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For other books about mathematics and mathematics education try: http://livros-matema.blogspot.com/.

quarta-feira, 16 de abril de 2014

Mathematics and Measurement

 Oswald Ashton Wentworth Dilke

University of California Press | 1987 | 66 páginas

online: google books

pdf - 9,27 Mb - link

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This fully illustrated book outlines the ancient systems of mathematics and measurement and describes how they were used in mapping, surveying, telling time, trade and commerce, as well as in leisure pursuits such as games and puzzles, and in the occult.

Contents
The Background 
2 Numbering by Letters 
1 Mathematical Education in the Greek World 
4. Measurement
5 Mathematics (or the Surveyor and Architect)
6 Mapping and the Concept of Scale 
7 Telling the Time
8. Calculatioos for Trade and Commerce
9. Mathematics in Leisure Pursuits and the Occult 
10 The Sequel 
Bibliography 62
Index 

quinta-feira, 10 de abril de 2014

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

Thomas Little Heath

Cambridge, University press | 1985 | 298 páginas

online: ualberta.ca
archive.org
hathitrust.org
forgottenbooks.org

pdf - link (google books)

The Greek mathematician Diophantos of Alexandria lived during the third century CE. Apart from his age (he reached eighty-four), very little else is known about his life. Even the exact form of his name is uncertain, and only a few incomplete manuscripts of his greatest work, Arithmetica, have survived. In this impressive scholarly investigation, first published in 1885, Thomas Little Heath (1861-1940) meticulously presents what can be gleaned from Greek, Latin and Arabic sources, and guides the reader through the algebraist's idiosyncratic style of mathematics, discussing his notation and originality. This was the first thorough survey of Diophantos' work to appear in English. Also reissued in this series are Heath's two-volume History of Greek Mathematics, his treatment of Greek astronomy through the work of Aristarchus of Samos, and his edition in modern notation of the Treatise on Conic Sections by Apollonius of Perga.

domingo, 6 de abril de 2014

Soviet studies in the psychology of learning and teaching mathematics - Volumes 7 - 14


This is one of a series that is a collection of translations from the extensive Soviet literature of the past 25 years on research in the psychology of mathematics instruction. It also includes works on methods of teaching mathematics directly influenced by the psychological research. Selected papers and books considered to be of value to the American mathematics educator have been translated from the Russian and appear in this series for the first time in English. The aim of this series is to acquaint mathematics educators and teachers with directions, ideas, and accomplishments in the psychology of mathematical instruction in the Soviet Union. 

Volume VII - Children's Capacity for Learning Mathematics
Steffe, Leslie P., Ed.; And Others 
1975 | 276 páginas | pdf 
online: ERIC

The work of El'konin, Davydov, and Minskaya reported in this volume represents a start toward the alleviation of the lack of theory-based experimental investigations of mathematics learning and teaching. 
TABLE OF CONTENTS
Introduction, Leslie Steffe
Learning Capacity and Age Level, D. B. El'konin and V. V..Davydov
Primary Schoolchildren's Intellectual Capabilities and the Content of Instruction, D. B. El'konin
Logical and Psychological Problems of Elementary Mathematics as an Academic Subject, V. V. Davydov
The Psychological Characteristics of the "Prenumerical" Period of Mathematics Instruction, V. V. Davydov 
Developing the Concept of Number by Means of the Relationship of Quantities, G. I. Minskaya 

Volume VIII - Methods of Teaching Mathematics
Steffe, Leslie P., Ed.; And Others 
1975 | 290 páginas | pdf 
online: ERIC

This volume contains four articles: Principles, Forms, and Methods of Mathematics Instruction; ; ; and Independent Work for Pupils in Arithmetic Lessons in the Early Grades
TABLE OF CONTENTS 
Introduction, Leslie  P. Steffe
Principles, Forms, and Methods of Mathematics Instruction, I. A. Gibsh 
The Relation Between Mathematics Instruction and Life, G. G. Maslova and. A. D. Semushin 
The Pupil's Activity as a Necessary Condition for Improving the Quality of Instruction, I. A. Gibsh 
Independent Work for Pupils in Arithmetic Lessons in the Early Grades, M. I. More

Volume IX - Problem Solving Processes of Mentally Retarded Children
Clarkson, Sandra P., Ed.; And Others
1975 | 184 páginas | pdf
online: ERIC

The articles in this volume are concerned with the instruction in problem solving of mentally retarded pupils in the auxiliary schools of the Soviet Union. Both articles in this volume describe research in problem solving and also provide concrete suggestions for improving instruction. The literature reviews contained in these articles provide us with much information on the state of research in the Soviet Union on problem solving in mathematics.
TABLE OF CONTENTS
The Solution of Complex Arithmetic Problems in Auxiliary School, K. A. Mikhal'skii 
Basic Difficulties Encountered in Auxiliary School Pupils in Solving Arithmetic Problems, M. I. Ku'mitskaya 

Volume X - Teaching Mathematics to Mentally Retarded Children
Clarkson, Sandra P., Ed.; And Others
1975 | 184 páginas | pdf
online: ERIC

The articles in this volume deal with the instruction in geometry and arithmetic of mentally retarded pupils in the Soviet Union. These pupils attend special schools, called auxiliary schools, where they are trained in content that can later be related to specific job skills. Authors of the articles have attempted to identify the specific knowledge that the pupils possess and to design more effective instructional methods for increasing that knowledge. 
TABLE OF CONTENTS
Introduction
Instructing Auxiliary School Pupils in Visual Geometry, P. G. Tishini
Visual.and Verbal Means in Pregaratory Exercises in Teaching Arithmetic Problem Solving, N. F. Kuimina-Syromyatnikova
Some Features of Elementary Arithmetic Instruction for Auxiliary School Pupils, T. V. Khanutina 

Volume XI - Analysis and Synthesis as Problem Solving Methods
Kantowski, Mary Grace, Ed.; And Others
1975 | 186 páginas | pdf
online: ERIC

This volume differs from the others in the series in that the entire volume records the search for a method of problem-solving instruction based on the analytic-synthetic nature of the problem-solving process. In this work, Kalmykova traces the history of the use of the analytic and synthetic methods in her country, explores elementary classroom situations involving teachers who had various degrees of success in problem-solving instruction, makes hypotheses regarding the use of certain techniques, and concludes with suggestions for "productive" methods to be used in the classroom
TABLE OF CONTENTS
Introduction, Mary C. Kantowski
Chapter I. Overview
Chapter II. Substantiation of the Problem of Analysis end Synthesis
Chapter III. Experimental Investigations of the Use of the Method of Analysis in School 
Chapter IV. Experimental Investigations of Analysis as a Method of Searching for a Solution
Chapter V. Productive Method of Analysis and Synthesis

Volume XII - Problems of Instruction
Wilson, James W., Ed.; And Others
1975 | 185 páginas | pdf
online: ERIC

The seven studies found in this volume are: ;; ;;; ; and Psychological Characteristics of Pupils' Assimilation of the Concept of a Function.
TABLE OF CONTENTS
Introduction
An Experiment in the Psychological Analysis of Algebraic Errors, P. A. Shevarev
Pupils' Comprehension of Geometric Proofs, F. N. Gonoboldn
Elements of the Historical Approach in Teaching Mathematics, I. N. Shevchenko
Overcoming Students' Errors in the Independent Solution of Arithmetic Problems, 0. T. Yochkovskaya
Stimulating Student Activity in the Study of Functional Relationships, Yu. I. Goldberg
Psychological Grounds for Extensive Use of Unsolvable Problems, Ya.  I.  Grudenov
Psychological Characteristics of Pupils' Assimilation of the Concept of a Function, I. A. Marnyanskii

Volume XIII - Analysis of Reasoning Processes
Wilson, James W., Ed.; And Others
1975 | 244 páginas | pdf
online: ERIC

The analysis of reasoning processes in the learning of concepts or the solving of problems is the theme common to the ten articles in this volume. These articles, except for the first one by Ushakova, were published between 1960 and 1967 and were part of the available literature during a revision of the Soviet school mathematics curriculum. The articles are interesting because of the topics they treat and because of the research styles they illustrate
TABLE OF CONTENTS
Introduction, James Wilson and Jeremy Kilpatrick
The Role of Comparison in-the Formation of Concepts do by Third-Grade Pupils,  M. N. Ushakova
On the Formation of an Elementary Concept of Number by the Child, V. V. Davydov
The Generalized Conception in Problem Solving, A. V. Brushlinskii
An Analysis of the Process of Solving Simple Arithmetic Problem, G. P. Shchedrovitskii and S. G. Yak'obson 
An Attempt at an Experimental Investigation of Psychological Regularity in Learning, B. B. Kopov
The Formation of Generalized Operations as a Method for Preparing Pupils to Solve Geometry Problems Independently, E. I. Mashbits
An Experimental Investigation of Problem Solving and Modeling the Thought Processes, D. N.Zavalishin and V. N. Pushkin 
The Composition of Pupils' Geometry Skills, A. K. Artemov
On the Process of Searching for an Unknown-While Solving a Mental Problem,  A. V. Brushlinskii
The Mechanisms of Solving Arithmetic Problems, L. M. Fridman

Volume XIV - Teaching Arithmetic in the Elementary School
Hooten, Joseph R., Ed.; And Others
1975 | 214 páginas | pdf
online: ERIC

The six chapter titles are: 
The Psychological and Didactic Principles of Teaching Arithmetic
The Introduction of Numbers, Counting, and the Arithmetical Operations;
Instruction in Mental and Written Calculation; Teaching Problem Solving; 
Geometry in the Primary Grades; 
Different Kinds of Pupils and How to Approach Them in Arithmetic Instruction.

quarta-feira, 2 de abril de 2014

Research on mathematical thinking of young children : six empirical studies

Leslie P. Steffe 

 National Council of Teachers of Mathematics | 1975 | 207 páginas | pdf | 3,2 Mb

online: ERIC

Para outros livros relacionados procure em: link

This volume includes reports of six studies of the thought processes of children aged four through eight. In the first paper Steffe and Smock outline a model for learning and teaching mathematics. Six reports on empirical studies are then presented in five areas of mathematics learning: (1) equivalence and order relations; (2) classification and seriation; (3) interdependence of classification, seriation, and number concepts; (4) Boolean Algebra; and (5) conservation and measurement. In a final chapter, the main findings of these papers are summarized and implications are discussed, with suggestions for further research.

Table of Contents
Introduction, Leslie P. Sleffe 1
I.On a Model for Learning and Teaching Mathematics, Leslie P. Sleffe and Charles D. Smock 4
II.Learning of Equivalence and Order Relations by Four- and Five-Year-Old Children, Leslie P. Sleffe and Russell L. Carey,19
III.Learning of Equivalence and Order Relations byDisadvantaged Five- and Six-Year-Old Children, Douglas T. Owens 47
IV.Learning of Classification and Seriation by Young Children, R Marlin L. Johnson 73
V.The Generalization of Piagetian Operations as It Relates to the Hypothesized Functional Interdependence between Classification, Seriation, and Number Concepts, Richard A. Lesh 94
VI.Learning of Selected Parts of a Boolean Algebra by Young Children, David C. Johnson 123
VII.The Performance of Mist- and Second -Grade Children on Liquid Conservation and Measurement Problems Employing Equivalence and Order Relations, Thomas P. Carpenter 145
Summary and Implications, Kennelh Lovell 171
References 191

sábado, 29 de março de 2014

A history of astronomy

Walter William Bryant

London Methuen 1907


online: archive.org


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A History of Astronomy, first published in 1907, offers a comprehensive introduction to the steady development of the science since its inception in the ancient world up to the momentous progress of the nineteenth century. It includes biographical material relating to the most famous names in the study of astronomy – Copernicus, Galileo, Newton, Herschel – and their contributions, clear and accessible discussions of key discoveries, as well as detailing the incremental steps in technology with which many of the turning points in astronomy were intimately bound up.

CONTENTS
CHAP. PAGE
I. EARLY NOTIONS
II. THE EASTERN NATIONS OF ANTIQUITY 8
III. THE GREEKS 14
IV. THE ARABS 25
V. THE REVIVAL-COPERNICUS-TYCHO BRAHE 28
VI. KEPLER-GALl LEO 39
'VII. NEWTON 47
VIII. NEWTON'S SUCCESSORS: LAPLACE 53
IX. FLAMSTEED-HALLEy-BRADLEy-HERSCHEL 63
X. THE EARLY NINETEENTH CENTURy-NEPTUNE 73
XI. HERSCHEL-BESSEL-STRUVE • 83
XII. COMETS • 96
XIII. THE SUN-EcLIPSES-PARALLAX 103
XIV. GENERAL ASTRONOMY AND CELESTIAL MECHANICS 118
XV. OBSERVATORIES AND INSTRUMENTS • 132
XVI. ADJUSTMENT OF OBSERVATIONS. PERSONAL ERRORS 141
XVII. THE SUN 146
XVIII. SOLAR SPECTROSCOPY 159
XIX. SOLAR ECLIPSES-SPECTROSCOPY 169
XX. THE MOON 183
XXI. THE EARTH 192
XXII. THE INTERIOR PLANETS 201
XXIII. MARS 209
XXIV. MINOR PLANETS 219
XXV. THE MAJOR PLANETS 226
XXVI. THE SOLAR SYSTEM • 24I
XXVII. COMETS, METEORS, ZODIACAL LIGHT 247
XXVIII. THE STARS-CATALOGUES-PROPER MOTION-PARALLAX-MAGNITUDE 27I
XXIX. DOUBLE STARS 292
XXX. VARIABLE STARS 303
XXXI. CLUSTERS-NEBULIE-MILKY WAY. 318
XXXII. STELLAR SPECTROSCOPY 327
XXXIII. CONCLUSION • 340

terça-feira, 25 de março de 2014

Selected lectures from the Seventh International Congress on Mathematical Education


ICME-7    1992      Québec (Canada) 

David E Robitaille, David H. Wheeler, Carolyn Kieran


Presses de l'Universite Laval | 1994 | 380 páginas | 
pdf (OCR) | 16,3 Mb

link

pdf (no OCR) | 35,1 Mb
online:  mathematik.uni-bielefeld.de

djvu (OCR) | 19 Mb
online: mathematik.uni-bielefeld.de

Contents
Preface p. IX Contribution de l'apprentissage de la géométrie à la formation scientifique - Gérard Audibert p. 1 Diagnostic Teaching - Alan Bell p. 19 Reading, Writing and Mathematics: Rethinking -Raffaella Borasi and Marjorie Siegel p. 35 Teachers Using Videotapes as Reference Points -John L. Clark p. 49 The Transition to Secondary School Mathematics -David Clarke p. 59 Mathematicians and Mathematical Education -Michael P. Closs p. 77 Les mathématiques comme reflet d'une culture -Jean Dhombres p. 89 Imagery and Reasoning in Mathematics and Mathematics Education - Tommy Dreyfus p. 107 Interweaving Numbers, Shapes, Statistics, and the Real World in Primary School and Primary Teacher Education - Andrejs Dunkels p. 123 Teaching Mathematics and Problem Solving to Deaf and Hard-of-Hearing Students - Harvey Goodstein p. 137 The Origin and Evolution of Mathematical Theories- Miguel de Guzmàn p. 147 Le calcul infinitésimal - Bernard R. Hodgson p. 157 Computer-Based Microworlds: a Radical Vision or a Trojan Mouse? - Celia Hoyles p. 171 Different Ways of Knowing: Contrasting Styles of Argument in India and the West - George Gheverghese Joseph p. 183 Mathematics Education in the Global Village : the Wedge and the Filter - Murad Jurdak p. 199 Bonuses of Understanding Mathematical Understanding - Thomas E. Kieren p. 211 Curriculum Change: An American-Dutch Perspective - Jan de Lange p. 229 Training Teachers or Educating Professionals? What are the Issues and How Are They Being Resolved? - Glenda Lappan and Sarah Theule-Lubienski p. 249 What is Discrete Mathematics and How Should We Teach It? - Jacobus H. van Lint p. 263 Intuition and Logic in Mathematics - Michael Otte p. 271 Vers une construction réaliste des nombres rationnels - Nicolas Rouche p. 285 Mathematics is a Language - Fritz Schweiger p. 297 Mathematical Thinking and Reasoning for All Students - Moving from Rhetoric to Reality - Edward A. Silver p. 311 Humanistic and Utilitarian Aspects of Mathematics - Thomas Tymoczko p. 327 From "Mathematics for Some" to "Mathematics for All" - Zalman Usiskin p. 341 On the Appreciation of Theorems by Students and Teachers - Hans-Joachim Vollrath p. 353 Geometry as an Element of Culture - Alexandr D. Alexandrov p. 365 


segunda-feira, 24 de março de 2014

Proceedings of the Seventh International Congress on Mathematical Education


ICME-7    1992      Québec (Canada)

Claude Gaulin, Bernard R. Hodgson, David H. Wheeler, John C. Egsgard

Les Presses de l'Universite Laval | 1994 | 529 páginas | pdf (OCR) |33,4  Mb

link

pdf - 496,6 Mb (no OCR) 
link direto: mathematik.uni-bielefeld.de

djvu - 50,7 Mb (OCR)
link direto:  mathematik.uni-bielefeld.de

Contents 
Preface p. XIII 
Codes of countries p. XXI 
Schedule p. XXIV 


PRESIDENTIAL ADDRESS1
Plenary Lectures 
Teachers of Mathematics - Geoffrey Howson p. 9 
Bringing Mathematical Research to Life in the Schools - Maria M. Klawe p. 27 
Enseigner la géométrie: permanences et révolutions - Colette Laborde p. 47 
Fractals, the Computer, and Mathematics Education - Benoit B. Mandelbrot p. 77 


Working Groups 
WG 1: La formation de concepts mathématiques élémentaires au primaire (Helen Mansfield, AUS) p. 101 
WG 2: Students' Misconceptions and Inconsistencies of Thought (Shlomo Vinner, ISR) p. 109 
WG 3: Students' Difficulties in Calculus (Michèle Artigue, FRA) p. 114 
WG 4: Theories of Learning Mathematics (Pearla Nesher, ISR) p. 120 
WG 5: Improving Students' Attitudes and Motivation (Gilah Leder, AUS) p. 128 
WG 6: Preservice and Inservice Teacher Education (John Dossey, USA) p. 134 
WG 7: Language and Communication in the Mathematics Classroom (Heinz Steinbring) 
WG 8: Innovative Assessment of Students in the Mathematics (Jùlianna Szendrei, HUN) 
WG 9: [Not listed] 
WG 10: Multicultural and Multilingual Classrooms (Patrick Scott, USA) p. 154 
WG 11: The Role of Geometry in General Education (Rina Hershkowitz, ISR) p. 160 
WG 12: Probability and Statistics for the Future Citizen (Mary Rouncefield, GBR) p. 168 
WG 13: The Place of Algebra in Secondary and Tertiary Education (Carolyn Kieran, CAN) 
WG 14: Mathematical Modelling in the Classroom (Trygve Breitag, NOR) p. 180 
WG 15: Undergraduate Mathematics for Different Groups of Students (Daniel Alibert, FRA) 
WG 16: The Impact of the Calculator on the Elementary School (Hilary Shuard †, GBR) 
WG 17: Technology in the Service of the Mathematics Curriculum (Klaus-D. Graf, GER)  
WG 18: Methods of Implementing Curriculum Change (Hugh Burkhard, GBR) p. 202 
WG 19: Early School Leavers (Carlos Vasco, COL) p. 205 
WG 20: Mathematics in Distance Learning (Gordon Knight, NZL) p. 211 
WG 21: The Public Image of Mathematics and Mathematicians (Thomas Cooney, USA)
WG 22: Mathematics Education with Reduced Resources (Elfriede Wenzelburger †, MEX)
WG 23: Methodologies in Research in Mathematics Education (Norbert Knoche, GER)


Topic Groups 
TG 1: Mathematical Competitions (Edward J. Barbeau) p. 239 
TG 2: Ethnomathematics and Mathematics Education (Ubiratan D'Ambrosio, BRA) p. 242 
TG 3: Mathematics for Work: Vocational Education (Rudolf Straesser, GER) p. 244 
TG 4: Indigenous Peoples and Mathematics Education (Bill Barton, NZL) p. 247 
TG 5: The Social Context of Mathematics Education (Alan J. Bishop) p. 250 
TG 6: The Theory of Practice and Proof (Gila Hanna, CAN) p. 253 
TG 7: Mathematical Games and Puzzles (Tibor Szentivanyi, HUN) p. 257 
TG 8: Teaching Mathematics through Project Work (Jarkko Leino, FIN) p. 260 
TG 9: Mathematics in the Context of the Total Curriculum (John Mack, AUS) p. 264 
TG 10: Constructivist Interpretations of Teaching and Learning Mathematics (John A. Malone and Peter S. Taylor, AUS) p. 268 
TG 11: Art and Mathematics (Rafael Pérez Gòmez, ESP) p. 272 
TG 12: Graduate Programs and the Formation of Researchers in Mathematics Education (Hans-Georg Steiner, DEU) p. 274 
TG 13: Television in the Mathematics Classroom (David Roseveare, GBR) p. 278 
TG 14: Cooperation between Theory and Practice in Mathematics Education (Falk Seeger, DEU) p. 282 
TG 15: Statistics in the School and College Curriculum (Richard Schaeffer, USA) p. 286 
TG 16: The Philosophy of Mathematics Education (Paul Ernest, GBR) p. 289 
TG 17: La documentation professionnelle des enseignants de mathématiques (Jeanne Bolon, FRA) p. 293 

Study Groups 
HPM: An Historical Perspective on Learning, Teaching and Using Mathematics p. 299 
IOWME: Gender and Mathematics Education p. 304 
PME: Report of Activities p. 310 
ICMI Studies 
S1: The Influence of Computers and Informatics on Mathematics and its Teaching p. 315 
S2: The Popularization of Mathematics p. 319 
S3: Assessment in Mathematics Education and its Effects p. 323 

Miniconference on Calculators and Computers p. 331 

Abstracts of Lectures p. 341-382 
[contains the abstracts of the Selected Lectures of the second volume and the abstracts of the lectures by following authors: Philip J. Davis, Jean-Marc Deshouillers, Joaquin Giménez, Fred Goffree, Ronald L. Graham, Magdalene Lampert, Ronald Lancaster, Fernand Lemay, Charles Lovitt, , Seymour Papert, Nancy Shelley, Uri Treisman, Marion Walter

Short Presentations and Round Tables p. 385 
Projects and Workshops p. 389 
Special Exhibitions and Math Trail p. 399 
National Presentations p. 407 


Special Sessions 
Probe p. 413 
Crossfire: Mathematical Competitions - Do the Benefits Outweigh the Disadvantages? p. 417 
Awarding of Honorary Degrees to Jean-Pierre Kahane and Henry Pollak p. 421 
Tribute to H.S.M. Coxeter p. 423 
A Celebration in Memory of Caleb Gattegno p. 425 
Films and Videos p. 429 
Special Meetings p. 433 

Secretary's Closing Remarks - Mogens Niss p. 437 
Committees and Sponsors p. 451 
List of Participants p. 463 
Distribution by Country p. 494