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Proof and Proving in Mathematics Education
*THIS BOOK IS AVAILABLE AS OPEN ACCESS BOOK ON SPRINGERLINK* One of the most significant tasks facing mathematics educators is to understand the role of mathematical reasoning and proving in mathematics teaching, so that its presence in instruction can be enhanced. This challenge has been given even greater importance by the assignment to proof of a more prominent place in the mathematics curriculum at all levels. Along with this renewed emphasis, there has been an upsurge in research on the teaching and learning of proof at all grade levels, leading to a re-examination of the role of proof in the curriculum and of its relation to other forms of explanation, illustration and justification. T...
Powerful Arguments
The essays in Powerful Arguments reconstruct the standards of validity underlying argumentative practices in a wide array of late imperial Chinese discourses, from the Song through the Qing dynasties. The fourteen case studies analyze concrete arguments defended or contested in areas ranging from historiography, philosophy, law, and religion to natural studies, literature, and the civil examination system. By examining uses of evidence, habits of inference, and the criteria by which some arguments were judged to be more persuasive than others, the contributions recreate distinct cultures of reasoning. Together, they lay the foundations for a history of argumentative practice in one of the richest scholarly traditions outside of Europe and add a chapter to the as yet elusive global history of rationality.
Statecraft and Intellectual Renewal in Late Ming China
This is the first comprehensive work on one of the key figures in early Chinese-Western relations. Xu Guangqi was one of the first promoters of Western science in China, worked together with the Jesuit Matteo Ricci on translations of Western science, was one of the first Chinese converts, a high-ranking statesman, organizer of a major calendar reform, introduced Western weapons into the Chinese army, etc. etc. His astonishingly multifarious activities are now for the first time pieced together within their (Chinese and Western) social, intellectual and cultural context. The result is a composite profile of this complex figure that is solidly anchored in Chinese (and Western) primary sources A major achievement.
Philosophy and Conceptual History of Science in Taiwan
Scholarly studies of mathematics and the sciences, carried out by philos ophers and historians in Taiwan in recent years, have two main goals: first, positive and critical participation in the logical analysis of scientific theories and scientific explanation; and second, conceptual clarification joined with faithful historical investigation of the sciences of traditional and modem China. In this book, Professors Cheng-hung Lin and Daiwie Fu have gathered fine representative essays from both endeavors. Their two introductory discussions guide the reader in three ways. First, we have insightful remarks concerning the development of science studies in Taiwan during the past three decades. Then we see the place of such studies, particularly those in the logic and methodology of science, in the philosophy of science as that discipline has evolved in the West in recent years. Finally we have an account of the changes that have occurred among philosophers and historians of Chinese science as they have turned away from an assump tion of Western definitions of scientific achievement, a tum that is common to Taiwanese, Chinese, Japanese and Western scholars.
A History of Chinese Mathematics
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.
A History of Mathematical Impossibility
Many of the most famous results in mathematics are impossibility theorems stating that something cannot be done. Good examples include the quadrature of the circle by ruler and compass, the solution of the quintic equation by radicals, Fermat's last theorem, and the impossibility of proving the parallel postulate from the other axioms of Euclidean geometry. This book tells the history of these and many other impossibility theorems starting with the ancient Greek proof of the incommensurability of the side and the diagonal in a square. Lützen argues that the role of impossibility results have changed over time. At first, they were considered rather unimportant meta-statements concerning math...
The New Era in American Mathematics, 1920–1950
"The 1920s witnessed the birth of a serious mathematical research community in America. Prior to this, mathematical research was dominated by scholars based in Europe-but World War I had made the importance of scientific and technological development clear to the American research community, resulting in the establishment of new scientific initiatives and infrastructure. Physics and chemistry were the beneficiaries of this renewed scientific focus, but the mathematical community also benefitted, and over time, began to flourish. Over the course of the next two decades, despite significant obstacles, this constellation of mathematical researchers, programs, and government infrastructure would...
John Fryer and The Translator’s Vade-mecum
This book is the winner of the Marthe Engelborghs-Bertels Prize for Sinology 2023, awarded by the Academy for Overseas Sciences (ARSOM), Brussels. In John Fryer and The Translator’s Vade-mecum, Tola offers for the first time a comprehensive study of the collection of scientific and technical glossaries, with English-Chinese parallel translation, compiled by the English scholar John Fryer (1839–1928). Other than contributing to the history of modern Chinese lexicon and translation in late Qing China, Tola analyses the role of The Translator’s Vade-mecum in the diffusion of ideas and terms between China and the West, at the same time providing new insights on the connection between religious efforts by missionaries in late Qing China and their secular attitude towards translation. The great number of resources presented also show a new perspective on the transcultural flows of knowledge, China’s modernisation process in the nineteenth and twentieth centuries and the history of nineteenth-century Protestant missions in China.
Max Dehn
Max Dehn (1878?1952) is known to mathematicians today for his seminal contributions to geometry and topology?Dehn surgery, Dehn twists, the Dehn invariant, etc. He is also remembered as the first mathematician to solve one of Hilbert?s famous problems. However, Dehn's influence as a scholar and teacher extended far beyond his mathematics. Dehn also lived a remarkable life, described in this book in three phases. The first phase focuses on his early career as one of David Hilbert?s most gifted students. The second, after World War I, treats his time in Frankfurt where he led an intimate community of mathematicians in explorations of historical texts. The final phase, after 1938, concerns his flight from Nazi Germany to Scandinavia and eventually to the United States where, after various teaching experiences, the Dehns settled at iconic Black Mountain College. This book is a collection of essays written by mathematicians and historians of art and science. It treats Dehn?s mathematics and its influence, his journeys, and his remarkable engagement in history and the arts. A great deal of the information found in this book has never before been published.
The First Sourcebook on Asian Research in Mathematics Education - 2 Volumes
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 regio...
