zazkis

Springer | 2010 | 250 páginas | RAR - PDF | 1,59 MB

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This volume explores how and when teachers' knowledge develops through teaching. The book presents international views on teachers' learning from their practice; the chapters are written by mathematicians or mathematics educators from Brazil, Canada, Israel, Mexico, UK, and USA. They address diverse content – numerical literacy, geometry, algebra, and real analysis – and a variety of levels – elementary school, secondary school, undergraduate mathematics, and teacher education courses. The authors employ different methodological tools and different theoretical perspectives as they consider teaching in different learning environments: lecturing, small group work on problems and tasks, mathematical explorations with the support of technological software, or e-learning. Despite these differences, the authors exemplify and analyze teachers’ learning that occurred and address the question: "What kinds of knowledge are developed as a result of teaching mathematics and what are the factors that support or impede such development?"Further, the chapters explore interactions and interrelationships between the enhancement of mathematical and pedagogical knowledge. The important and original contribution of this book is that it ties together the notions of teachers’ knowledge and complexity of teacher’s work, while presenting them from a relatively unexplored perspective – learning through teaching mathematics
Índice:
Part I: Theoretical and Methodological Perspectives on Teachers’ Learning through Teaching

Roza Leikin and Rina Zazkis - Teachers’ opportunities to learn mathematics through teaching

John Mason - Attention and intention: Learning about teaching through teaching

Ron Tzur - What and How might mathematics teachers learn via teaching: Contributions to closing an unspoken gap

Roza Leikin - Learning through teaching though the lens of multiple solution tasks

Part II: Examples of Learning through teaching: Pedagogical mathematics

Rina Zazkis - What have I learned: Mathematical insights and pedagogical implication

Marcelo Borba and Rúbia B. A. Zulatto - Dialogical education and learning mathematics online from teachers.

Carolyn Kieran and José Guzmán - Role of task and technology in provoking teacher change: A case of proofs and proving in high school Algebra

Nick Jackiw and Nathalie Sinclair - Learning through teaching when teaching machines: Discursive interaction design in Sketchpad

Robin Marcus and Daniel Chazan - What experienced teachers have learned from helping students think about solving equations in the one-variable-first algebra curriculum

Part III: Examples of Learning through teaching: Mathematical pedagogy

Michal Yerushalmy and Shulamit Elikan - Exploring reform ideas of teaching Algebra: Analysis of videotaped episodes and conversations about them

Peter Liljedahl - On rapid professional growth: cases of learning through teaching

Lara Alcock - Interactions between teaching and research: Developing pedagogical content knowledge for Real Analysis

Helen Doerr and Stephen Lerman - Teachers learning from their teaching: The case of communicative practices

Dave Hewitt - Feedback: Expanding a repertoire and making choices