Mathematical Knowledge: Its Growth Through Teaching

(Mathematics Education Library, 10)

 Alan Bishop, Stieg Mellin-Olsen e Joop van Dormolen

Springer | 2010 -  reprint of 1st ed. 1991 edition | 214 páginas | rar - pdf | 21,6 Mb

link (password: matav)

CONTENTS
Introduction 1
G. BROUSSEAU AND M. OITE / The Fragility of Knowledge 13
S. MELLIN-OLSEN / The Double Bind as a Didactical Trap 39
W. D6RFLER / Forms and Means of Generalization in Mathematics 63
J. VAN DORMOLEN / Metaphors Mediating the Teaching and Understanding of Mathematics 89
R. DOUADY / Tool, Object, Setting, Window: Elements for Analysing and Constructing Didactical Situations in Mathematics 109
T. WERNER / Observing Conceptual Complexity
C. HOYLES / Developing Mathematical Knowledge Through Microworlds
N. BALACHEFF / The Benefits and Limits of Social Interaction: The Case of Mathematical Proof
A. J. BISHOP / Mathematical Values in the Teaching Process
Index of Names
Index of Subjects

Teaching Secondary Mathematics

David Rock e Douglas K. Brumbaugh

Routledge | 2013 -  4ª edição | 360 páginas | rar - pdf | 3,6 Mb

link (password: matav)

Solidly grounded in up-to-date research, theory and technology, Teaching Secondary Mathematics is a practical, student-friendly, and popular text for secondary mathematics methods courses. It provides clear and useful approaches for mathematics teachers, and shows how concepts typically found in a secondary mathematics curriculum can be taught in a positive and encouraging way. The thoroughly revised fourth edition combines this pragmatic approach with truly innovative and integrated technology content throughout. Synthesized content between the book and comprehensive companion website offers expanded discussion of chapter topics, additional examples and technological tips.

Each chapter features tried-and-tested pedagogical techniques, problem solving challenges, discussion points, activities, mathematical challenges, and student-life based applications that will encourage students to think and do.

New to the 4th edition:

• A fully revised and updated chapter on technological advancements in the teaching of mathematics

• Connections to both the updated NCTM Focal Points as well as the new Common Core State Standards are well-integrated throughout the text

• Problem solving challenges and sticky questions featured in each chapter to encourage students to think through everyday issues and possible solutions.

• A fresh interior design to better highlight pedagogical elements and key features

• A companion website with chapter-by-chapter video lessons, teacher tools, problem solving , helpful links and resources, and embedded graphing calculators.

Contents
Preface ix
Acknowledgments xi
Part 1: General Fundamentals
1 Introduction 3
2 Learning Theory, Curriculum, and Assessment 21
3 Planning 49
4 Skills in Teaching Mathematics 66
Part 2: Mathematics Education Fundamentals
5 Technology 93
6 Problem Solving 122
7 Discovery 144
8 Proof 161
Part 3: Content and Strategies
9 General Mathematics 179
10 Algebra I 212
11 Geometry 244
12 Advanced Algebra and Trigonometry 263
13 Pre-Calculus 284
14 Calculus 297
15 Probability and Statistics 312

2ª edição  

Forgotten Calculus

Barbara Lee Bleau

Barron's Educational Series | 2001 - 3ª edição | 480 páginas | rar - mobi | 10 Mb

link (password: matav)

Updated and expanded to include the optional use of graphing calculators, this combination textbook and workbook is a good teach-yourself refresher course for men and women who took a calculus course in school, have since forgotten most of what they learned, and now need some practical calculus for business purposes or advanced education. The book is also very useful as a supplementary text for students who are taking calculus and finding it a struggle. Each progressive work unit offers clear instruction and worked-out examples. Special emphasis has been placed on business and economic applications. Topics covered include functions and their graphs, derivatives, optimization problems, exponential and logarithmic functions, integration, and partial derivatives.

Mathematical Olympiad In China (2009-2010): Problems And Solutions

(Mathematical Olympiad Series)

Bin Xiong e Peng Yee Lee

World Scientific Publishing Company | 2013 | 205  páginas | rar - pdf | 15 Mb

link (password: matav)

epub - 8 Mb - link

The International Mathematical Olympiad (IMO) is a competition for high school students. China has taken part in the IMO 21 times since 1985 and has won the top ranking for countries 14 times, with a multitude of gold's for individual students. The six students China has sent every year were selected from 20 to 30 students among approximately 130 students who took part in the annual China Mathematical Competition during the winter months. This volume of comprises a collection of original problems with solutions that China used to train their Olympiad team in the years from 2009 to 2010. Mathematical Olympiad problems with solutions for the years 2002 - 2008 appear in an earlier volume, "Mathematical Olympiad in China".

Jeux de l'esprit et divertissements mathématiques

Jean-Pierre Alem

Seuil | 1990| French | DJVU | 328 pages | 4,2 Mb

link
link1

Ce recueil propose 128 problèmes où les mathématiques se mêlent parfois étroitement à la logique particulière des jeux ou de la cryptographie et même à la fantaisie. L'auteur a inséré de nombreuses notes relatives à des curiosités mathématiques.

The Book of My Life

Girolamo Cardano
tradução de Jean Stoner

 New York: ep Dutton & Co. | 1930 | 362 páginas | pdf | 6,8 Mb

 djm.cc (link direto)

A bright star of the Italian Renaissance, Girolamo Cardano was an internationally-sought-after astrologer, physician, and natural philosopher, a creator of modern algebra, and the inventor of the universal joint. Condemned by the Inquisition to house arrest in his old age, Cardano wrote The Book of My Life, an unvarnished and often outrageous account of his character and conduct. Whether discussing his sex life or his diet, the plots of academic rivals or meetings with supernatural beings, or his deep sorrow when his beloved son was executed for murder, Cardano displays the same unbounded curiosity that made him a scientific pioneer. At once picaresque adventure and campus comedy, curriculum vitae, and last will, The Book of My Life is an extraordinary Renaissance self-portrait.

Livro relacionado:

Cardano the gambling scholar por Oystein Ore Idioma: Inglês   Editora: Princeton : Princeton university press, 1953.

Revolutions of Geometry

 (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts)

Michael O'Leary

Wiley | 2010 | 607 páginas | pdf | 7 Mb

link
link1

Guides readers through the development of geometry and basic proof writing using a historical approach to the topic
In an effort to fully appreciate the logic and structure of geometric proofs, Revolutions of Geometry places proofs into the context of geometry's history, helping readers to understand that proof writing is crucial to the job of a mathematician. Written for students and educators of mathematics alike, the book guides readers through the rich history and influential works, from ancient times to the present, behind the development of geometry. As a result, readers are successfully equipped with the necessary logic to develop a full understanding of geometric theorems.
Following a presentation of the geometry of ancient Egypt, Babylon, and China, the author addresses mathematical philosophy and logic within the context of works by Thales, Plato, and Aristotle. Next, the mathematics of the classical Greeks is discussed, incorporating the teachings of Pythagoras and his followers along with an overview of lower-level geometry using Euclid's Elements. Subsequent chapters explore the work of Archimedes, Viete's revolutionary contributions to algebra, Descartes' merging of algebra and geometry to solve the Pappus problem, and Desargues' development of projective geometry. The author also supplies an excursion into non-Euclidean geometry, including the three hypotheses of Saccheri and Lambert and the near simultaneous discoveries of Lobachevski and Bolyai. Finally, modern geometry is addressed within the study of manifolds and elliptic geometry inspired by Riemann's work, Poncelet's return to projective geometry, and Klein's use of group theory to characterize different geometries

Table of Contents
Preface.
Acknowledgments.
PART I FOUNDATIONS.
1 The First Geometers.
1.1 Egypt.
1.2 Babylon.
1.3 China.
2 Thales.
2.1 The Axiomatic System.
2.2 Deductive Logic.
2.3 Proof Writing.
3 Plato and Aristotle.
3.1 Form.
3.2 Categorical Propositions..
3.3 Categorical Syllogisms.
3.4 Figures.
PART II THE GOLDEN AGE.
4 Pythagoras.
4.1 Number Theory.
4.2 The Pythagorean Theorem.
4.3 Archytas.
4.4 The Golden Ratio.
5 Euclid.
5.1 The Elements.
5.2 Constructions.
5.3 Triangles.
5.4 Parallel Lines.
5.5 Circles.
5.6 The Pythagorean Theorem Revisited.
6 Archimedes.
6.1 The Archimedean Library.
6.2 The Method of Exhaustion.
6.3 The Method.
6.4 Preliminaries to the Proof.
6.5 The Volume of a Sphere.
PART III ENLIGHTENMENT.
7 François Viète.
7.1 The Analytic Art.
7.2 Three Problems.
7.3 Conic Sections.
7.4 The Analytic Art in Two Variables.
8 René Descartes.
8.1 Compasses.
8.2 Method.
8.3 Analytic Geometry.
9 Gérard Desargues.
9.1 Projections.
9.2 Points at Infinity.
9.3 Theorems of Desargues and Menelaus.
9.4 Involutions.
PART IV A STRANGE NEW WORLD.
10 Giovanni Saccheri.
10.1 The Question of Parallels.
10.2 The Three Hypotheses.
10.3 Conclusions for Two Hypotheses.
10.4 Properties of Parallel Lines.
10.5 Parallelism Redefined.
11 Johann Lambert.
11.1 The Three Hypotheses Revisited.
11.2 Polygons.
11.3 Omega Triangles.
11.4 Pure Reason.
12 Nicolai Lobachevski and János Bolyai.
12.1 Parallel Fundamentals.
12.2 Horocycles.
12.3 The Surface of a Sphere.
12.4 Horospheres.
12.5 Evaluating the Pi Function.
PART V NEW DIRECTIONS.
13 Bernhard Riemann.
13.1 Metric Spaces.
13.2 Topological Spaces.
13.3 Stereographic Projection.
13.4 Consistency of Non-Euclidean Geometry.
14 Jean-Victor Poncelet.
14.1 The Projective Plane.
14.2 Duality.
14.3 Perspectivity.
14.4 Homogeneous Coordinates.
15 Felix Klein.
15.1 Group Theory.
15.2 Transformation Groups.
15.3 The Principal Group.
15.4 Isometries of the Plane.
15.5 Consistency of Euclidean Geometry.
References.
Index.