The Ambitious Horse - Ancient Chinese Mathematics Problems

Lawrence Swienciki

Key Curriculum | 2000 | 135 páginas | pdf | 7,94 Mb

online: math.utep.edu


pdf (OCR) - 5,72 Mb - link

• Numbers and Arithmetic includes subjects such as Chinese writing; The Calculating Rods of Ancient China: and ancient Chinese multiplication.

• Geometry and Dissection problems includes subjects such as tangrams, the Measure of Heaven and Ancient Chinese Philosophy.

• Algebra Integrated with Geometry includes subjects such as Square Roots; Quadratic Equations; and mathematical treats such as the "Pillar of Delightful Contemplation", the "Exalted Treasure of Jade" and the "Precious Golden Rope".

On the one hand this book is far beyond what many 7th and 8th grader students are capable of. On the other hand, it is so interesting and so well done that it might just be that this is the book that helps transforms your child from a grudging math student to an enthusiastic one!

Filled with stories, puzzles and plenty of hands-on problems, this book is a treasure. It is divided into three sections:

Answers and solutions included.

Note: The problems get more difficult as the book progresses and so can be used for several years. Suitable for a very math-able 7th grader, a solid 8th grader and to enthuse and inspire high school students

Tricks, Games, and Puzzles With Matches

Maxey Brooke

Dover Pubns | 1973 | 64 páginas | pdf | 267 kb

online: arvindguptatoys.com

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With a handful of matches you can challenge yourself and your friends to match hundreds of match tricks, games and puzzles. The quipment is simple and can easily be carried with you. The tricks, games and puzzles range from the simple to the advanced. No matter how many match tricks and puzzles you have previously done you are sure to find new twists, new challenges in the puzzles in this collection.
There are classic match problems, problems by foremost puzzlers, and a number of Makey Brooke's own creations. There is match-arithmetic, where you are required to balance equations by removing or adding matches, including a few that require advanced mathematical notation. There are match spellings, match story games, tricks that involve kitchen matches, paper match books and match boxes, and simple mathematical games you can play with matches. A rich selection of match constructions, in which you are required to build, unbuild, or reconstruct squares and other geometrical units by simply moving matches, is made even richer by the inclusion of a special selection from T.R. Dawson's works. The solutions section gives complete information for solving the puzzles plus material on winning games and working the tricks.

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 

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.

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.

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

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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

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

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

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online:  mathematik.uni-bielefeld.de

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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 

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) 
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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 

Proceedings of the Sixth International Congress on Mathematical Education

ICME-6    1988      Budapest (Hungary) 

Ann & Keith Hirst

Janos Bolyai Mathematical Society | 398 páginas 

pdf (no OCR) | 38 Mb
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djvu (OCR)| 21,6 Mb
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The contributions to the Fifth Day Special were published in C. Keitel, A. Bishop, P. Damerow & P. Gerdes (Eds.) Mathematics, Education, and Society. Paris, UNESCO, Science and Technology Education, Document Series, 1989. 

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Contents
Foreword (p. 5) 
Plenary Presentations B. Nebres: School Mathematics in the 1990's: the Challenge of Change especially for Developing Countries (p. 11) G. Vergnaud: Theoretical Frameworks and Empirical Facts in the Psychology of Mathematics Educationn (p. 29) A. Ershov: Computerization of Schools and Mathematical Education (p. 49) L. Lovász: Algorithmic Mathematics: An Old Aspect with a New Emphasis (p. 67) J. - P. Kahane: La Grande Figure de Georges Polya (p. 79) 
Action Groups A1. L. P. Steffe: Early Childhood Years (Ages 4 - 8) (p. 101) A2. A. C. J. Colomb: Elementary School (Ages 7-12) (p. 117) A3. I. Hirabayashi: Junior Secondary School (Ages 11-16) (p. 133) A4. J. Da Lange: Senior Secondary School (Ages 15-19) (p. 143) A5. J. Mack: Tertiary (Post-Secondary) academic institutions (ages 18+) (p. 159) A6. W. Dörfler: Pre-Service Teacher Education (p. 177) A7. R. Strässer: Adult, Technical and Vocational Education (p. 191) 
Theme Groups T1. P. A. House: The Profession of Teaching (p. 205) T2. R. Fraser: Computers and the Teaching of Mathematics (p. 215) T3. M. Niss: Problem Solving, Modelling and Applications (p. 237) T4. D. F. Robitaille: Evaluation and Assessment (p. 253) T5. N. Balacheff: The Practice of Teaching and Research in Didactics (p. 263) T6. W. Blum: Mathematics and Other Subjects (p. 277) T7. H. Burkhardt, J. A. Malone: Curriculum Towards the Year 2000 (p. 293) 
Fifth Day Special: MES A. Bishop, P. Damerow, P. Gerdes, Ch. Keitel: Mathematics, Education, Society (p. 311) 

Topic Areas and International Study Groups 

To1. M. Emmer: Video, Film (p. 329) 
To2. I. Lénárt: Visualization (p. 332) 
To3. G. Berzsenyi: Competitions (p. 334) 
To4. E. Csocsán: Problems of Handicapped Students (p. 339) 
To5. D. A. Quadling: Comparative Education (p. 342) 
To6. K. J. Travers: Probability Theory and Statistics (p. 346) 
To7. D. Pimm: Proofs, Justification and Conviction (p. 350) 
To8. C. Laborde: Language and Mathematics (p. 354) 
To9. [NOT LISTED] 
To10. P. S. Kenderov: Students of High Ability (p. 358) 
To11. D. Singmaster: Mathematical Games and Recreation (p. 361) 
To12. [NOT LISTED] 
To13. L. Burton: Women and Mathematics (p. 365) 
To14. [NOT LISTED] 
To15. H.-G. Steiner: Theory of Mathematics Education (p. 371) 
To16. W. R. Bloom: Spaces and Geometry (p. 375) 
To17. G. König: Information and Documentation (p. 379) 
To18. B. Christiansen, P. F. L. Verstappen: Systematic Cooperation between Theory and Practice in Mathematics Education (p. 382) 
HPM. U. D'Ambrosio: History and Pedagogy of Mathematics (p. 389) 
Projects (p. 393) 
ICMI 
A. G. Howson: The International Commission on Mathematical Instruction (p. 395) 
Projects (p. 393) 
ICMI 
A. G. Howson: The International Commission on Mathematical Instruction (p. 395) 

Proceedings of the Fourth International Congress on Mathematical Education

Marilyn Zweng, Thomas Green, Jeremy Kilpatrick, Henry Pollak, Marilyn Suydam

ICME-4    1980      Berkeley (USA)

Birkhäuser Boston | 1983 | 739 páginas | pdf 

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TABLE OF CONTENTS
CHAPTER I - Plenary Session Addresses
1.1 Mathematics Improves the Mind
George Polya
1.2 Major Problems of Mathematics Education
Hans Freudenthal
1.3 Young Children's Acquisition of Language and Understanding of Mathematics
Hermina Sinclair
1.4 Reactions to Hermina Sinclair's Plenary Lecture 13
Bill Higginson
Some Experiences in Popularizing Mathematical Methods
Hua Loo-keng
Reactions to Hua Loo-keng's Plenary Lecture 23
Dorothy Bernstein, J.S. Gyakye Jackson
CHAPTER 2 - Universal Basic Education 27
2.1 Mathematics in General Primary Education
Romanus O. Ohuche
2.2 Back-to-Basics: Past, Present, Future
Max Sobel
2.3 Suggested Mathematics Curricula for Students Who Leave School at Early Ages
Shirley Frye, Alonso B. Viteri Garrido
CHAPTER 3 - Elementary Education  36
3.1 Roots of Failure in Primary School Arithmetic
Frederique Papy
3.2 Do We Still Need Fractions in the ELementary Curriculum?
Peter Hilton, Mary Laycock
CHAPTER 4 - Post-Secondary Education 44
4.1 Decline in Post-Secondary Students Continuing the Study of Mathematics
James T. Fey, R.R. McLone, Bienvenide F. Nebres
4.2 Is Calculus Essential? 50
Margaret E. Rayner, Fred Roberts
4.3 Mathematics and the Physical Science and Engineering
Gerhard Becker, Daniela Gori-Giorgi, Jean-Pierre Provost
4.4 Why We Must and How We Can Improve the Teaching of Post-Secondary Mathematics
Henry L. Alder, Detlef Laugwitz
4.5 Alternate Approaches to Beginning'the Teaching of Calculus and the Effectiveness of These Methods
George Papy, Daniel Reisz
4.6 In What Ways Have the Mathematical Preparation of Students for Post-Secondary Mathematics Courses Changed? 70
Kathleen Cross, S.M. Sharfuddin
4.7 Curriculum for A Mathematical Sciences Major
Alan Tucker
4.8 University Programs with an Industrial Problem Focus
Jerome Spanier, Germund Dahlquist, A.Clayton Aucoin, Willian E. Boyce, J.L. Agnew
CHAPTER 5 - The Profession of Teoching 89
5.1 Current Status and Trends in Teacher Education
David Alexander, Jeffrey Baxter, Sr. lluminada C. Coronel, f.m.m., Hilary Shuard
5.2 Integration of Content and Pedagogy in Pre-Service Teacher Education
Zbigniew Semadeni, Julian Weissglass
5.3 Preparation in Mathematics of a Prospective Elementary Teacher Today, in View of the Current Trends in Mathematics, in Schools, and in Society 100
James E. Schultz
5.4 Evaluation of Teachers and Their Teaching 102
Thomas J. Cooney, Edward C. Jacobsen
5.5 Hand-held Calculators and Teacher Education 107
Willy Vanhamme
5.6 Computers in Mathematics Teacher Education 109
Rosemary Fraser
5.7 The Mathematicol Preparation of Secondary Teachers - Content and Method
Trevor Fletcher
5.8 Special Assistance for the Beginning Teacher
Edith Biggs, Mervyn DlKlkley
5.9 The Making of a Professional Mathematics Teacher
Gerald Rising, Geoffry Howson
5.10 The Dilemma of Teachers Between Teaching What They Like and Teaching What the Pupils Need to Know: How Much Freedom Should Teachers Have to Add Materials, How Much Material, Which Teachers? 124
Andrew C. Porter
5.11 Integration of Mathematical and Pedagogical Content In-Service Teacher Education: Successful and Unsuccessful Attempts 126
David A. Sturgess, E. Glenodine Gibb
5.12 In-Service Educati on for Secondary Teachers 1 31
Martin Barner, Michel Darche, Richard Pallascio
5.13 Support Services for Teachers of Mathematics 1 40
Michael Silbert, Max Stephens
5.14 What is a Professional Teacher of Mathematics?
John C. Egsgard, Jacques Nimier, Leopoldo Varela
CHAPTER 6 - Geometry 153
6.1 Geometry in the Secondary School 153
Eric Gower, G. Holland, Jean Pederson, Julio Castineira Merino
6.2 Geometric Activities in the Elementary School
Koichi Abe. John Del Grande
6.3 The Death of Geometry at the Post-Secondary Level
Branko Grunbaum, Robert Osserman
6.4 The Development of Children's Spatial Ideas
Michael C. Mitchelmore, Dieter Lunkenbein, Kiyoshi Yokochi. Alan J. Bishop
CHAPTER 7 - Stochastics
7.1 Statistics: Probability: Computer Science: Mathematics. Many Phases of One Program?
Leo Klingen, Richard S. Pieters
7.2 Vigor, Variety and Vision - - the Vitality of Statistics and Probability
I.J. Good
7.3 The Place of Probability in the Curriculum
Ruma Falk, Tibor Nemetz
7.4 The Nature of Statistics to be Taught in Schools 198
Jim Swift, A.P. Shulte, Peter Holmes
7.5 Statistics and Probability in Teacher Education 202
Peter Holmes, Luis A. Santalo
CHAPTER 8 - Applications 207
8.1 Mathematics and the Biological Sciences -Implications for Teaching
Sam O. Ale, Diego Bricio Hernandez, Lilia del Riego
8.2 The Relationship of Mathematics and the Teaching of Mathematics with the Social Sciences
John Ling, Ivo W. Molenaar, Samuel Goldberg
8.3 Applications, Modeling and Teacher Education
Aristedes C. Barreto, Hugh Burkhardt

8.4 The Use of Modules to Introduce Applied Mathematics into the Curriculum
John Gaffney
8.5 Teaching Applications of Mathematics
F. van der Blij, Douglas A. Quadling, Paul C. Rosenbloom
8.6 The Interface between Mathematics and Imployment
Connie Knox, David R. Mathews, Rudolf Straesser, Robert Li ndsay, P.C. Price, Werner Blum
8.7 How Effective are Integrated Courses in Mathematics and Science for the Teaching of Mathematics?
Mogens Niss, Helmut Siemon
8.8 Materials Available Worldwide for Teaching Applications of Mathematics at the School Level
Max S. Bell
8.9 Mutualism in Pure and Applied Mathematics
Maynard Thompson, Donald Bushaw, Candido Sitia
CHAPTER  9 - Problem Solving 276
9.1 Teaching for Effective Problem Solving: A Challenging Problem
Shmuel Avital, Jose R. Pascual Ibarra, Ian Isaacs
9.2 Real Problem Solving 283
Diana Burkhardt
9.3 Mathematization, Its Nature and Its Use in Education
Eric Love, Marion Walter, David Wheeler
9.4 The Mathematization of Situations Outside Mathematics from an Educational Point of View
Rolf Biehler, Tatsuro Miwa, Christopher Ormell, Vern Treilibs
CHAPTER 10 - Special Mathematical Topics 299
10.1 Algebraic Coding Theory
J.H. van Lint
10.2 Combinatorics 303
Nicolas Balacheff, David Singmaster
10.3 The Impact of Algorithms on Mathematics Teaching 312
Arthur Engel
10.4 Operations Research 330
William F. Lucas
10.5 Maxima and Minima Without Calculus
A.J. Lohwater, Ivan Niven
10.6 Exploratory Data Analysis
Ram Gnanadesikan, Paul Tukey, Andrew F. Siegel, Jon R. Kettenring
CHAPTER 11- Mathematics Curriculum 358
11.1 Successes and Failures of Mathematics Curricula in the Past Two Decades
H. Brian Griffiths, Ubiratan D'Ambrosio, Stephen S. Willoughby
11.2 Curriculum Recommendations for the 1980's by Several National Committees
Mohammed EI Tom, W.H. Cockcroft, David F. Robitaille
11.3 Curriculum Changes During the 1980's
Shigeo Katagiri, Alan Osborne, Hans-Christian Reichel
11.4 The Changing Curriculum - An International Perspective
E.E. Oldham
11.5 Models of Curriculum Development 384
Tashio Miyamoto and Ko Gimbayasgu, James M. Moser
11.6 Mathematics for Secondary School Students
Harold C. Trimble
11.7 What Should be Dropped from the Secondary School Mathematics Curriculum to Make Room for New Topics?
Ping-tung Chong, Zolman Usiskin
11.8 Alternative Approaches to the Teaching of Algebra in the Secondary School
Harry S.J. Instone
11.9 How Can You Use History of Mathematics in Teaching Mathematics in Primary and Secondary Schools?
Cosey Humphreys, Bruce Meserve, Leo Rogers, Maassouma M. Kazim
CHAPTER 12 - The Begle Memorial Series on Research in Mathematics Education 405
12.1 Critical Variables in Mathematics Education
Richard E. Snow, Herbert J. Walberg, 12.2 Some Critical Variables Revisited
Christine Keitel-Kreidt, Donald J. Dessart, L. Roy Corry, Jens H. Lorenz, Nicholas A. Bronco
12.3 Some New Directions for Research in Mathematics Education
Richard E. Moyer, Edward A. Silver, Robert B. Davis, Gunnar Gjone, John P. Keeves, Thomas Cooney
CHAPTER 13 - Research in Mathematics Education 444
13.1 The Relevance of Philosophy and History of Science and Mathematics for Mathematical Education
Niels Jahnke, Rolando Chauqui, Giles Lachaud, David Pimm
13.2 Research in Mathematical Problem Solving 452
Gerald A. Goldin, Alan H. Schoenfeld
13.3 Researchable Questions Asked by Teachers 456
Elaine Bologna, Sadaaki Fujimori, Douglas E. Scott, Richard J. Shumway
13.4 Alternative Methodologies for Research in Mathematics Education
George Booker, Jack Easley, Francois Pluvinage, R.W. Scholz, Leslie P. Steffe, Joan Yates
13.5 Error Analyses of Childrens' Arithmetic Performance
Annie Bessot, Leroy C. Callahan, Roy Hollands, Fredricka Reisman
13.6 Comparative Study of the Development of Mathematical Education as a Professional Discipline in Different Countries 482
Gert Schubring, Mahdi Abdeljaauad, Phillip S. Jones, Janine Rogalski, Gert Shubring, Derek Woodrow, Vaclaw Zawadowski
13.7 The Development of Mathematical Abilities in Children
Jeremy Kilpatrick, Horacio Rimoldi, Raymond Sumner, Ruth Rees
13.8 The Child's Concept of Number
Karen Fuson, Shuntaro Sato, Claude Comiti, Tom Kieren, Gerhard Steiner
13.9 Relation Between Research on Mathematics Education and Research on Science Education. Problems ofCommon Interest and Future Cooperation 511
Charles Taylor, Anthony P. French, Robert Karplus, Gerard Vergnaud
13.10 Central Research Institutes for Mathematical Education. What Can They Contribute to the Development of the Discipline and the Interrelation between Theory and Practice? 
Edward Esty, Georges Glaeser, Heini Halberstam, Yoshihiko Hoshimoto, Thomas Romberg, Christine Keitel, B. Winkelman
13.11 The Functioning of Intelligence and the Understanding of Mathematics 530
Richard Lesh, Richard Skemp, Laurie Buxton, Nicholas Herscovics
13.12 The Young Adolescent's Understanding of Mathematics
Stanley Bezuska, Kath Hart
CHAPTER 14 - Assessment 546
14.1 Assessing Pupils' Performance in Mathematics 546
Norbert Knoche, Robert Lindsay, Ann McAloon
14.2 Issues, Methods and Results of National Mathematics Assessments
Bob Roberts
CHAPTER 15 - Competitions 557
15.1 Mathematical Competitions, Contests, Olympiads
Jan van de Croats, Neville Gale, Jose Ipina, Lucien Kieffer, Murray Klamkin, Peter J. O'Halloran, Peter R. Sanders, Janos Suranyi
15.2 Mathematics Competitions: Philosophy, Organization and Content
Albert Kalfus
CHAPTER 16 - Language and Mathematics 568
16.1 Language and the Teaching of Mathematics
A. Geoffrey Howson
16.2 The Relationship Between the Development of Language in Children and the Development of Mathematical Concepts in Children 573
F .D. Lowenthal, Michele Pellerey, Colette Laborde, Tsutomu Hosoi
16.3 Teaching Mathematics in a Second Language
Maurizio Gnere, Althea Young
CHAPTER 17 - Objectives 587
17.1 Teaching for Combined Process and Content Objectives
Alan W. Bell, A.J. Dawson, P.G. Human
17.2 The Complementary Role of Intuitive and Analytical Reasoning
Erich Wittmann, Efraim Fischbein, Leon A. Henkin
CHAPTER 18 - Technology 605
18.1 The Effect of the Use of Calculators on the Initial Development and Acquisition of Mathematical Concepts and Skills 605
Hartwig Meissner
18.2 A Mini-Course on Symbolic and Algebraic Computer Programming Systems
Richard J. Fateman
18.3 The Use of Programmable Calculators in the Teaching of Mathematics
Klaus-D. Graf, Guy Noel, K.A. Keil, H. Lothe
18.4 Perspectives and Experiences with Computer-Assisted Instruction in Mathematics
D. Alderman, R. Gunzehauser
18.5 Computer Literacy / Awareness in Schools; What, How and for Whom? 627
David C. Johnson, Claudette Vieules, Andrew Molnar
18.6 The Technological Revolution and Its Impact on Mathematics Education 632
Andrea DiSessa
18.7 Calculators in the Pre-Secondary School, Marilyn Suydam, A. Wynands
CHAPTER 19 - Forms and Modes of Instruction 641
19.1 Distance Education for School-age Children 641
David Roseveare
19.2 Teaching Mathematics in Mixed-Ability Groups 643
Denis C. Kennedy, David Lingard
19.3 Approaching Mathematics through the Arts 648
Emma Castel nuovo, Paul Delannoy, James R.C. Leitzel
19.4 The Use and Effectiveness of Mathematics Instructional Games
Margariete Montague Wheeler
19.5 Strategies for Improving Remediation Efforts
Ronald Davis, Deborah Hughes Hallett, Gerald Kulm, Joan R. Leitzel
19.6 Individualized Instruction and Programmed Instruction
F. Alvarada
CHAPTER 20 - Women and Mathematics 665
20.1 A Community Action Model to Increase the Participation of Girls and Young Women in Mathematics
Elizabeth Stage, Kay Gilliland. Nancy Kreinberg, Elizabeth Fennerna
20.2 Contributions by Women to Mathematics Education
Kristina Leeb-Lundberg
20.3 The Status of Women and Girls in Mathematics: Progress and Problems 674
Marjorie C. Carss, Eileen L Poiani, Nancy Shelley, Dora Helen Skypek
20.4 Special Problems of Women in Mathematics
Erika Schildkamp-Kundiger
CHAPTER 21 - Special Groups of Students 688
21.1 Curriculum Organizations and Teaching Modes That Successfully Provide for the Gifted Learner
A.L. Blakers, Isabelle P. Rucker, Burt A. Kaufman, Gerald Rising, Dorothy S. Strong, Arnold E. Ross, Graham T.Q. Hoare
21.2 Distance Education for Adults
Michael Crampin
21.3  Adult Numeracy - Programmes for Adults Not in School
Anna Jackson, Peter Kaner
21.4  Problems of Defining the Mathematics Curriculum in Rural Communities
Desmond Broomes, P.K. Kuperus
21.5 Participation of the Handicapped in Mathematics
Robert Dieschbourg, Carole Greenes, Esther Pillar Grossi