Famous geometrical theorems and problems, with their history

William Whitehead Rupert

Boston, D.C. Heath & Co. | 1900

online: 
archive.org
hathitrust.org
forgottenbooks.org

The author, having derived much pleasure and inspiration from the brief historical notes in some of the mathematical text-books that he studied when a student in college, has thought that, by giving the history of a few of the most celebrated geometrical theorems and problems, he might place a light in the window which may throw a cheerful ray adown the long and sometimes dusty pathway that leads to geometrical truth. In the preparation of this little book most valuable assistance has been derived from Florian Cajori sHistory of Mathematics, James Gows History of Greek Mathematics, and G, J. Allmans Greek Geometry from Thales to Euclid, It is, however, toW. W.Rourse Balls reniarkably interesting Short History of Mathematics that Famous Geometrical Theorems and Problems owes the largest debt. To Professor A, D. Eisenhower, Principal of the Norristown High School, George Q.Sheppard, Professor of Mathematics, Hill School, Pottstown, Pa., Dr. George M.Philips, Principal West Chester State Normal School, and Daniel Carhart, Ce., Dean and Professor of Civil Engineering, Western University of Pennsylvania, who have read this book in manuscript, the author is indebted for valuable, suggestions and many kind words of encouragement.

Second Handbook of Research on Mathematics Teaching and Learning

Frank K. Jr. Lester

Information Age Publishing | 2007 | 1381 páginas | rar - pdf | 11,4 Mb

link
password: matav

The audience remains much the same as for the 1992 Handbook, namely, mathematics education researchers and other scholars conducting work in mathematics education. This group includes college and university faculty, graduate students, investigators in research and development centers, and staff members at federal, state, and local agencies that conduct and use research within the discipline of mathematics.
The intent of the authors of this volume is to provide useful perspectives as well as pertinent information for conducting investigations that are informed by previous work. The Handbook should also be a useful textbook for graduate research seminars. In addition to the audience mentioned above, the present Handbook contains chapters that should be relevant to four other groups: teacher educators, curriculum developers, state and national policy makers, and test developers and others involved with assessment.

Taken as a whole, the chapters reflects the mathematics education research community's willingness to accept the challenge of helping the public understand what mathematics education research is all about and what the relevance of their research fi ndings might be for those outside their immediate community.
The intent of the authors of this volume is to provide useful perspectives as well as pertinent information for conducting investigations that are informed by previous work. The Handbook should also be a useful textbook for graduate research seminars. In addition to the audience mentioned above, the present Handbook contains chapters that should be relevant to four other groups: teacher educators, curriculum developers, state and national policy makers, and test developers and others involved with assessment.
Taken as a whole, the chapters reflects the mathematics education research community's willingness to accept the challenge of helping the public understand what mathematics education research is all about and what the relevance of their research fi ndings might be for those outside their immediate community.
Taken as a whole, the chapters reflects the mathematics education research community's willingness to accept the challenge of helping the public understand what mathematics education research is all about and what the relevance of their research fi ndings might be for those outside their immediate community. 

CONTENTS

Preface. 
Acknowledgements.
Part I: Foundations. 
Putting Philosophy to Work: Coping With Multiple Theoretical Perspectives, Paul Cobb.
Theory in Mathematics Education Scholarship, Edward A. Silver & Patricio G. Herbst
Method, Alan H. Schoenfeld. 
Part II: Teachers and Teaching. 
Assessing Teachers' Mathematical Knowledge: What Knowledge Matters and What Evidence Counts? Heather C. Hill, Laurie Sleep, Jennifer M. Lewis, & Deborah Loewenberg Ball. 
The Mathematical Education and Development of Teachers, Judith T. Sowder.
Understanding Teaching and Classroom Practice in Mathematics, Megan Loef Franke, Elham Kazemi and Daniel Battey. 
Mathematics Teachers' Beliefs and Affect, Randolph A. Philipp. 
Part III: Influences on Student Outcomes. 
How Curriculum Influences Student Learning, Mary Kay Stein, Janine Remillard and Margaret Smith. 
The Effects of Classroom Mathematics Teaching on Students' Learning, James S. Hiebert and Douglas A. Grouws. 
Culture, Race, Power, and Mathematics Education, Diversity in Mathematics Education Center for Learning and Teaching. 
The Role of Culture in Teaching and Learning Mathematics, Norma G. Presmeg. 
Part IV: Students and Learning. 
Early Childhood Mathematics Learning, Douglas H. Clements and Julie Sarama. 
Whole Number Concepts and Operations, Lieven Verschaffel, Brian Greer, and Erik DeCorte.
Rational Numbers and Proportional Reasoning: Toward a Theoretical Framework for Research, Susan J. Lamon. Early Algebra, David W. Carraher and Analucia D. Schliemann. 
Learning and Teaching of Algebra at the Middle School through College Levels: Building Meaning for Symbols and Their Manipulation, Carolyn Kieran. 
Problem Solving and Modeling, Richard Lesh and Judith Zawejewski. 
Toward Comprehensive Perspectives on the Learning and Teaching of Proof, Guershon Harel and Larry Sowder. 
The Development of Geometric and Spatial Thinking, Michael T. Battista. 
Research in Probability: Responding to Classroom Realities, Graham A. Jones, Cynthia W. Langrall and Edward S. Mooney. 
Research on Statistics Learning and Reasoning, J. Michael Shaughnessy. 
Mathematics Thinking and Learning at Post-secondary Level, Michele Artigue, Carmen Batanero and Phillip Kent. 
Part V: Assessment. 
Keeping Learning on Track: Classroom Assessment and the Regulation of Learning, Dylan Wiliam. 
High Stakes Testing in Mathematics, Linda Dager Wilson. 
Large-scale Assessment of Mathematics Education, Jan DeLange. 
Part VI: Issues and Perspectives. 
Issues in Access and Equity in Mathematics Education, Alan J. Bishop and Helen J. Forgasz. 
Research on Technology in Mathematics Education: The Perspective of Constructs, Rose Mary Zbiek, M. Kathleen Heid, Glendon Blume and Thomas P. Dick. 
Engineering Change in Mathematics Education: Research, Policy, and Practice, William F. Tate and Celia Rousseau. 
Educational Policy Research and Mathematics Education, Joan Ferrini-Mundy & Robert Floden. 
Mathematics Content Specification in the Age of Assessment, Norman L. Webb. 
Reflections on the State and Trends in Research on Mathematics Teaching and Learning: From Here to Utopia, Mogens Niss.

Third International Handbook of Mathematics Education

M.A. (Ken) Clements, Alan Bishop, Christine Keitel-Kreidt e Jeremy Kilpatrick

Springer | 2013 | 1119 páginas | pdf | 9 Mb

link

The four sections in this Third International Handbook are concerned with: (a) social, political and cultural dimensions in mathematics education; (b) mathematics education as a field of study; (c) technology in the mathematics curriculum; and (d) international perspectives on mathematics education. These themes are taken up by 84 internationally-recognized scholars, based in 26 different nations. Each of section is structured on the basis of past, present and future aspects. The first chapter in a section provides historical perspectives (“How did we get to where we are now?”); the middle chapters in a section analyze present-day key issues and themes (“Where are we now, and what recent events have been especially significant?”); and the final chapter in a section reflects on policy matters (“Where are we going, and what should we do?”). Readership: Teachers, mathematics educators, ed.policy makers, mathematicians, graduate students, undergraduate students. Large set of authoritative, international authors.​

Contents
Part I Introduction to Section A: Social, Political and Cultural Dimensions in Mathematics Education .. 1
Christine Keitel
1 From the Few to the Many: Historical Perspectives on Who Should Learn Mathematics... 7
M. A. (Ken) Clements, Christine Keitel, Alan J. Bishop, Jeremy Kilpatrick, and Frederick K. S. Leung
2 Theories for Studying Social, Political and Cultural Dimensions of Mathematics Education ... 41
Eva Jablonka, David Wagner, and Margaret Walshaw
3 Understanding and Overcoming “Disadvantage” in Learning Mathematics.... 69
Lulu Healy and Arthur B. Powell
4 Beyond Deficit Models of Learning Mathematics: Socio-cultural Directions for Change and Research .... 101
Cristina Frade, Nadja Acioly-Régnier, and Li Jun
5 Studying Learners in Intercultural Contexts ... 145
Yoshinori Shimizu and Gaye Williams
6 Learners in Transition Between Contexts.... 169
Tamsin Meaney and Troels Lange
7 Critical Perspectives on Adults’ Mathematics Education ... 203
Jeff Evans, Tine Wedege, and Keiko Yasukawa
8 The Politics of Equity and Access in Teaching and Learning Mathematics..... 243
Neil A. Pateman and Chap Sam Lim
Part II Introduction to Section B: Mathematics Education as a Field of Study ... 265
Alan J. Bishop
9 From Mathematics and Education, to Mathematics Education .... 273
Fulvia Furinghetti, José Manuel Matos, and Marta Menghini
10 Theories in Mathematics Education: Some Developments and Ways Forward .... 303
Bharath Sriraman and Elena Nardi
11 Research Methods in Mathematics Teacher Education ... 327
Uwe Gellert, Rosa Becerra Hernández, and Olive Chapman
12 Linking Research to Practice: Teachers as Key Stakeholders in Mathematics Education Research ..... 361
Carolyn Kieran, Konrad Krainer, and J. Michael Shaughnessy
13 Teachers Learning from Teachers ... 393
Allan Leslie White, Barbara Jaworski, Cecilia Agudelo-Valderrama, and Zahra Gooya
14 Developing Mathematics Educators .... 431
Jarmila Novotná, Claire Margolinas, and Bernard Sarrazy
15 Institutional Contexts for Research in Mathematics Education ...... 459
Tony Brown and David Clarke
16 Policy Implications of Developing Mathematics Education Research .... 485
Celia Hoyles and Joan Ferrini-Mundy
Part III Introduction to Section C: Technology in the Mathematics Curriculum ..... 517
Frederick K. S. Leung
17 From the Slate to the Web: Technology in the Mathematics Curriculum .... 525
David Lindsay Roberts, Allen Yuk Lun Leung, and Abigail Fregni Lins
18 Modelling with Mathematics and Technologies .. 549
Julian Williams and Merrilyn Goos
19 Technology and the Role of Proof: The Case of Dynamic Geometry ... 571
Nathalie Sinclair and Ornella Robutti
20 How Might Computer Algebra Systems Change the Role of Algebra in the School Curriculum?.... 597
M. Kathleen Heid, Michael O. J. Thomas, and Rose Mary Zbiek
21 Technology for Enhancing Statistical Reasoning at the School Level .... 643
Rolf Biehler, Dani Ben-Zvi, Arthur Bakker, and Katie Makar
22 Learning with the Use of the Internet ... 691
Marcelo C. Borba, Philip Clarkson, and George Gadanidis
23 Technology and Assessment in Mathematics .... 721
Kaye Stacey and Dylan Wiliam
24 Technology-Driven Developments and Policy Implications for Mathematics Education .... 753
L. Trouche, P. Drijvers, G. Gueudet, and A. I. Sacristán
Part IV Introduction to Section D: International Perspectives on Mathematics Education .... 791
Jeremy Kilpatrick
25 From the Local to the International in Mathematics Education .... 797
Alexander Karp
26 International Collaborative Studies in Mathematics Education ... 827
Parmjit Singh and Nerida F. Ellerton
27 Influence of International Studies of Student Achievement on Mathematics Teaching and Learning... 861
Vilma Mesa, Pedro Gómez, and Ui Hock Cheah
28 International Organizations in Mathematics Education .... 901
Bernard R. Hodgson, Leo F. Rogers, Stephen Lerman, and Suat Khoh Lim-Teo
29 Toward an International Mathematics Curriculum .... 949
Jinfa Cai and Geoffrey Howson
30 Methods for Studying Mathematics Teaching and Learning Internationally .... 975
Mogens Niss, Jonas Emanuelsson, and Peter Nyström
31 Implications of International Studies for National and Local Policy in Mathematics Education .. 1009
John A. Dossey and Margaret L. Wu
Brief Biographical Details of Authors .... 1043
Names of Reviewers .. 1063

The Intuitive Sources of Probabilistic Thinking in Children

H. Fischbein

Springer | 1975 | 228 páginas | pdf | 22 Mb

link

Contents

PREFACE IX
TRANSLATOR'S ACKNOWLEDGEMENT XI
ACKNOWLEDGEMENTS XIII
CHAPTER I Introduction 1
CHAPTER II Intuition and Intelligence 5
CHAPTER III Probability Learning 20
CHAPTER IV Probability Learning in Children 32
CHAPTER V The Intuition of Relative Frequency 58
CHAPTER VI Estimating Odds and The Concept of Probability 66
CHAPTER VII Combinatorial Analysis 99
CHAPTER VIII Summary and Conclusions 117
BIBLIOGRAPHY 132
APPENDIX I. Primary and Secondary Intuitions in the Introduction of Probability, 
by E. Fischbein, Ileana Barbat, and I. Minzat 138
APPENDIX II. The Child's Intuition of Probability, 
by E. Fischbein, Ileana Pampu, and I. Minzat 156
APPENDIX III. Comparison of Ratios and the Chance Concept in Children,
by E. Fischbein, Ileana Pampu, and I. Minzat 175
APPENDIX IV. Effects of Age and Instruction on Combinatory Ability in Children, 
by E. Fischbein, Ileana Pampu, and I. Minzat

From Calculus to Computers Using the last 200 years of mathematics history in the classroom

(Mathematical Association of America Notes)

Amy Shell-Gellasch e Dick Jardine

The Mathematical Association of America | 2005 | 268 páginas | rar - pdf | 1,9 Mb

link (password: matav)

To date, much of the literature prepared on the topic of integrating mathematics history into undergraduate teaching contains, predominantly, ideas from the 18th century and earlier. This volume focuses on nineteenth- and twentieth-century mathematics, building on the earlier efforts but emphasizing recent history in the teaching of mathematics, computer science, and related disciplines. From Calculus to Computers is a resource for undergraduate teachers that provides ideas and materials for immediate adoption in the classroom and proven examples to motivate innovation by the reader. Contributions to this volume are from historians of mathematics and college mathematics instructors with years of experience and expertise in these subjects. Examples of topics covered are probability in undergraduate statistics courses, logic and programming for computer science, undergraduate geometry to include non-Euclidean geometries, numerical analysis, and abstract algebra.
Emphasizes mathematics history from the nineteenth and twentieth centuries
Provides ideas and material for immediate adoption in the classroom
Topics covered range from Galois theory to using the history of women and minorities in teaching

Table of Contents
Preface
Introduction
Part I. Algebra, Number Theory, Calculus, and Dynamical Systems:
1. Arthur Cayley and the first paper on group theory David J. Pengelley
2. Putting the differential back into differential calculus Robert Rogers
3. Using Galois' idea in the teaching of abstract algebra Matt D. Lunsford
4. Teaching elliptic curves using original sources Lawrence D'Antonio
5. Using the historical development of predator-prey models to teach mathematical modeling Holly P. Hirst
Part II. Geometry:
6. How to use history to clarify common confusions in geometry Daina Taimina and David W. Henderson
7. Euler on Cevians Eisso J. Atzema and Homer White
8. Modern geometry after the end of mathematics Jeff Johannes
Part III. Discrete Mathematics, Computer Science, Numerical Methods, Logic, and Statistics:
9. Using 20th century history in a combinatorics and graph theory class Linda E. MacGuire
10. Public key cryptography Shai Simonson
11. Introducing logic via Turing machines Jerry M. Lodder
12. From Hilbert's program to computer programming William Calhoun
13. From the tree method in modern logic to the beginning of automated theorem proving Francine F. Abeles
14. Numerical methods history projects Dick Jardine
15. Foundations of Statistics in American Textbooks: probability and pedagogy in historical context Patti Wilger Hunter
Part IV. History of Mathematics and Pedagogy:
16. Incorporating the mathematical achievements of women and minority mathematicians into classrooms Sarah J. Greenwald
17. Mathematical topics in an undergraduate history of science course David Lindsay Roberts
18. Building a history of mathematics course from a local perspective Amy Shell-Gellasch
19. Protractors in the classroom: an historical perspective Amy Ackerberg-Hastings
20. The metric system enters the American classroom:
1790-1890 Peggy Aldrich Kidwell
21. Some wrinkles for a history of mathematics course Peter Ross
22. Teaching history of mathematics through problems John R. Prather

Alternative Forms of Knowing (in) Mathematics: Celebrations of Diversity of Mathematical Practices

Swapna Mukhopadhyay e  Wolff-Michael Roth

Sense Publishers |  2012 | 321 páginas | pdf | 24 Mb

link


This book grew out of a public lecture series, Alternative forms of knowledge construction in mathematics, conceived and organized by the first editor, and held annually at Portland State University from 2006. Starting from the position that mathematics is a human construction, implying that it cannot be separated from its historical, cultural, social, and political contexts, the purpose of these lectures was to provide a public intellectual space to interrogate conceptions of mathematics and mathematics education, particularly by looking at mathematical practices that are not considered relevant to mainstream mathematics education. One of the main thrusts was to contemplate the fundamental question of whose mathematics is to be valorized in a multicultural world, a world in which, as Paolo Freire said, "The intellectual activity of those without power is always characterized asnon-intellectual". To date, nineteen scholars (including the second editor) have participated in the series. All of the lectures have been streamed for global dissemination at:http://www.media.pdx.edu/dlcmedia/events/AFK/. Most of the speakers contributed a chapter to this book, based either on their original talk or on a related topic. The book is divided into four sections dealing with: • Mathematics and the politics of knowledge • Ethnomathematics • Learning to see mathematically • Mathematics education for social justice.


CONTENTS
Preface vii
Contributors ix
Celebrating Diversity, Realizing Alternatives: An Introduction 1
Brian Greer, Swapna Mukhopadhyay, & Wolff-Michael Roth
PART I: MATHEMATICS AND POLITICS OF KNOWLEDGE 9
Introduction 11
1 Mathematics and Accounting in the Andes before and after the Spanish Conquest 17
Gary Urton
2 Contemporary Indigenous Education: Thoughts for American Indian Education in a 21st-Century World 33
Gregory Cajete
3 Crisis as a Discursive Frame in Mathematics Education Research and Reform: Implications for Educating Black Children
Delaina Washington, Zayoni Torres, Maisie Gholson, & Danny Bernard Martin
4 Whose Language is it? Reflections on Mathematics Education and Language Diversity from Two Contexts 71
Marta Civil & Núria Planas
PART II: ETHNOMATHEMATICS 91
Introduction 93
5 Consulting the Divine: The (Ethno)mathematics of Divination 97
John Kellermeier
6 Map-Making in São Paulo, Southern Brazil: Colonial History, Social Diversity, and Indigenous Peoples’ Rights 115
Mariana Leal Ferreira
7 Developing an Alternative Learning Trajectory for Rational Number Reasoning, Geometry, and Measuring based on Indigenous Knowledge 159
Jerry Lipka, Monica Wong, Dora Andrew-Ihrke, & Evelyn Yanez
8 In Seeking a Holistic Tool for Ethnomathematics: Reflections on Using Ethnomodeling as a Pedagogical Action for Uncovering Ethnomathematical Practices 183
Daniel Clark Orey & Milton Rosa
9 From Ethnomathematics to Ethnocomputing: Indigenous Algorithms in Traditional Context & Contemporary Simulation 205
Bill Babbitt, Dan Lyles, & Ron Eglash
PART III: LEARNING TO SEE MATHEMATICALLY 221
Introduction 223
10 The Work of Seeing Mathematically 227
Wolff-Michael Roth
11 Running the Numbers: A Conversation 247
Chris Jordan
12 To Know How to See: The Realities of Learning and Teaching Mathematics 261
Frank Swetz
PART IV: MATHEMATICS EDUCATION FOR SOCIAL JUSTICE 277
Introduction 279
13 Quantitative Form in Argument 283
Marilyn Frankenstein
14 Connecting Community, Critical, and Classical Knowledge in Teaching Mathematics for Social Justice 299
Rico Gutstein
Epilogue: Why Bother about Diversity of Mathematical Practices? 313

Swapna Mukhopadhyay, Wolff-Michael Roth, & Brian Greer

Introduction to Cultural Mathematics : With Case Studies in the Otomies and the Incas

Thomas E. Gilsdorf

 Wiley| 2012 | 307 páginas | rar - pdf |  6 Mb


link (password: matav)

Cultural mathematics, or ethnomathematics as it is also known, studies the relationship between mathematics and culture—with the ultimate goal of contributing to an appreciation of the connection between the two. Introduction to Cultural Mathematics: With Case Studies in the Otomies and Incas integrates both theoretical and applied aspects of the topic, promotes discussions on the development of mathematical concepts, and provides a comprehensive reference for teaching and learning about multicultural mathematical practices.

This illuminating book provides a nontraditional, evidence-based approach to mathematics that promotes diversity and respect for cultural heritages. Part One covers such major concepts as cultural aspects of mathematics, numeration and number symbols, kinship relations, art and decoration, games, divination, and calendars. Part Two takes those concepts and applies them to fascinating case studies of both the Otomies of Central Mexico and the Incas of South America.

Throughout the book, numerous illustrations, examples, and motivational questions promote an interactive understanding of the topic. Each chapter begins with questions that encourage a cooperative, inquiry-based approach to learning and concludes with a series of exercises that allow readers to test their understanding of the presented material.

Introduction to Cultural Mathematics is an ideal book for courses on cultural mathematics, the history of mathematics, and cultural studies. The book is also a valuable resource and reference for anyone interested in the connections between mathematics, culture, anthropology, and history.

CONTENTS

PREFACE ix

INTRODUCTION xi

PART I GENERAL CONCEPTS

1 Understanding the Culture in Mathematics 3

2 Numeration Systems 24

3 Number Gestures and Number Symbols 39

4 Kinship and Social Relations 57

5 Art and Decoration 73

6 Divination 103

7 Games 123

8 Calendars 142

PART II - CASE STUDIES

9 Hñähñu Math: The Otomies 181

10 Tawantinsuyu Math: The Incas 211

HINTS TO SELECTED EXERCISES 253