Proceedings of the First International Congress on Mathematical Education

ICME-1    1969      Lyon (France)

D. Reidel Publishing Company | 1969 | 286 páginas | pdf | 27,4 Mb
online: mathematik.uni-bielefeld.de

djvu - 13,8 Mb
online: mathematik.uni-bielefeld.de

All the papers of the congress are also published in 
Educational Studies in Mathematics (1969-70), Vol. 2, 134-418. 

Contents

H. FREUDENTHAL, Allocution (p. 3) 
B. CHRISTIANSEN, Induction and Deduction in the Learning of Mathematics and in Mathematical Instruction (p. 7) 
W. SERVAIS, Logique et enseignement mathématique (p. 28) 
J. V. ARMITAGE, The Relation between Abstract and 'Concrete' Mathematics at School (p. 48) 
R. GAUTHIER, Essai d'individualisation de l'enseignement (Enfants de dix à quatorze ans)(p. 57) 
G. G. MASLOVA, Le développement des idées et des concepts mathématiques fondamentaux dans l'enseignement des enfants de 7 a 15 ans (p. 69) 
A. ROUMANET, Une classe de mathématique: motivations et méthodes (p. 80) 
E. G. BEGLE, The Role of Research in the Improvement of Mathematics Education (p. 100) 
A. DELESSERT, De quelques problèmes touchant à la formation des maîtres de mathématiques (p. 113) 
A. ENGEL, The Relevance of Modern Fields of Applied Mathematics for Mathematical Education (p. 125) 
A. REVUZ, Les premiers pas en analyse (p. 138) 
A. MARKOUCHEVITCH, Certains problèmes de l'enseignement des mathématiques à l'école (p. 147) 
E. FISHBEIN, Enseignement mathématique et développement intellectuel (p. 158) 
E. CASTELNUOVO, Différentes représentations utilisant la notion de barycentre (p. 175) 
F. PAPY, Minicomputer (p. 201) 
B. THWAITES, The Role of the Computer in School Mathematics (p. 214) 
Z. KRYGOWSKA, Le texte mathématique dans l' enseignement (p. 228) 
H.-G. STEINER, Magnitudes and Rational Numbers - A Didactical Analysis (p. 239) 
H. O. POLLAK, How Can we Teach Applications of Mathematics? (p. 261) 
P. C. ROSENBLOOM, Vectors and Symmetry (p. 273) Resolutions (English) (p. 284) Résolutions (French) (p. 285) 

Mathematics in Western Culture

Morris Kline

Oxford University Press | 1964 | 512 páginas |

online : archive.org

This book gives a remarkably fine account of the influences mathematics has exerted on the development of philosophy, the physical sciences, religion, and the arts in Western life.

Table of Contents
I Introduction. True and False Conceptions, 3
II The Rule of Thumb in Mathematics, 13
III The Birth of the Mathematical Spirit, 24
IV The Elements oi Euclid, 40
V Placing a Yardstick to the Stars, 60
VI Nature Acquires Reason, 74
VII Interlude, 89
VIII Renewal of the Mathematical Spirit, 99
IX The Harmony of the World, no
X Painting arid Perspective, 126
XI Science Born of Art: Projective Geometry, 144
XII A Discourse on Method, 159
XIII The Quantitative Approach to Nature, 182
XIV The Deduction of Universal Laws, 196
XV Grasping the Fleeting Instant: The Calculus, 214
XVI The Newtonian Influence: Science and Philosophy, 234
XVII The Newtonian Influence: Religion, 257
XVIII The Newtonian Influence: Literature and Aesthetics, 272
XIX The Sine of G Major, 287
XX Mastery of the Ether Waves, 304
XXI The Science of Human Nature, 322
XXII The Mathematical Theory of Ignorance: The Statistical Approach
to the Study of Man, 340
XXIII Prediction and Probability, 359
XXIV Our Disorderly Universe: The Statistical View of Nature, 376
XXV The Paradoxes of the Infinite, 395
XXVI New Geometries, New Worlds, 410
XXVII The Theory of Relativity, 432
XXVIII Mathematics: Method and Art, 453

A Handbook of Mathematical Discourse

Charles Wells


Infinity Publishing | 2003 | 300 páginas 

pdf (versão draft - 2002) - online: 
ljk.imag.fr
abstractmath.org

Para mais livros sobre linguagem e comunicação em matemática procure em: link

What sort of book is this? It is a dictionary of sorts of all those words and conventions you had questions about as an undergraduate or graduate student but were afraid to ask, for fear of sounding dumb. Nobody, especially not your professors, bothered to explain these words, because they knew them so well and used them so automatically that it never occurred to them that you might not know to use them.
For example, a student might be confused by the many different ways mathematicians use let. This book explains, with illustrative examples, that let can mean assume or suppose, that it can be used to introduce a new symbol when considering successive cases (Let n > 0.... Now let n<0 font="" nbsp="">to introduce an arbitrary object when proving a for all statement (Let g∈G; we need to prove that…), or
to define a concept (Let an integer be even if it is divisible by 2),
as well as several other meanings. That students are not clear about the use of words like let can be seen from Steve Maurer’s PRIMUS article, “Advice for undergraduates on special aspects of writing mathematics” (Vol. 1, pp. 9–28, 1991).
A student might want to know what a bound variable is — not many transition-to-proof course textbooks cover that very well, if at all. There is a definition here, and it comes with a picture. Whether or not you like the somewhat quirky line drawings, however, depends on your sense of humor: next to the entry for bound variable, one finds an X with lots of rope around its middle. If you know already know the meaning of bound variable, you may be amused by this play on words. However, if you are a student trying to understand its meaning, I doubt it would help.
You can browse the book like a coffee table book (though its size is much smaller at 8 by 8 inches) or like a dictionary, which it resembles. Give it to your favorite math major or beginning graduate student to help enculturate him/her into mathematicians’ sometimes unusual usage of terms and phrases. You might also consider using it as a prize for a math contest or as an addition to your departmental math library.

A Mathematician's Apology

University of Alberta Mathematical Sciences Society | 2005 | 56 páginas | pdf | 174 kb

online: math.ualberta.ca

Cambridge University Press | 1967 | 80 páginas

online: archive.org

G. H. Hardy was one of this century's finest mathematical thinkers, renowned among his contemporaries as a 'real mathematician ... the purest of the pure'. He was also, as C. P. Snow recounts in his Foreword, 'unorthodox, eccentric, radical, ready to talk about anything'. This 'apology', written in 1940 as his mathematical powers were declining, offers a brilliant and engaging account of mathematics as very much more than a science; when it was first published, Graham Greene hailed it alongside Henry James's notebooks as 'the best account of what it was like to be a creative artist'. C. P. Snow's Foreword gives sympathetic and witty insights into Hardy's life, with its rich store of anecdotes concerning his collaboration with the brilliant Indian mathematician Ramanujan, his aphorisms and idiosyncrasies, and his passion for cricket. This is a unique account of the fascination of mathematics and of one of its most compelling exponents in modern times.

Para mais livros sobre filosofia da matemática procure em: link

A History of Mathematics

Carl B. Boyer

 John Wiley & Sons Inc; International Ed edition | 1968 | 738 páginas

online: archive.org

Para mais livros sobre história da matemática procure em: link

Contents

Chapter I. Primitive Origins 

Chapter II. Egypt 

Chapter III. Mesopotamia 

Chapter IV. Ionia and the Pythagoreans

Chapter V. The Heroic Age

Chapter VI. The Age of Plato and Aristotle 

Chapter VII. Euclid of Alexandria

Chapter VIII. Archimedes of Syracuse

Chapter IX. Apollonius of Perga

Chapter X. Greek Trigonometry and Mensuration

Chapter XI. Revival and Decline of Greek Mathematics

Chapter XII. China and India

Chapter XIII. The Arabic Hegemony

Chapter XIV. Europe in the Middle Ages

Chapter XV. The Renaissance

Chapter XVI. Prelude to Modern Mathematics

Chapter XVII. The Time of Fermat and Descartes

Chapter XVIII. A Transitional Period

Chapter XIX. Newton and Leibniz 

Chapter XX. The Bernoulli Era 

Chapter XXI. The Age of Euler

Chapter XXII. Mathematicians of the French Revolution

Chapter XXIII. The Time of Gauss and Cauchy

Chapter XXIV. The Heroic Age in Geometry

Chapter XXV. The Arithmetization of Analysis

Chapter XXVI. The Rise of Abstract Algebra

Chapter XXVII. Aspects of the Twentieth Century

General Bibliography 679

Appendix: Chronological Table 683

Index 697

Mathematics, Education and Society

Christine Keitel, P. Damerow, A. Bishop, P. Gerdes (Editores)

6.º International Congress on Mathematical Education (1988 : Budapest, Hungary)

Unesco Document Series Nº. 35

Unesco | 1989 | 200 páginas | pdf | 23,61 Mb

on-line: unesdoc.unesco.org

Table of Contents 
Mathematics, Education, and Society (MES) . . . 1 
Mathematics Education and Culture . . . . . 1 
Social History of Mathematics Education . . . . . 1 
Arpad Szabd: Mathematics and Dialectics.. . . . 2 
Ahmed Djebbar: The Content of Mathematics Teaching in North Africa in the Middle Ages  and its Role in Present Day Teaching.. . . 3 
John Fauvel: Should We Bring Back the Mathematical Practitioner? Learning From the  Social History of Mathematics Education in the British Renaissance.. . 4 
Gert Schubring: Theoretical Categories for Investigations in the Social History of Mathematics Education and Some Characteristic Patterns . . 6 
Cultural Diversity and Conflicts in Mathematics Education 
Terezinha Nunes Carraher: Material Embodiments of Mathematics Models  in Everyday Life 
Lloyd Dawe: Mathematics Teaching and Learning in Village Schools of the South Pacific
Murad Jurdak: Religion and Language as Cultural Carriers and Barriers in Mathematics Education
Claudia Zaslavsky: Integrating Mathematics With the Study of Cultural Traditions 
The Cultural Role of Mathematics Education in the Future
Leone Burton: Mathematics as a Cultural Experience: Whose Experience? 
Desmond Broomes: The Mathematical Demands of a Rural Economy 
Kathryn Crawford: Knowing What Versus Knowing How: The Need for a Change in Emphasis for Minority Group Education in Mathematics 
Philip J. Davis: Applied Mathematics as Social Contract 
Rik Pinxten: World View and Mathematics Teaching.
Society and Institutionalized Mathematics Education . 30 
Mathematics as a Cultural Product. 
Jens Hoyrup: On Mathematics and War 
George Ghevarghcse Joseph: Eurocentrism in Mathematics: The Historical Dimensions  
Sam O. Ale: Mathematics in Rural Societies  
Leo Rogers: The Cultural History of Mathematics as a Basis for Philosophies of Mathematics Education 
The Image of Mathematics in Society 
Gilah C. Leder: The Image of Mathematics in Society: A Case Study 
Stephen Lerman: A Social View of Mathematics-Implications for Mathematics Education 
Chandler Davis: A Hippocratic Oath for Mathematicians?
Sociology of Institutionalized Mathematics.
Eduard Glas: Social Determinants of Mathematical Change: The Ecole Polytechnique 1794-1809
Renate Tobies: The Activities of Felix Klein in the Teaching Commission of the 2nd Chamber of the Prussian Parliament
Emma Castelnuovo: The Teaching of Geometry in Italian High Schools During the Last Two Centuries: Some Aspects Related to Society 
Michael H. Price: Some Reflections on the Role of Associations in Mathematics Education
The Mathematics Curriculum as a Social Issue 
Michael Otte: “Mathematics for All” and the Epistemological Problems of Mathematics Education
Neil Bibby and John Abraham: Social History of Mathematical Controversies: Some Implications for the Curriculum
Bernard Charlot: Institutional and Socio-Economic Context of the “Modem Mathematics” Reform in France 
Non-School Alternatives for Mathematics Education 
John D. Volmink: Non-School Alternatives in Mathematics Education
Sixto Romero Sanchez: The Necessity of Popularizing Mathematics via Radio Programs 
Virginia Thompson: FAMILY MATH: Linking Home and Mathematics
Jeffrey T. Evans: Mathematics for Adults: Community Research and the “Barefoot Statistician” 
The Mathematical Demands of the Economy
Guida Maria Correia P. de Abreu and David William Carraher: The Mathematics of Brazilian Sugar Cane Farmers 
Wang Chang Pei: Differences in Mathematics Education Between Rural Area and Urban Area in China..
Howard Russell: The Generic Skills Economic Dcvelopmcnt Project: The Mathematical Demands of the Economy 
Bemhelm Boo&Bavnbck and Glen Pate: Expanding Risk in Technological Society Through Progress in Mathematical Modeling 
Mathematics Education Under Different Cultural Constraints
Siaka Bamba Kanti: Critical Issues of Mathematics Education in the Ivory Coast
Jens Naumann: Practical Aspects of Basic Mathematics Teaching in Senegalese Villages
Diana C. Rosenberg: Knowledge Transfer From one Culture to Another: HEWET From the Netherlands to Argentina
Munir Fasheh: Mathematics in a Social Context: Math Within Education as Praxis Versus Within Education as Hegemony.
Society as a Source of Ideas for Mathematics Teaching
Brian Hudson: Global Perspectives in the Mathematics Classroom
Tadasu Kawaguchi: Mathematical Thoughts Being Latent in Various Artistic Activities
Diana Schultz: PRIMITl-Projects in Real-Life Integrated Mathematics in Teacher Education
Joop van Dormolen: Values of Texts for Learning Mathematics for Real Life
How Autonomous is the Mathematics Teacher?.
Dianne E. Siemon: How Autonomous is the Teacher of Mathematics?
Paul Ernest: The Impact of Beliefs on the Teaching of Mathematics
Kurt Kreith: The Recruitment and Training of Master Teachers
John Suffolk: The Role of the Mathematics Teacher in Developing Countries
Ethnomathematics and Schools
Gloria F. Gilmer: World-wide Developments in Ethnomathematics 
Randall Souviney: The Indigenous Mathematics Project: Mathematics Instruction in Papua New Guinnea 
Eduardo Sebastiani Ferreira: The Genetic Principle and the Ethnomathematics
Social Needs and Reforms in Mathematics Education 
Feiyu Cao: School Mathematics Education Should Suit the Needs of Social Development
Fidel Oteiza and Nadja Antonijevic: On the Light of Present and Future Needs, are we Teaching the Proper Mathematics? The Case of Chile
Teresa Smart and Zelda Isaacson: “It was Nice Being Able to Share Ideas”: Women Learning Mathematics. 
George Malaty: ICMI and the Crisis of Mathematics Education: What Kind of Reform is Needed? 
Educational Institutions and the Individual Learner 
Individual and Social Learning Motivations
Anne-Nelly Perret-Clermont and Maria-Luisa Schubauer-Leoni: The Social Construction of Meaning in Math Class Interactions
Timothy E. Erickson: Cooperative Learning in Mathematics: A Way to Engage All Students 
Albrecht Abele: Socialization and Learning Mathematics 
Cultural Influences on Learning 
Analucia Dias Schliemann and Nadja Maria Acioly: Numbers and Operations in Everyday Problem Solving .
Frederick K. S. Leung: The Chinese Culture and Mathematics Learning 
Martin R. Hoffman and Arthur B. Powell: Mathematical and Commentary Writing: Vehicles for Student Reflection and Empowerment.
Are Girls Underprivileged Around the World? 
Gila Hanna: Girls and Boys About Equal in Mathematics Achievement in Eighth Grade: Results From Twenty Countries
Erika Kuendiger: Mathematics-A Male Subject?!
Frank J. Swetz: Cross-Cultural Insights Into the Question of Male Superiority in Mathematics: Some Malaysian Findings
Societal Determinants of Learning
Joan Bliss, Ruffina Guttierez, Vasilios Koulaidis, Jon Ogbom, and Haralambos N. Sakonidis: A Cross-Cultural Study of Children’s Ideas About What is ReaZly True in Four Curricula Subjects: Science, Religion, History, and Mathematics 
Gustav Adolf Liircher: Learning Mathematics in a Foreign Language
Ali Rejali: Lack of Interest of Students for Studying Mathematics 
Bemd Zimmermann: Mathematics for All and Teaching the Gifted
The Social Arena of the Mathematics Classroom
Josette Adda: The Mathematics Classroom as a Microsociety
Tom Cooper: Negative Power, Hegemony, and the Primary Mathematics Classroom: A Summary
Andrea L. Petitto: The Structure of Mathematical Discourse Among Teachers and Children in Elementary School .
Terry Wood: Whole-Class Interaction as the Negotiation of Social Contexts Within Which to Construct Mathematical Knowledge
Learning Under Difficult Conditions 
Marilyn Frankenstein and Arthur B. Powell: Mathematics Education and Society: Empowering Non-Traditional Students 
FranCoise Cerquetti-Aberkane: Teaching Mathematics in Special Classes for Children With Serious Difficulties in France.
Nick Taylor: “Let Them Eat Cake”-Desire, Cognition, and Culture in Mathematics Learning.. . Mathematics Education in Multi-Cultural Contexts 
Raymond A. Zepp: New Direction in Research on Language in Mathematics 
Ina Kurth: Learning Mathematics in a Foreign Language
Helen Watson: Mathematics Education From a Bicultural Point of View
Norma C. Presmeg: Mathematics Education and Cultural Continuity
Ethnomathematical Practices.
Salimata Doumbia: Mathematics in Traditional African Games
Sergio Roberto Nobre: The Ethnomathematics of the Most Popular Lottery in Brazil: The “Animal Lottery” .
Nigel Langdon: Cultural Starting Points
Social Construction of Mathematical Meaning
Paul Cobb: Children’s Construction of Arithmetical Knowledge in Social Context 
Ema Yackel: The Negotiation of Social Context for Small-Group Problem Solving in Mathematics 
Stieg Mellin-Olsen: Creative Uses of Mathematics in Social Contexts
Jean-Franeois Perret: The Meaning of Mathematical Tasks for Pupils and Teachers 
Jan Waszkiewicz and Agnieszka Wojciechowska: The Future Cultural Role of Mathematics and its Impact on Math Education
Mathematics Education in the Global Village.
Hearing I: Which and Whose Interests are Served by Mathematics Education?
Hearing 2: How Does Mathematics Education Relate to Destructive Technological Developments?
Hearing 3: Do Mathematics Educators Know What they are Doing?
Hearing 4: What are the Challenges for ICMI in the Next Decade? 
Hearing 5: What can we Expect From Ethnomathematics?

The teaching of statistics

Robert W. Morris

International Conference on Teaching Statistics, n.º 2
Studies in mathematics education. vol. 7.

UNESCO | 1989 | 258 páginas

online: unesdoc.unesco.org

Descrição: This volume examines the teaching of statistics in the whole range of education, but concentrates on primary and secondary schools. It is based upon selected topics from the Second International Congress on Teaching Statistics (ICOTS 2), convened in Canada in August 1986. The contents of this volume divide broadly into four parts: statistics in primary education; statistics in secondary education; theoretical concepts; and two case studies. Part 1 comprises four contributions, three of them based on discovery. The fourth is a comparative study of what is currently taught to children in the age range of 5 to 11 years in Canada, the United Kingdom, and the United States. Part 2 provides an account of recent developments in the teaching of statistics in Australia, the Federal Republic of Germany, the Netherlands, and the United States. Part 3 of the volume is a collection of four contributions for the consideration of teachers in the collection and representation of data. Two case studies make up Part 4. The first describes the competition for the annual statistics prize in the United Kingdom and the second is a wide-ranging account of the growth of the teaching of probability and statistics in Italian schools. There is also a personal view by Ed Jacobsen called "Why in the World Should We Teach Statistics?" and a history of the teaching of statistics by Maria Gabriella Ottaviani, devoted to the growth of statistics in the universities of Europe and the Americas