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A History of Chinese Mathematics by Jean-Claude Martzloff Pdf
This book is made up of two parts, the first devoted to general, historical and cultural background, and the second to the development of each subdiscipline that together comprise Chinese mathematics. The book is uniquely accessible, both as a topical reference work, and also as an overview that can be read and reread at many levels of sophistication by both sinologists and mathematicians alike.
The book has been written by an international group of very activeresearchers and scholars who have a passion for the study of Chinesemathematics education. It aims to provide readers with a comprehensiveand updated picture of the teaching and learning of mathematicsinvolving Chinese students from various perspectives, including theways in which Chinese students learn mathematics in classrooms, schools and homes, the influence of the cultural and socialenvironment on Chinese students'' mathematics learning, and thestrengths and weaknesses of the ways in which Chinese learnmathematics
Chinese Mathematics in the Thirteenth Century by Ulrich Libbrecht Pdf
An exploration of the life and work of the thirteenth-century mathematician Ch'in, this fascinating book examines a range of mathematical issues that reflect Chinese life of a millennium ago. Its first part consists of four closely related studies of Ch'in and his work. The first study brings together what is known of the mathematician's life and of the history of his only extant work, the Shu-shu chiu-chang. Subsequent studies examine the entire range of mathematical techniques and problems found within Ch'in's book. The core of this book consists of an in-depth study of what modern mathematicians still refer to as the Chinese remainder theorem for the solution of indeterminate equations of the first degree. This was Ch'in's most original contribution to mathematics--so original that no one could correctly explain Ch'in's procedure until the early nineteenth century. This volume's concluding study unites information on artisanal, economic, administrative, and military affairs dispersed throughout Ch'in's writings, providing rare insights into thirteenth-century China.
The book provides highlights on the key concepts and trends of evolution in Chinese Mathematics History, as one of the series of books of “China Classified Histories”.
Reviving Ancient Chinese Mathematics by Jiri Hudecek Pdf
Twentieth-century China has been caught between a desire to increase its wealth and power in line with other advanced nations, which, by implication, means copying their institutions, practices and values, whilst simultaneously seeking to preserve China’s independence and historically formed identity. Over time, Chinese philosophers, writers, artists and politicians have all sought to reconcile these goals and this book shows how this search for a Chinese way penetrated even the most central, least contested area of modernity: science. Reviving Ancient Chinese Mathematics is a study of the life of one of modern China’s most admired scientific figures, the mathematician Wu Wen-Tsun. Negotiating the conflict between progress and tradition, he found a path that not only ensured his political and personal survival, but which also brought him renown as a mathematician of international status who claimed that he stood outside the dominant western tradition of mathematics. Wu Wen-Tsun’s story highlights crucial developments and contradictions in twentieth -century China, the significance of which extends far beyond the field of mathematics. On one hand lies the appeal of radical scientific modernity, "mechanisation" in all its forms, and competitiveness within the international scientific community. On the other is an anxiety to preserve national traditions and make them part of the modernisation project. Moreover, Wu’s intellectual development also reflects the complex relationship between science and Maoist ideology, because his turn to history was powered by his internalisation of certain aspects of Maoist ideology, including its utilitarian philosophy of science. This book traces how Wu managed to combine political success and international scientific eminence, a story that has wider implications for a new century of increasing Chinese activity in the sciences. As such, it will be of great interest to students and scholars of Chinese history, the history of science and the history and philosophy of mathematics.
The Mathematics of Egypt, Mesopotamia, China, India, and Islam by Victor J. Katz,Annette Imhausen Pdf
In recent decades it has become obvious that mathematics has always been a worldwide activity. But this is the first book to provide a substantial collection of English translations of key mathematical texts from the five most important ancient and medieval non-Western mathematical cultures, and to put them into full historical and mathematical context. The Mathematics of Egypt, Mesopotamia, China, India, and Islam gives English readers a firsthand understanding and appreciation of these cultures' important contributions to world mathematics. The five section authors--Annette Imhausen (Egypt), Eleanor Robson (Mesopotamia), Joseph Dauben (China), Kim Plofker (India), and J. Lennart Berggren (Islam)--are experts in their fields. Each author has selected key texts and in many cases provided new translations. The authors have also written substantial section introductions that give an overview of each mathematical culture and explanatory notes that put each selection into context. This authoritative commentary allows readers to understand the sometimes unfamiliar mathematics of these civilizations and the purpose and significance of each text. Addressing a critical gap in the mathematics literature in English, this book is an essential resource for anyone with at least an undergraduate degree in mathematics who wants to learn about non-Western mathematical developments and how they helped shape and enrich world mathematics. The book is also an indispensable guide for mathematics teachers who want to use non-Western mathematical ideas in the classroom.
Astronomy and Calendars – The Other Chinese Mathematics by Jean-Claude Martzloff Pdf
Presented from the viewpoint of the history of mathematics, this book explores both epistemological aspects of Chinese traditional mathematical astronomy and lunisolar calendrical calculations. The following issues are addressed: (1) connections with non-Chinese cultural areas; (2) the possibility or impossibility of using mathematics to predict astronomical phenomena, a question that was constantly raised by the Chinese from antiquity through medieval times; (3) the modes of representation of numbers, and in particular the zero, found in the context of Chinese calendrical calculations; and (4) a detailed analysis of lunisolar calendrical calculations. Fully worked-out examples and comparisons between the results of calculations and the content of Chinese historical calendars from various periods are provided. Traditional Chinese calendrical and mathematical astronomy consists of permanently reformed mathematical procedures designed to predict, but not explain, phenomena pertaining to astronomy and related areas. Yet, despite appearances, models of the mathematical techniques hidden behind this voluminous corpus reveal that they depend on a limited number of clear-cut mathematical structures. Although only a small fraction of these techniques have been fully studied, what is known surprisingly broadens our knowledge of the history of Chinese mathematics. Sinologists interested in the history of Chinese science, and anyone interested in the history of Chinese mathematics, the Chinese calendar, and the history of Chinese mathematical astronomy from its origin (104 BC) to its European reform (AD 1644) will find this book very useful. The present English language edition is a fully revised and updated version of the French original. Even though this is a research monograph in sinology, no particular sinological background is required, although a basic understanding of ‘concrete mathematics’ is needed. From the reviews of the French edition: This is a demanding, rigorous book to read ... worth the concentrated study it requires. The rewards are not only in the details but in the general overview that ...[it] provides. Joseph Dauben, EASTM, 2011 ...first Work in a Western language to turn to for anyone interested in the details of Chinese calendrical computations. Benno Van Dalen, ISIS, 2011 Martzloff’s careful scholarship and his overall look at the calendar beyond astronomical calculations, ..., make this book a most valuable contributions to a field of increasing interest. U. D’Ambrosio, Mathematical Reviews, 2013
This volume presents a record of mathematical developments in China over a period of more than 2000 years. It goes into greater detail than ever previously available in English. Because the emphasis in Chinese mathematics is on algorithms rather than proofs, readers will find results such as Bezout's theorem and Horner's method appearing in a very different context from the familiar tradition of Euclidean deductive geometry. The Chinese always preferred algebraic methods, and by the 13th century A.D. they were the best algebraists in the world. The original Chinese point of view is retained by the translators. They have supplemented the text with short explanatory comments and references to all relevant reference sources available in the West. An extensive bibliography is included, creating a work which will appeal to general readers interested in Chinese history as well as historians of mathematics.
The Chinese Roots of Linear Algebra by Roger Hart Pdf
A monumental accomplishment in the history of non-Western mathematics, The Chinese Roots of Linear Algebra explains the fundamentally visual way Chinese mathematicians understood and solved mathematical problems. It argues convincingly that what the West "discovered" in the sixteenth and seventeenth centuries had already been known to the Chinese for 1,000 years. Accomplished historian and Chinese-language scholar Roger Hart examines Nine Chapters of Mathematical Arts—the classic ancient Chinese mathematics text—and the arcane art of fangcheng, one of the most significant branches of mathematics in Imperial China. Practiced between the first and seventeenth centuries by anonymous and most likely illiterate adepts, fangcheng involves manipulating counting rods on a counting board. It is essentially equivalent to the solution of systems of N equations in N unknowns in modern algebra, and its practice, Hart reveals, was visual and algorithmic. Fangcheng practitioners viewed problems in two dimensions as an array of numbers across counting boards. By "cross multiplying" these, they derived solutions of systems of linear equations that are not found in ancient Greek or early European mathematics. Doing so within a column equates to Gaussian elimination, while the same operation among individual entries produces determinantal-style solutions. Mathematicians and historians of mathematics and science will find in The Chinese Roots of Linear Algebra new ways to conceptualize the intellectual development of linear algebra.
How Chinese Teach Mathematics by Lianghuo Fan,Ngai-Ying Wong,Jinfa Cai,Shiqi Li Pdf
This unique book represents another concerted research effort concerning Chinese mathematics education, with contributions from the world's leading scholars and most active researchers. The book presents the latest original research work with a particular focus on the "teaching" side of Chinese mathematics education to a wide international audience. There are mainly three sections in the book. The first section introduces readers to a historical and contemporary perspective, respectively, on traditional mathematical teaching in ancient China and on how modern Chinese mathematics teachers teach and pursue their pre-service training and in-service professional development. The second section presents studies investigating a wide range of issues at both the macro- and micro-levels on how Chinese mathematics teachers teach mathematics. The third section focuses on Chinese mathematics teachers, investigating issues about their knowledge, belief, teacher training and professional development. Like its predecessor, How Chinese Learn Mathematics: Perspectives from Insiders, this book is a must for educational researchers, practitioners, and policy-makers who are interested in knowing more about mathematics teaching, teachers, teacher education and professional development concerning Chinese teachers and learners. Contents:Focusing on Chinese Mathematics Teaching, Teachers and Teacher Education: An IntroductionHistorical and Contemporary Perspectives:The Wisdom of Traditional Mathematical Teaching in China (DAI Qin and CHEUNG Ka Luen) How Chinese Teachers Teach Mathematics and Pursue Professional Development: Perspectives from ContemporaryInternational Research (FAN Lianghuo, MIAO Zhenzhen and MOK Ah Chee Ida) Understanding the Chinese Ways of Teaching Mathematics: Mathematics Teaching in a Chinese Classroom: A Hybrid-Model Analysis of Opportunities for Students' Learning (HUANG Rongjin, MILLER L Diane and TZUR Ron)Achieving Coherence in the Mathematics Classroom: Toward a Framework for Examining Instructional Coherence (WANG Tao, CAI Jinfa and HWANG Stephen) Elementary School Teachers' Instruction in Measurement: Cases of Classroom Teaching of Spatial Measurement in Taiwan (HUANG Hsin-Mei E) Pedagogical and Curriculum Potentials of Homework: A Case Study about Geometric Proofs in Shanghai (FANG Yanping) Teaching Calculation of Time Intervals: Comparing Mathematics Competence of Students in Macau, Hong Kong and the Netherlands (LI Titus Siu Pang) Teaching Number Sense via Interactive Multimedia in a Primary School in Taiwan (YANG Der-Ching, CHEN Pei-Chieh, TSAI Yi Fang and HSIEH Tien-Yu)Teaching Geometrical Theorems in Grade 8 Using the “Shen Tou” Method: A Case Study in Shanghai (DING Liping, JONES Keith and ZHANG Dianzhou) Implementation of Objectives Based on the Curriculum Standards: A Case of Teaching Using Letter to Represent Number at a Chinese Primary School in Chinese Mainland (HUANG Xingfeng, YANG Jinglei and LI Shiqi) Chinese Project-based Classroom Practices: Promoting Students' Engagement in Mathematical Activities (XU Binyan and ZHU Guangtian)A Large-Scale Video Survey on Taiwanese Fourth-Grade Classrooms of Mathematical Teaching Behaviors (LEE Yuan-Shun and LIN Fou-Lai) Features of Exemplary Lessons under the Curriculum Reform in Chinese Mainland: A Study of Thirteen Elementary Mathematics Lessons (MA Yunpeng and ZHAO Dongchen) Qingpu Mathematics Teaching Reform and Its Impact on Student Learning (GU Lingyuan, YANG Yudong and HE Zhenzhen)Chinese Mathematics Teachers, Teacher Education and Teacher Professional Development:Beliefs, Knowledge and Teaching: A Series of Studies about Chinese Mathematics Teachers (ZHANG Qiaoping and WONG Ngai-Ying)What Makes a Master Teacher? A Study of Thirty-One Mathematics Master Teachers in Chinese Mainland (FAN Lianghuo, ZHU Yan and TANG Caibin)Chinese Teachers' Mathematics Beliefs in the Context of Curriculum Reform (CHEN Qian and LEUNG Koon Shing Frederick) "Same Content Different Designs" Activities and Their Impact on Prospective Mathematics Teachers' Professional Development: The Case of Nadine (YUAN Zhiqiang and LI Xuhui)Exploration into Chinese Mathematics Teachers' Perceptions of Concept Map (JIN Haiyue, LU Jun and ZHONG Zhihua) Assisting Teachers in Maintaining High-Level Cognitive Demands of Mathematical Tasks in Classroom Practices: A Training Course in Taiwan (LIN Pi-Jen and TSAI Wen-Huan) The Relationships between Religious Beliefs and Teaching among Mathematics Teachers in Chinese Mainland, Taiwan and Hong Kong (LEU Yuh-Chyn, CHAN Yip-Cheung and WONG Ngai-Ying)Epilogue: Why the Interest in the Chinese Learner? (FAN Lianghuo, WONG Ngai-Ying, CAI Jinfa and LI Shiqi) Readership: Researchers, educators, lecturers, and graduate students in mathematics and education. Keywords:Mathematics;Mathematics Teaching and Learning;Mathematics Education;Chinese Education;China Study;Asian EducationKey Features:Concerted research effort. The book is well-planned, structured, and organizedUnique treatment of the topic: comprehensive and in-depth coverage on teaching, teacher, and teacher education for a wide range of international readersProminent authors and contributors: Many of them are the world's leading scholars or most active researchers
Chinese Mathematical Astrology by Ho Peng Yoke Pdf
Though there are a number of well-written works on Chinese divination, there are none that deal with the three sophisticated devices that were employed by the Chinese Astronomical Bureau in the eleventh century and for hundreds of years thereafter. Chinese experts applied the methods associated with these devices to both weather forecasting and to the interpretation of human affairs. Hidden by a veil of secrecy, these methods have always been relatively little known other than by their names. The first work in any language to explore these three methods, known as sanshi (three cosmic boards), this book sheds light on a topic which has been shrouded in mystery for centuries, having been kept secret for many years by the Chinese Astronomical Bureau.
Knowing and Teaching Elementary Mathematics by Liping Ma Pdf
Studies of teachers in the U.S. often document insufficient subject matter knowledge in mathematics. Yet, these studies give few examples of the knowledge teachers need to support teaching, particularly the kind of teaching demanded by recent reforms in mathematics education. Knowing and Teaching Elementary Mathematics describes the nature and development of the knowledge that elementary teachers need to become accomplished mathematics teachers, and suggests why such knowledge seems more common in China than in the United States, despite the fact that Chinese teachers have less formal education than their U.S. counterparts. The anniversary edition of this bestselling volume includes the original studies that compare U.S and Chinese elementary school teachers’ mathematical understanding and offers a powerful framework for grasping the mathematical content necessary to understand and develop the thinking of school children. Highlighting notable changes in the field and the author’s work, this new edition includes an updated preface, introduction, and key journal articles that frame and contextualize this seminal work.
The 21st Century Mathematics Education in China by Yiming Cao,Frederick K.S. Leung Pdf
This book intends to provide a comprehensive introduction to the status of development of Chinese mathematics education in the 21st century. To this end, the book summarizes and presents the research and practices of Chinese mathematics education in the following aspects: (1) characteristics of Chinese school mathematics curriculum and textbooks, (2) Chinese ways and strategies of teaching mathematics and the characteristics of mathematics classroom instruction in China, (3) Chinese instructional practices in developing (both gifted and underachieving) students’ mathematical capabilities, (4) how professional development of mathematics teachers is promoted in China, including mathematics teachers’ pre-service and in-service education, and how Chinese mathematics teachers design and implement teaching and research activities, and (5) how mathematics education is assessed and evaluated, including how to evaluate teachers’ teaching and students’ achievements. Relevant research in Chinese mathematics education involving methods of surveys, interviews, text analysis, etc., are reviewed and analyzed. Results of a number of video studies of Chinese mathematics classroom teaching and learning are also integrated into this book.
Science and Civilisation in China: Volume 3, Mathematics and the Sciences of the Heavens and the Earth by Joseph Needham Pdf
After two volumes mainly introductory, Dr Needham now embarks upon his systematic study of the development of the natural sciences in China. The Sciences of the Earth follow: geography and cartography, geology, seismology and mineralogy. Dr Needham distinguishes parallel traditions of scientific cartography and religious cosmography in East and West, discussing orbocentric wheel-maps, the origins of the rectangular grid system, sailing charts and relief maps, Chinese survey methods, and the impact of Renaissance cartography on the East. Finally-and here Dr Needham's work has no Western predecessors-there are full accounts of the Chinese contribution to geology and mineralogy.
The Mathematics of Egypt, Mesopotamia, China, India, and Islam by Victor J. Katz Pdf
In recent decades it has become obvious that mathematics has always been a worldwide activity. But this is the first book to provide a substantial collection of English translations of key mathematical texts from the five most important ancient and medieval non-Western mathematical cultures, and to put them into full historical and mathematical context. The Mathematics of Egypt, Mesopotamia, China, India, and Islam gives English readers a firsthand understanding and appreciation of these cultures' important contributions to world mathematics. The five section authors—Annette Imhausen (Egypt), Eleanor Robson (Mesopotamia), Joseph Dauben (China), Kim Plofker (India), and J. Lennart Berggren (Islam)—are experts in their fields. Each author has selected key texts and in many cases provided new translations. The authors have also written substantial section introductions that give an overview of each mathematical culture and explanatory notes that put each selection into context. This authoritative commentary allows readers to understand the sometimes unfamiliar mathematics of these civilizations and the purpose and significance of each text. Addressing a critical gap in the mathematics literature in English, this book is an essential resource for anyone with at least an undergraduate degree in mathematics who wants to learn about non-Western mathematical developments and how they helped shape and enrich world mathematics. The book is also an indispensable guide for mathematics teachers who want to use non-Western mathematical ideas in the classroom.