Exploiting Mental Imagery with Computers in Mathematics Education

Rosamund Sutherland e John Mason

Springer | 1995 | 337 páginas | pdf |10 Mb

link

The advent of fast and sophisticated computer graphics has brought dynamic and interactive images under the control of professional mathematicians and mathematics teachers. This volume in the NATO Special Programme on Advanced Educational Technology takes a comprehensive and critical look at how the computer can support the use of visual images in mathematical problem solving. The contributions are written by researchers and teachers from a variety of disciplines including computer science, mathematics, mathematics education, psychology, and design. Some focus on the use of external visual images and others on the development of individual mental imagery. The book is the first collected volume in a research area that is developing rapidly, and the authors pose some challenging new questions.

Contents
Part 1. Emphasizing the External
Imagery for diagrams
Tommy Dreyfus
External representations in arithmetic problem solving
Giuliana Dettori and Enrica Lemut
Visualisation in mathematics and graphical mediators: an experience with 11-12 year old pupils
Angela Pesci
Visual organisers for formal mathematics
David Tall
Mediating mathematical action
Rosamund Sutherland
Mathematical objects, representations, and imagery
Willibald D6rjler
Part 2. Imagery in Support of Geometry
Images and concepts in geometrical reasoning
M. Alessandra Mariotti
Between drawing and figure
Reinhard Holzl
The functions of visualisation in learning geometry
Eric Love
Geometrical pictures: kinds of representation and specific processings 142
Raymond Duval
Part 3. Linking Screen and Mental Imagery 159
Overcoming physicality and the external present: cybernetic manipulatives 161
James J. Kaput
On visual and symbolic representations 178
Luis E. Moreno A. and Ana Isabel Sacristan R.
The dark side of the Moon 190
Richard Noss and Celia Hoyles
Ruminations about dynamic imagery (and a strong plea for research) 202
E. Paul Goldenberg
On designing screen images to generate mental images
Richard J. Phillips, John Gillespie, and Daniel Pead
Learning as embodied action .233
Stephen Campbell and A. J. (Sandy) Dawson
Part 4. Employing Imagery 251
The importance of mental perception when creating research pictures 252
Monique Sicard and Jean-Alain Marek
Random images on mental images
Mario Barra
Imagery as a tool to assist the teaching of algebra
Dave Hewitt
Mathematical screen metaphors
John Mason and Benedict Heal
Exploiting mental imaging: reflections of an artist on a mathematical excursion .
Stephen A.R. Scrivener
Index 323

Abstracts of The First Sourcebook on Asian Research in Mathematics Education: China, Korea, Singapore, Japan, Malaysia, and India

 Bharath Sriraman, Jinfa Cai e Kyeong-Hwa Lee

Information Age Publishing LLC | 2012 | 270 páginas | rar - pdf | 3 Mb

link (password: matav)

Mathematics and Science education have both grown in fertile directions in different geographic regions. Yet, the mainstream discourse in international handbooks does not lend voice to developments in cognition, curriculum, teacher development, assessment, policy and implementation of mathematics and science in many countries. Paradoxically, in spite of advances in information technology and the "flat earth" syndrome, old distinctions and biases between different groups of researcher's persist. In addition limited accessibility to conferences and journals also contribute to this problem. The International Sourcebooks in Mathematics and Science Education focus on under-represented regions of the world and provides a platform for researchers to showcase their research and development in areas within mathematics and science education. The First Sourcebook on Asian Research in Mathematics Education: China, Korea, Singapore, Japan, Malaysia and India provides the first synthesized treatment of mathematics education that has both developed and is now prominently emerging in the Asian and South Asian world. The book is organized in sections coordinated by leaders in mathematics education in these countries and editorial teams for each country affiliated with them. The purpose of unique sourcebook is to both consolidate and survey the established body of research in these countries with findings that have influenced ongoing research agendas and informed practices in Europe, North America (and other countries) in addition to serving as a platform to showcase existing research that has shaped teacher education, curricula and policy in these Asian countries. The book will serve as a standard reference for mathematics education researchers, policy makers, practitioners and students both in and outside Asia, and complement the Nordic and NCTM perspectives.

Contents
CHINA
PART I: CULTURE, TRADITION, AND HISTORY
1. “Zhi Yì Xíng Nán (Knowing Is Easy and Doing Is Difficult)” or Vice Versa?: A Chinese Mathematician’s Observation on History and Pedagogy of Mathematics Activities
Man-Keung Siu . . . . 5
2. The Study on Application of Mathematics History in Mathematics Education in China
Zezhong Yang and Jian Wang . . . 7
3. Cultural Roots, Traditions, and Characteristics of Contemporary Mathematics Education in China
Xuhui Li, Dianzhou Zhang and Shiqi Li . . . 9
PART II: ASSESSMENT AND EVALUATION
4. Factors Affecting Mathematical Literacy Performance of 15-Year-Old Students in Macao: The PISA Perspective
Kwok-Cheung Cheung . . . 13
5. Has Curriculum Reform Made A Difference in the Classroom?: An Evaluation of the New Mathematics
Curriculum in Mainland China
Yujing Ni, Qiong Li, Jinfa Cai, and Kit-Tai Hau . . .  15
6. Effect of Parental Involvement and Investment on Mathematics Learning: What Hong Kong Learned
From PISA
Esther Sui Chu Ho . . . . . . 17PART III: CURRICULUM
7. Early Algebra in Chinese Elementary Mathematics Textbooks: The Case of Inverse Operations
Meixia Ding . . . . . . . 21
8. The Development of Chinese Mathematics Textbooks for Primary and Secondary Schools Since
the Twentieth Century
Shi-hu Lv, Ting Chen, Aihui Peng, and Shangzhi Wang . . . . 23
9. Mathematics Curriculum and Teaching Materials in China from 1950–2000
Jianyue Zhang, Wei Sun, and Arthur B. Powell . . . . . . 2510. Chinese Mathematics Curriculum Reform in the Twenty-first Century: 2000-2010
Jian Liu, Lidong Wang, Ye Sun, and Yiming Cao . . . 27
11. Basic Education Mathematics Curriculum Reform in the Greater Chinese Region: Trends and Lessons Learned
Chi-Chung Lam, Ngai-Ying Wong, Rui Ding, Siu Pang Titus Li, and Yun-Peng Ma . 29
12. Characterizing Chinese Mathematics Curriculum: A Cross-National Comparative Perspective
Larry E. Suter and Jinfa Cai . .  . . . 31
PART IV: MATHEMATICAL COGNITION
13. Promoting Young Children’s Development of Logical- Math Thinking Through Addition, Subtraction,
Multiplication, and Division in Operational Math
Zi-Juan Cheng . . . .. 35
14. Development of Mathematical Cognition in Preschool Children
Qingfen Hu and Jing Zhang . . . 37
15. Chinese Children’s Understanding of Fraction Concepts
Ziqiang Xin and Chunhui Liu . . . . . 39
16. Teaching and Learning of Number Sense in Taiwan
Der-Ching Yang . . . .. . . . . 41
17. Contemporary Chinese Investigations of Cognitive Aspects of Mathematics Learning
Ping Yu, Wenhua Yu, and Yingfang Fu . . . .. . . . 43
18. Chinese Mathematical Processing and Mathematical Brain
Xinlin Zhou, Wei Wei, Chuansheng Chen, and Qi Dong . . . . . . . . . . . . 45
PART V: TEACHING AND TEACHER EDUCATION
19. Comparing Teachers’ Knowledge on Multidigit Division Between the United States and China
Shuhua An and Song A. An . . .. . 49
20. Problem Solving in Chinese Mathematics Education: Research and Practice
Jinfa Cai, Bikai Nie, and Lijun Ye . . . . . .. 51
21. Developing a Coding System for Video Analysis of Classroom Interaction
Yiming Cao, Chen He, and Liping Ding . .. 53
22. Mathematical Discourse in Chinese Classrooms: An Insider’s Perspective
Ida Ah Chee Mok, Xinrong Yang, and Yan Zhu . .. . 55
23. Reviving Teacher Learning: Chinese Mathematics Teacher Professional Development in the Context of Educational Reform
Lynn W. Paine, Yanping Fang, and Heng Jiang .  . . . 57
24. The Status Quo and Prospect of Research on Mathematics Education for Ethnic Minorities in China
Hengjun Tang, Aihui Peng, Bifen Chen, Yu Bo, Yanping Huang, and Naiqing Song . .. . 59
25. Chinese Elementary Teachers’ Mathematics Knowledge for Teaching: Role of Subject Related Training, Mathematic Teaching Experience, and Current Curriculum Study in Shaping Its Quality
Jian Wang . . . 61
26. Why Always Greener on the Other Side?: The Complexity of Chinese and U.S. Mathematics Education
Thomas E. Ricks . .  . . 63
PART VI: TECHNOLOGY
27. A Chinese Software SSP for the Teaching and Learning of Mathematics: Theoretical and Practical Perspectives
Chunlian Jiang, Jingzhong Zhang, and Xicheng Peng . .. . 67
28. E-Learning in Mathematics Education
Siu Cheung Kong . . .. . . 69
KOREA
29. Korean Research in Mathematics Education
Kyeong-Hwa Lee, Jennifer M. Suh, Rae Young Kim, and Bharath Sriraman . . . 73
30. A Review of Philosophical Studies on Mathematics Education
JinYoung Nam . . . . . 77
31. Mathematics Curriculum
Kyungmee Park . . . .  . 79
32. Mathematics Textbooks
JeongSuk Pang . . . . . . . 81
33. Using the History of Mathematics to Teach and Learn Mathematics
Hyewon Chang . . . . . 83
34. Perspectives on Reasoning Instruction in the Mathematics Education
BoMi Shin . . .. . 85
35. Mathematical Modeling
Yeong Ok Chong . .  . . . 87
36. Gender and Mathematics
Eun Jung Lee . . . . . . 89
37. Mathematics Assessment
GwiSoo Na . . . 91
38. Examining Key Issues in Research on Teacher Education
Gooyeon Kim . .. . . . . 93
39. Trends in the Research on Korean Teachers’ Beliefs About Mathematics Education
Dong-Hwan Lee . .  . 95
SINGAPORE
40. A Review of Mathematical Problem-Solving Research Involving Students in Singapore Mathematics Classrooms (2001 to 2011): What’s Done and What More Can be Done
Chan Chun Ming Eric . . . . . . . . 99
41. Research on Singapore Mathematics Curriculum and Textbooks: Searching for Reasons Behind Students’ Outstanding Performance
Yan Zhu and Lianghuo Fan . . . 103
42. Teachers’ Assessment Literacy and Student Learning in Singapore Mathematics Classrooms
Kim Hong Koh .. . . 107
43. A Theoretical Framework for Understanding the Different Attention Resource Demands of Letter-Symbolic Versus Model Method
Swee Fong Ng . .  . . 111
44. A Multidimensional Approach to Understanding in Mathematics Among Grade 8 Students in Singapore
Boey Kok Leong, Shaljan Areepattamannil, and Berinderjeet Kaur . . . 115

MALAYSIA
45. Mathematics Education Research in Malaysia: An Overview
Chap Sam Lim, Parmjit Singh, Liew Kee Kor, and Cheng Meng Chew . . . 121
46. Research Studies in the Learning and Understanding of Mathematics: A Malaysian Context
Parmjit Singh and Sian Hoon Teoh . . . . . . 123
47. Numeracy Studies in Malaysia
Munirah Ghazali and Abdul Razak Othman . . .  . 125
48. Malaysian Research in Geometry
Cheng Meng Chew . .  . . . . 127
49. Research in Mathematical Thinking in Malaysia: Some Issues and Suggestions
Shafia Abdul Rahman  . . . 129
50. Studies About Values in Mathematics Teaching and Learning in Malaysia
Sharifah Norul Akmar Syed Zamri and Mohd Uzi Dollah . .  . . 131
51. Transformation of School Mathematics Assessment
Tee Yong Hwa, Chap Sam Lim, and Ngee Kiong Lau . . . . . . 133
52. Mathematics Incorporating Graphics Calculator Technology in Malaysia
Liew Kee Kor . .  . . . 135
53. Mathematics Teacher Professional Development in Malaysia
Chin Mon Chiew, Chap Sam Lim, and Ui Hock Cheah . . . 137

JAPAN
54. Mathematics Education Research in Japan: An Introduction
Yoshinori Shimizu . . . . . 141
55. A Historical Perspective on Mathematics Education Research in Japan
Naomichi Makinae . . . 143
56. The Development of Mathematics Education as a Research Field in Japan
Yasuhiro Sekiguchi . .  . . . 147
57. Research on Proportional Reasoning in Japanese Context
Keiko Hino . . . .. . 149
58. Japanese Student’s Understanding of School Algebra
Toshiakira Fujii . . . . . . 153
59. Proving as an Explorative Activity in Mathematics Education
Mikio Miyazaki and Taro Fujita .. . 157
60. Developments in Research on Mathematical Problem Solving in Japan
Kazuhiko Nunokawa . .  . . 161
61. Research on Teaching and Learning Mathematics With Information and Communication Technology
Yasuyuki Iijima . . . .. . . . . 165
62. “Inner Teacher”: The Role of Metacognition in Learning Mathematics and Its Implication to Improving Classroom Practice
Keiichi Shigematsu . .  . . 167
63. Cross-Cultural Studies on Mathematics Classroom Practices
Yoshinori Shimizu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
64. Systematic Support of Life-Long Professional Development for Teachers Through Lesson Study
Akihiko Takahashi . . . . . . . 175

INDIA
65. Evolving Concerns Around Mathematics as a School Discipline: Curricular Vision, Classroom Practice and the National Curriculum Framework (2005)
Farida Abdulla Khan . . . . 181
66. Curriculum Development in Primary Mathematics: The School Mathematics Project
Amitabha Mukherjee and Vijaya S. Varma . .. . . . 185
67. Intervening for Number Sense in Primary Mathematics
Usha Menon . . . . . . . 191
68. Some Ethical Concerns in Designing Upper Primary Mathematics Curriculum: A Report From the Field
Jayasree Subramanian, Sunil Verma, and Mohd. Umar . . . . . 199
69. Students’ Understanding of Algebra and Curriculum Reform
Rakhi Banerjee . . . .. . 207
70. Professional Development of In-Service Mathematics Teachers in India
Ruchi S. Kumar, K. Subramaniam, and Shweta Naik . . . . . 213
71. Insights Into Students’ Errors Based on Data From Large-Scale Assessments
Aaloka Kanhere, Anupriya Gupta, and Maulik Shah .  . . 219
72. Assessment of Mathematical Learning: Issues and Challenges
Shailesh Shirali . . . . 227
73. Technology and Mathematics Education: Issues and Challenges 233
Jonaki B. Ghosh . . .  . . 233
74. Mathematics Education in Precolonial and Colonial South India
Senthil Babu D. . . . . .. . . . . 243
75. Representations of Numbers in the Indian Mathematical Tradition of Combinatorial Problems
Raja Sridharan and K. Subramaniam . . .  . . 249

Outros livros sobre o ensino da matemática na região asiática:

Reforms and issues in school mathematics in East Asia : sharing and understanding mathematics education policies and practices por Frederick K S Leung; Yeping Li; Não  disponível em ebook Idioma: Inglês   Editora: Rotterdam ; Boston : Sense Publishers, ©2010. online: cap 1. Sharing and Understanding Mathematics Education Policies and Practices  cap.2 - Mathematics Curriculum Reform in the Chinese Mainland: Changes and Challenges cap. 9 - What can we teach mathematics terachers? Lessons from Hong Kong (versão draft)

Mathematics curriculum in Pacific rim countries--China, Japan, Korea, and Singapore : proceedings of a conference por Zalman Usiskin; Edwin Willmore; Idioma: Inglês   Editora: Charlotte, N.C. : Information Age Pub., ©2008.

Mathematics education in different cultural traditions : a comparative study of East Asia and the West por Frederick K S Leung; Klaus-D Graf; Francis J Lopez-Real; International Commission on Mathematical Instruction.;  Publicação de conferência Idioma: Inglês   Editora: New York : Springer, ©2006.

Goedel's Way: Exploits into an undecidable world

Gregory Chaitin, Francisco A Doria e Newton C.A. da Costa

CRC Press | 2011 | 162 páginas | pdf | 1,1 Mb

link

Kurt Gödel (1906-1978) was an Austrian-American mathematician, who is best known for his incompleteness theorems. He was the greatest mathematical logician of the 20th century, with his contributions extending to Einstein’s general relativity, as he proved that Einstein’s theory admits time machines. 
The Gödel incompleteness theorem - one cannot prove nor disprove all true mathematical sentences in the usual formal mathematical systems- is frequently presented in textbooks as something that happens in the rarefied realm of mathematical logic, and that has nothing to do with the real world. Practice shows the contrary though; one can demonstrate the validity of the phenomenon in various areas, ranging from chaos theory and physics to economics and even ecology. In this lively treatise, based on Chaitin’s groundbreaking work and on the da Costa-Doria results in physics, ecology, economics and computer science, the authors show that the Gödel incompleteness phenomenon can directly bear on the practice of science and perhaps on our everyday life.
This accessible book gives a new, detailed and elementary explanation of the Gödel incompleteness theorems and presents the Chaitin results and their relation to the da Costa-Doria results, which are given in full, but with no technicalities. Besides theory, the historical report and personal stories about the main character and on this book’s writing process, make it appealing leisure reading for those interested in mathematics, logic, physics, philosophy and computer science.
See also: http://www.youtube.com/watch?v=REy9noY5Sg8

Contents
1. Gödel, Turing 
2. Complexity, randomness 
3. A list of problems 
4. The halting function and its avatars 
5. Entropy, P vs. NP
6. Forays into uncharted landscapes.

Learning Mathematics and Logo

Celia Hoyles e Richard Noss

The MIT Press | 1992 | 492 páginas | pdf | 22,4 Mb

link
link1

These original essays summarize a decade of fruitful research and curriculum development using the LISP-derived language Logo. They discuss a range of issues in the areas of curriculum, learning, and mathematics, illustrating the ways in which Logo continues to provide a rich learning environment, one that allows pupil autonomy within challenging mathematical settings.
Essays in the first section discuss the link between Logo and the school mathematics curriculum, focusing on the ways in which pupils' Logo activities relate to and are influenced by the ideas they encounter in the context of school algebra and geometry.
In the second section the contributions take up pedagogical styles and strategies. They tackle such cognitive and metacognitive questions as, What range of learning styles can the Logo setting accommodate? How can teachers make sense of pupils' preferred strategies? And how can teachers help students to reflect on the strategies they are using?
Returning to the mathematical structures, essays in the third section consider a variety of mathematical ideas, drawing connections between mathematics and computing and showing the ways in which constructing Logo programs helps or does not help to illuminate the underlying mathematics.

Contents
Contributors vii
Series Foreword ix
Foreword by Seymour Papert xi
Preface xvii
Acknowledgments xxiii
LOGO IN THE CURRICULUM
Introduction to Part I 3
The Notion of Variable in the Context of Turtle Graphics 11
Joel Hillel
2 What Is Algebraic about Programming in Logo? 37
Rosamund Sutherland
3 Conceptually Defined Turtles 55
Herbert Loethe
4 The Turtle Metaphor as a ToOl for Children's Geometry 97
Chronis Kynigos
5 A Logo Microworld for Transformation Geometry 127
Laurie D. Edwards
II STYLES AND STRATEGIES
Introduction to Part II 159
6 LEGO-Logo: A Vehicle for Learning 165
Sylvia Weir
7 On Intra- and Interlndividual Differences in Children's Learning Styles 191
Tamara Lemerise
8 Mathematics in a Logo Environment: A Recursive Look at a Complex Phenomenon 223
Thomas E. Kieren
9 Between Logo and Mathematics: A Road of Tunnels and Bridges 247
Jean-Luc Gurtner
III EXPRESSING MATHEMATICAL STRUCTURES
Introduction to Part ", 27 1
10 Processes: A Dynamical Integration of Computer Science into Mathematical Education 279
Bruno Vitale
Of Geometry, Turtles, and Groups
Uri Leron and Rina Zazkis
Patterns, Permutations, and Groups
Trevor Fletcher
Avoiding Recursion 393
Brian Harvey
IV AFTERWORD
Introduction to Part IV 429
Looking Back and Looking Forward
Richard Noss and Celia Hoyles
Index 47 1

Computers and Exploratory Learning

Andrea A. DiSessa, Celia Hoyles, Richard Noss e L.D. Edwards

Springer | 1995 | 483 páginas | pdf | 30 Mb

link
link1

Computers are playing a fundamental role in enhancing exploratory learning techniques in education. This volume in the NATO Special Programme on Advanced Educational Technology covers the state of the art in the design and use of computer systems for exploratory learning. Contributed chapters treat principles, theory, practice, and examples of some of the best contemporary computer-based learning environments: Logo, Boxer, Microworlds, Cabri-Géomètre, Star Logo, Table Top, Geomland, spreadsheets, Function Machines, and others. Emphasis is on mathematics and science education. Synthetic chapters provide an overview of the current scene in computers and exploratory learning, and analyses from the perspectives of epistemology, learning, and socio-cultural studies.

Table of Contents
1. Computers and Exploratory Learning: Setting the Scene .... 1
Andrea A. diSessa, Celia Hoyles, Richard Noss, Laurie D. Edwards
Section I: Computers and Knowledge
2. Thematic Chapter: Epistemology and Systems Design .... 15
Andrea A. diSessa
3. New Paradigms for Computing, New Paradigms for Thinking .... 31
Mitchel Resnick
4. From Local to Global: Programming and the Unfolding of Local Models in the Exploratory Learning of Mathematics and Science ... 45
Bruno Vitale
5. East or West-GEOMLAND is Best, or Does the Answer Depend on the Angle? ... 59
Bojidar Sendov, Evgenia Sendova
6. Computational Media to Support the Learning and Use of Functions ... 79
Al Cuoco
7. Knowledge Representation in a Learning Environment for Euclidean Geometry .. 109
Maria Alberta Alberti, Daniele Marini
8. Microworlds as Representations ..... 127
Laurie D. Edwards
9. Visualizing Formal and Structural Relationships with Spreadsheets ... 155
Erich Neuwirth
10. Creating Software Applications for Children: Some Thoughts About Design .... 175
Michael Eisenberg
Section II: Computers and Learning
11. Thematic Chapter: Exploratory Software, Exploratory Cultures? .... 199
Celia Hoyles
12. The Medium and the Curriculum: Reflections on Transparent Tools and Tacit Mathematics ..221
Chris Hancock
13. What About a Learning Environment Where Euclidean Concepts are Manipulated with a Mouse? ..... 241
Colette and lean-Marie Laborde
14. Four Steps to the Right ..... 263
Augusto Chioccariello, Nadia Culotta Leccioli, Chiara Oreste
15. Learning Dynamic Geometry: Implementing Rotations ..... 275
Angel Gutierrez
16. Sketching a Multidisciplinary Microworld: A Collaborative Exploration in Boxer ..... 289
Jeremy Roschelle, John Mason
17. Design of Computer-Based Cognitive Tools ..... 305
Emrah Orhun
18. The Spreadsheet as a Tool for Mathematical Modeling: A Case Study ... 321
João Filipe Matos
19. The Many Faces of a Computational Medium: Teaching the Mathematics of Motion .. 337
Andrea A. diSessa
Section III: Computers and Cultures
20. Thematic Chapter: Computers as Commodities .... 363
Richard Noss
21. Exploring the Sketch Metaphor for Presenting Mathematics Using Boxer .... 383
John Mason
22. Programming as a Means of Expressing and Exploring Ideas: Three Case Studies Situated in a Directive Educational System .. 399
Chronis Kynigos
23. Do Users Inhabit Or Build Their Boxer Environment? .. 421
Liddy Nevile
24. Designing, Exploring and Interacting: Novice Activities in the Boxer Computational Medium .... 443
Kathryn Crawford
25. Learning Opportunities Provided by Domain-Oriented Design Environments ..... 463
Gerhard Fischer
Subject Index ..... 481

Learning from Computers: Mathematics Education and Technology

 Christine Keitel-Kreidt e Kenneth Ruthven

Springer | 2011 - reprint of the original 1st ed. 1993 edition | páginas | rar - pdf |10,3 Mb

link (password : matav)

This study offers a re-examination of the mathematics curriculum and the teaching of mathematics in the light of changing technological possibilities. Recent developments in cognitive technologies and the impact of technology on mathematics teaching are amongst the topics explored.

Contents
1. Microworlds/Schoolworlds: The Transformation of an Innovation.
1.1 The story of microworlds.
1.2 The genesis.
1.3 From designers to mathematics educators.
1.4 Generating mathematics through microworlds: some illustrations.
1.5 Evocative computational objects and situated abstractions.
1.6 Microworlds in school mathematics.
1.7 Microworlds in the curriculum.
1.8 Reflections and implications.
2. Computer Algebra Systems as Cognitive Technologies: Implication for the Practice of Mathematics Education.
2.1 CAS: Some examples of symbol manipulations.
2.2 Computers and computer algebras in relation to pure mathematics.
2.3 Computer Algebra Systems in relation to mathematics education.
2.4 Opposition to instructional uses of Computer Algebra Systems.
2.5 Strengths of Computer Algebra Systems as learning tools.
2.6 Computer algebra in an educational context: One example.
2.7 CAS: From amplifiers to reorganisers.
3. The Computer as Part of the Learning Environment: The Case of Geometry.
3.1 The dual nature of geometrical figures.
3.2 Difficulties of students.
3.3 The notion of geometric figure as mediated by the computer.
3.4 Changes brought by computers to the relationship to the figure.
3.5 Interactions between student and software.
4. Software Tools and Mathematics Education: The Case of Statistics.
4.1 Didactical transposition and software tools.
4.2 The revolution in statistics.
4.3 Graphical and interactive data analysis: an example.
4.4 Making sense of statistical software tools.
4.5 Statistics education.
4.6 Statistics and a re-defined school mathematics
5. Didactic Design of Computer-based Learning Environments.
5.1 Understanding mathematics and the use of computers.
5.2 Designing QuadFun - A case description.
5.3 Interlude: Experimental aspects of mathematics.
5.4 Design issues.
5.5 A systemic view of didactic design.
6. Artificial Intelligence and Real Teaching.
6.1 Didactical interaction revisited.
6.2 The input of artificial intelligence.
6.3 Student-computer interaction, an overview.
6.4 Educational software in the classroom, a new complexity.
6.5 Open questions for future practice.
7. Computer Use and Views of the Mind.
7.1 The notion of cognition.
7.2 Cognitive reorganization by using tools.
7.3 Cognitive models and concreteness of thinking.- 7.4 Situated thinking and distributed cognition
7.5 The computer as a medium for prototypes.
7.6 Modularity of thought.
7.7 Conclusion.
8. Technology and the Rationalisation of Teaching.
8.1 The rationalisation of social practice.
8.2 The elusive rationality of teaching.
8.3 The marginal impact of machines on teaching.
8.4 The dynamics of pedagogical change.
8.5 The programming microworld.
8.6 The tutoring system.
8.7 The computer and the rationalisation of teaching.
9. Computers and Curriculum Change in Mathematics.
9.1 Locating the curriculum.-
9.2 Curriculum change as institutional change.
9.3 Redefining school mathematics.
9.4 Planning curriculum change.
9.5 Alternative scenarios.
10. On Determining New Goals for Mathematical Education.
10.1 Goals for mathematics education.
10.2 Goals for mathematics learners.
10.3 Role of the teacher and the educational institution.
10.4 Needed research on goals in mathematics education.
11. Beyond the Tunnel Vision: Analysing the Relationship Between Mathematics, Society and Technology.
11.1 Setting the stage.
11.2 Technology in society.
11.3 Mathematics shaping society?.
11.4 Living (together) with abstractions.
11.5 Mathematical technology as social structures.
11.6 Structural problems in an abstraction society.
11.7 Mathematics education as a social enterprise.
11.8 Mathematics education as a democratic forum.
11.9 Reflecting on computers in the classroom: Hardware-software-be(a)ware.
12. Towards a Social Theory of Mathematical Knowledge.
12.1 The Mechanistic Age - a historical introduction.
12.2 Mathematical and social individuation.
12.3 How can we master technology?.
12.4 Engineers versus mathematicians since the turn of the century.
References
Software.

Using lCT in Primary Mathematics Practice and Possibilities

 

Bob Fox, Ann Montague-Smith e Sarah Wilkes

David Fulton Publishers | 2000 | 161 páginas | rar - pdf | 4,66 Mb

link (password: matav)

This work explores the development and classroom application of hardware and software for primary mathematics. It reviews available software, considers pedagogy and best practice in mathematics and provides examples of ICT in mathematics.

Contents

Acknowledgements and notes about the authors IV

Introduction V

1 Background to ICT in the primary school

Bob Fox 1

2 Mathematics teaching and learning: past, present and future

Ann Montague-Smith 24

3 Mathematics software and its use

Bob Fox, Ann Montague-Smith and Sarah Wilkes 52

4 Mathematics on-line

Bob Fox 107

5 ICT in the daily mathematics lesson

Bob Fox and Sarah Wilkes 112

6 Conclusion

Bob Fox 139

Resources: software and hardware 143

Bibliography 144

Index 150

A Female Genius: How Ada Lovelace Started the Computer Age

James Essinger

Gibson Square | 2013 | 304 páginas | rar - epub | 1,45 Mb

link (password: matav)

The daughter of Lord Byron, Ada was the visionary who recognised the true potential of Babbage's of cog-wheel computer, The Analytical Engine. She demonstrated to the world that computers wouldn't merely be adding machines, but that they would be able to think.

Contents
Preface
1. Poetic Beginnings
2. Lord Byron: A Scandalous Ancestry
3. Annabella: Anglo-Saxon Attitudes
4. The Manor of Parallelograms
5. The Art of Flying
6. Love
7. Silken Threads
8. When Ada Met Charles
9. The Thinking Machine
10. Kinship
11. Mad Scientist
12. A Window on the Future
13. The Jacquard Loom
14. A Mind with a View
15. Ada’s Offer to Babbage
16. The Enchantress of Number
17. A Horrible Death
18. Redemption
Afterword
Acknowledgement

It Began with Babbage: The Genesis of Computer Science

Subrata Dasgupta

Oxford University Press |  2014 | páginas | rar - pdf | 2,9 Mb

link (password: matav)

epub - 4,8 Mb - link

As a field, computer science occupies a unique scientific space, in that its subject matter can exist in both physical and abstract realms. An artifact such as software is both tangible and not, and must be classified as something in between, or "liminal." The study and production of liminal artifacts allows for creative possibilities that are, and have been, possible only in computer science. In It Began with Babbage, computer scientist and writer Subrata Dasgupta examines the distinct history of computer science in terms of its creative innovations, reaching back to Charles Babbage in 1819. Since all artifacts of computer science are conceived with a use in mind, the computer scientist is not concerned with the natural laws that govern disciplines like physics or chemistry; instead, the field is more concerned with the concept of purpose. This requirement lends itself to a type of creative thinking that, as Dasgupta shows us, has exhibited itself throughout the history of computer science. More than any other, computer science is the science of the artificial, and has a unique history to accompany its unique focus.The book traces a path from Babbage's Difference Engine in the early 19th century to the end of the 1960s by when a new academic discipline named "computer science" had come into being. Along the way we meet characters like Babbage and Ada Lovelace, Turing and von Neumann, Shannon and Chomsky, and a host of other people from a variety of backgrounds who collectively created this new science of the artificial. And in the end, we see how and why computer science acquired a nature and history all of its own.

Contents
Acknowledgments ix
Prologue 1
1. Leibniz’s Th eme, Babbage’s Dream 9
2. Weaving Algebraic Patterns 17
3. Missing Links 28
4. Entscheidungsproblem : What’s in a Word? 44
5. Toward a Holy Grail 60
6. Intermezzo 83
7. A Tangled Web of Inventions 8 9
8. A Paradigm Is Born 108
9. A Liminal Artifact of an Uncommon Nature 1 34
10. Glimpses of a Scientifi c Style 1 49
11. I Compute, Th erefore I Am 1 57
12. “Th e Best Way to Design . . .” 178
13. Language Games 1 90
14. Going Heuristic 2 25
15. An Explosion of Subparadigms 2 41
16. Aesthetica 2 65
Epilogue 277
Dramatis personae 287
Bibliograph

The Universal History of Computing: From the Abacus to the Quantum Computer

Georges Ifrah

Wiley | 2001 | 413 páginas

PDF - 17 Mb - link

djvu - 3 Mb
link
link1

"A fascinating compendium of information about writing systems–both for words and numbers."

"A truly enlightening and fascinating study for the mathematically oriented reader."

"Well researched. . . . This book is a rich resource for those involved in researching the history of computers."

In this brilliant follow-up to his landmark international bestseller, The Universal History of Numbers, Georges Ifrah traces the development of computing from the invention of the abacus to the creation of the binary system three centuries ago to the incredible conceptual, scientific, and technical achievements that made the first modern computers possible. Ifrah takes us along as he visits mathematicians, visionaries, philosophers, and scholars from every corner of the world and every period of history. We learn about the births of the pocket calculator, the adding machine, the cash register, and even automata. We find out how the origins of the computer can be found in the European Renaissance, along with how World War II influenced the development of analytical calculation. And we explore such hot topics as numerical codes and the recent discovery of new kinds of number systems, such as "surreal" numbers.

Adventurous and enthralling, The Universal History of Computing is an astonishing achievement that not only unravels the epic tale of computing, but also tells the compelling story of human intelligence–and how much further we still have to go.

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

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

The Mathematics Teacher in the Digital Era: An International Perspective on Technology Focused Professional Development

(Mathematics Education in the Digital Era, 2)

Alison Clark-Wilson, Ornella Robutti e Nathalie Sinclair

 Springer | 2014 | 419 páginas | rar - pdf | 4,5 Mb

link
password: matav

This volume addresses the key issue of the initial education and lifelong professional learning of teachers of mathematics to enable them to realize the affordances of educational technology for mathematics. With invited contributions from leading scholars in the field, this volume contains a blend of research articles and descriptive texts.

In the opening chapter John Mason invites the reader to engage in a number of mathematics tasks that highlight important features of technology-mediated mathematical activity.

This is followed by three main sections

·        an overview of current practices in teachers’ use of digital technologies in the classroom and explorations of the possibilities for developing more effective practices drawing on a range of research perspectives (including grounded theory, enactivism and Valsiner’s zone theory).

·        a set of chapters that share many common constructs (such as instrumental orchestration, instrumental distance and double instrumental genesis) and research settings that have emerged from the French research community, but have also been taken up by other colleagues.

·        meta-level considerations of research in the domain by contrasting different approaches and proposing connecting or uniting elements

Contents

Introduction .... 1

Alison Clark-Wilson , Ornella Robutti , and Nathalie Sinclair

Interactions Between Teacher, Student, Software and Mathematics: Getting a Purchase on Learning with Technology .... 11

John Mason

Part I Current Practices and Opportunities for Professional Development

Exploring the Quantitative and Qualitative Gap Between Expectation and Implementation: A Survey of English Mathematics Teachers’ Uses of ICT ....... 43

Nicola Bretscher

Teaching with Digital Technology: Obstacles and Opportunities .............. 71

Michael O.J. Thomas and Joann M. Palmer

A Developmental Model for Adaptive and Differentiated Instruction Using Classroom Networking Technology ... 91

Allan Bellman , Wellesley R. Foshay , and Danny Gremillion

Integrating Technology in the Primary School Mathematics Classroom: The Role of the Teacher ..... 111

María Trigueros , María-Dolores Lozano , and Ivonne Sandoval

Technology Integration in Secondary School Mathematics: The Development of Teachers’ Professional Identities .... 139

Merrilyn Goos

Teaching Roles in a Technology Intensive Core Undergraduate Mathematics Course .... 163

Chantal Buteau and Eric Mulle

Part II Instrumentation of Digital Resources in the Classroom

Digital Technology and Mid-Adopting Teachers’ Professional Development: A Case Study .. 189

Paul Drijvers , Sietske Tacoma , Amy Besamusca , Cora van den Heuvel , Michiel Doorman , and Peter Boon

Teaching Mathematics with Technology at the Kindergarten Level: Resources and Orchestrations ..... 213

Ghislaine Gueudet , Laetitia Bueno-Ravel , and Caroline Poisard

Teachers’ Instrumental Geneses When Integrating Spreadsheet Software........ 241

Mariam Haspekian

A Methodological Approach to Researching the Development of Teachers’ Knowledge in a Multi-Representational Technological Setting .... 277

Alison Clark-Wilson

Teachers and Technologies: Shared Constraints, Common Responses ..... 297

Maha Abboud-Blanchard

Didactic Incidents: A Way to Improve the Professional Development of Mathematics Teachers ..... 319

Gilles Aldon

Part III Theories on Theories

Meta-Didactical Transposition: A Theoretical Model for Teacher Education Programmes ...... 347

Ferdinando Arzarello, Ornella Robutti, Cristina Sabena, Annalisa Cusi,

Rossella Garuti, Nicolina Malara, and Francesca Martignone

Frameworks for Analysing the Expertise That Underpins Successful Integration of Digital Technologies into Everyday Teaching Practice ....... 373

Kenneth Ruthven

Summary and Suggested Uses for the Book ...... 395

Alison Clark-Wilson , Ornella Robutti , and Nathalie Sinclair

Glossary ....... 403

Index ........ 407

The Universal Computer: The Road from Leibniz to Turing

Martin Davis

A K Peters/CRC Press | 2011 |  240 páginas | pdf

link

The breathtakingly rapid pace of change in computing makes it easy to overlook the pioneers who began it all. Written by Martin Davis, respected logician and researcher in the theory of computation, The Universal Computer: The Road from Leibniz to Turing explores the fascinating lives, ideas, and discoveries of seven remarkable mathematicians. It tells the stories of the unsung heroes of the computer age – the logicians.

The story begins with Leibniz in the 17^th century and then focuses on Boole, Frege, Cantor, Hilbert, and Gödel, before turning to Turing. Turing’s analysis of algorithmic processes led to a single, all-purpose machine that could be programmed to carry out such processes—the computer. Davis describes how this incredible group, with lives as extraordinary as their accomplishments, grappled with logical reasoning and its mechanization. By investigating their achievements and failures, he shows how these pioneers paved the way for modern computing.

Bringing the material up to date, in this revised edition Davis discusses the success of the IBM Watson on Jeopardy, reorganizes the information on incompleteness, and adds information on Konrad Zuse. A distinguished prize-winning logician, Martin Davis has had a career of more than six decades devoted to the important interface between logic and computer science. His expertise, combined with his genuine love of the subject and excellent storytelling, make him the perfect person to tell this story.

Visual Mathematics and Cyberlearning

(Mathematics Education in the Digital Era, 1)

Dragana Martinovic, Viktor Freiman e Zekeriya Karadag

Springer | 2013 | 255 páginas | pdf | 3,9 Mb

link

This first book in the series will describe the Net Generation as visual learners who thrive when surrounded with new technologies and whose needs can be met with the technological innovations. These new learners seek novel ways of studying, such as collaborating with peers, multitasking, as well as use of multimedia, the Internet, and other Information and Communication Technologies. Here we present mathematics as a contemporary subject that is engaging, exciting and enlightening in new ways. For example, in the distributed environment of cyber space, mathematics learners play games, watch presentations on YouTube, create Java applets of mathematics simulations and exchange thoughts over the Instant Messaging tool. How should mathematics education resonate with these learners and technological novelties that excite them?
Contents
Patterns of Collaboration: Towards Learning Mathematics in the Era of the SemanticWeb.  . . 1
Keith Jones, Eirini Geraniou, and Thanassis Tiropanis
Collaborative Mathematics Learning in Online Environments . . 23
Gorjan Alagic and Mara Alagic
The Integration of Mathematics Discourse, Graphical Reasoning and Symbolic Expression by a Virtual Math Team  . . 49
Murat Perit Cakir & Gerry StahlInvestigating the Mathematical Discourse of Young Learners Involved in Multi-Modal Mathematical Investigations: The Case of Haptic Technologies .. . 97
 Beste Güçler, Stephen Hegedus, Ryan Robidoux, & Nicholas JackiwEmbodied Interaction as Designed Mediation of Conceptual Performance. . 119
Dragan Trninic and Dor Abrahamson
Sensuous Cognition .. . . 141
Luis Radford
New Media and Online Mathematics Learning for Teachers  . . . . 163
George Gadanidis and Immaculate Kizito Namukasa
Web-Based Video Clips: A Supplemental Resource for Supporting Pre-service Elementary Mathematics Teachers
Ann LeSage
Visual Mathematics and Cyberlearning in View of Affordance and Activity Theories . . . 209
Dragana Martinovic, Viktor Freiman, and Zekeriya Karadag

The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age

Paul J. Nahin

Princeton University Press | 2012 | pdf | 5,3 Mb

link direto
link

epub - 5 Mb - link

Boolean algebra, also called Boolean logic, is at the heart of the electronic circuitry in everything we use--from our computers and cars, to our kitchen gadgets and home appliances. How did a system of mathematics established in the Victorian era become the basis for such incredible technological achievements a century later? In The Logician and the Engineer, best-selling popular math writer Paul Nahin combines engaging problems and a colorful historical narrative to tell the remarkable story of how two men in different eras--mathematician and philosopher George Boole (1815-1864) and electrical engineer and pioneering information theorist Claude Shannon (1916-2001)--advanced Boolean logic and became founding fathers of the electronic communications age.
Presenting the dual biographies of Boole and Shannon, Nahin examines the history of Boole's innovative ideas, and considers how they led to Shannon's groundbreaking work on electrical relay circuits and information theory. Along the way, Nahin presents logic problems for readers to solve and talks about the contributions of such key players as Georg Cantor, Tibor Rado, and Marvin Minsky--as well as the crucial role of Alan Turing's "Turing machine"--in the development of mathematical logic and data transmission. Nahin takes readers from fundamental concepts to a deeper and more sophisticated understanding of how a modern digital machine such as the computer is constructed. Nahin also delves into the newest ideas in quantum mechanics and thermodynamics in order to explore computing's possible limitations in the twenty-first century and beyond.
The Logician and the Engineer shows how a form of mathematical logic and the innovations of two men paved the way for the digital technology of the modern world.

Contents
Preface xi
1 What You Need to Know to Read This Book 1
2 Introduction 6
3 George Boole and Claude Shannon: Two Mini-Biographies 17
3.1 The Mathematician 17
3.2 The Electrical Engineer 28
4 Boolean Algebra 43
4.1 Boole’s Early Interest in Symbolic Analysis 43
4.2 Visualizing Sets 44
4.3 Boole’s Algebra of Sets 45
4.4 Propositional Calculus 48
4.5 Some Examples of Boolean Analysis 52
4.6 Visualizing Boolean Functions 59
5 Logical Switching Circuits 67
5.1 Digital Technology: Relays versus Electronics 67
5.2 Switches and the Logical Connectives 68
5.3 A Classic Switching Design Problem 71
5.4 The Electromagnetic Relay and the Logical NOT 73
5.5 The Ideal Diode and the Relay Logical AND and OR 76
5.6 The Bi-Stable Relay Latch 81
6 Boole, Shannon, and Probability 88
6.1 A Common Mathematical Interest 88
6.2 Some Fundamental Probability Concepts 89
6.3 Boole and Conditional Probability 96
6.4 Shannon, Conditional Probability, and Relay Reliability 99
6.5 Majority Logic 106
7 Some Combinatorial Logic Examples 114
7.1 Channel Capacity, Shannon’s Theorem, and Error-Detection Theory 114
7.2 The Exclusive-OR Gate (XOR) 122
7.3 Error-Detection Logic 127
7.4 Error-Correction Theory 128
7.5 Error-Correction Logic 132
8 Sequential-State Digital Circuits 139
8.1 Two Sequential-State Problems 139
8.2 The NOR Latch 142
8.3 The Clocked RS Flip-Flop 146
8.4 More Flip-Flops 154
8.5 A Synchronous, Sequential-State Digital Machine Design Example 158
9 Turing Machines 161
9.1 The First Modern Computer 162
9.2 Two Turing Machines 164
9.3 Numbers We Can’t Compute 168
10 Beyond Boole and Shannon 176
10.1 Computation and Fundamental Physics 176
10.2 Energy and Information 178
10.3 Logically Reversible Gates 180
10.4 Thermodynamics of Logic 184
10.5 A Peek into the Twilight Zone: Quantum Computers 188
10.6 Quantum Logic—and Time Travel, Too! 197
Epilogue For the Future: The Anti-Amphibological Machine 210
Appendix Fundamental Electric Circuit Concepts 219

Sugestão de tibu