Thomas Jefferson and his Decimals 1775–1810: Neglected Years in the History of U.S. School Mathematics PDF Download
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Author: M.A. (Ken) Clements
Publisher: Springer
ISBN: 3319025058
Category : Education
Languages : en
Pages : 219
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Book Description
This well-illustrated book, by two established historians of school mathematics, documents Thomas Jefferson’s quest, after 1775, to introduce a form of decimal currency to the fledgling United States of America. The book describes a remarkable study showing how the United States’ decision to adopt a fully decimalized, carefully conceived national currency ultimately had a profound effect on U.S. school mathematics curricula. The book shows, by analyzing a large set of arithmetic textbooks and an even larger set of handwritten cyphering books, that although most eighteenth- and nineteenth-century authors of arithmetic textbooks included sections on vulgar and decimal fractions, most school students who prepared cyphering books did not study either vulgar or decimal fractions. In other words, author-intended school arithmetic curricula were not matched by teacher-implemented school arithmetic curricula. Amazingly, that state of affairs continued even after the U.S. Mint began minting dollars, cents and dimes in the 1790s. In U.S. schools between 1775 and 1810 it was often the case that Federal money was studied but decimal fractions were not. That gradually changed during the first century of the formal existence of the United States of America. By contrast, Chapter 6 reports a comparative analysis of data showing that in Great Britain only a minority of eighteenth- and nineteenth-century school students studied decimal fractions. Clements and Ellerton argue that Jefferson’s success in establishing a system of decimalized Federal money had educationally significant effects on implemented school arithmetic curricula in the United States of America. The lens through which Clements and Ellerton have analyzed their large data sets has been the lag-time theoretical position which they have developed. That theory posits that the time between when an important mathematical “discovery” is made (or a concept is “created”) and when that discovery (or concept) becomes an important part of school mathematics is dependent on mathematical, social, political and economic factors. Thus, lag time varies from region to region, and from nation to nation. Clements and Ellerton are the first to identify the years after 1775 as the dawn of a new day in U.S. school mathematics—traditionally, historians have argued that nothing in U.S. school mathematics was worthy of serious study until the 1820s. This book emphasizes the importance of the acceptance of decimal currency so far as school mathematics is concerned. It also draws attention to the consequences for school mathematics of the conscious decision of the U.S. Congress not to proceed with Thomas Jefferson’s grand scheme for a system of decimalized weights and measures.
Author: M.A. (Ken) Clements
Publisher: Springer
ISBN: 3319025058
Category : Education
Languages : en
Pages : 219
Get Book Here
Book Description
This well-illustrated book, by two established historians of school mathematics, documents Thomas Jefferson’s quest, after 1775, to introduce a form of decimal currency to the fledgling United States of America. The book describes a remarkable study showing how the United States’ decision to adopt a fully decimalized, carefully conceived national currency ultimately had a profound effect on U.S. school mathematics curricula. The book shows, by analyzing a large set of arithmetic textbooks and an even larger set of handwritten cyphering books, that although most eighteenth- and nineteenth-century authors of arithmetic textbooks included sections on vulgar and decimal fractions, most school students who prepared cyphering books did not study either vulgar or decimal fractions. In other words, author-intended school arithmetic curricula were not matched by teacher-implemented school arithmetic curricula. Amazingly, that state of affairs continued even after the U.S. Mint began minting dollars, cents and dimes in the 1790s. In U.S. schools between 1775 and 1810 it was often the case that Federal money was studied but decimal fractions were not. That gradually changed during the first century of the formal existence of the United States of America. By contrast, Chapter 6 reports a comparative analysis of data showing that in Great Britain only a minority of eighteenth- and nineteenth-century school students studied decimal fractions. Clements and Ellerton argue that Jefferson’s success in establishing a system of decimalized Federal money had educationally significant effects on implemented school arithmetic curricula in the United States of America. The lens through which Clements and Ellerton have analyzed their large data sets has been the lag-time theoretical position which they have developed. That theory posits that the time between when an important mathematical “discovery” is made (or a concept is “created”) and when that discovery (or concept) becomes an important part of school mathematics is dependent on mathematical, social, political and economic factors. Thus, lag time varies from region to region, and from nation to nation. Clements and Ellerton are the first to identify the years after 1775 as the dawn of a new day in U.S. school mathematics—traditionally, historians have argued that nothing in U.S. school mathematics was worthy of serious study until the 1820s. This book emphasizes the importance of the acceptance of decimal currency so far as school mathematics is concerned. It also draws attention to the consequences for school mathematics of the conscious decision of the U.S. Congress not to proceed with Thomas Jefferson’s grand scheme for a system of decimalized weights and measures.
Author: Nerida F. Ellerton
Publisher: Springer
ISBN: 3319466577
Category : Education
Languages : en
Pages : 340
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Book Description
This book tells one of the greatest stories in the history of school mathematics. Two of the names in the title—Samuel Pepys and Isaac Newton—need no introduction, and this book draws attention to their special contributions to the history of school mathematics. According to Ellerton and Clements, during the last quarter of the seventeenth century Pepys and Newton were key players in defining what school mathematics beyond arithmetic and elementary geometry might look like. The scene at which most of the action occurred was Christ’s Hospital, which was a school, ostensibly for the poor, in central London. The Royal Mathematical School (RMS) was established at Christ’s Hospital in 1673. It was the less well-known James Hodgson, a fine mathematician and RMS master between 1709 and 1755, who demonstrated that topics such as logarithms, plane and spherical trigonometry, and the application of these to navigation, might systematically and successfully be taught to 12- to 16-year-old school children. From a wider history-of-school-education perspective, this book tells how the world’s first secondary-school mathematics program was created and how, slowly but surely, what was being achieved at RMS began to influence school mathematics in other parts of Great Britain, Europe, and America. The book has been written from the perspective of the history of school mathematics. Ellerton and Clements’s analyses of pertinent literature and of archival data, and their interpretations of those analyses, have led them to conclude that RMS was the first major school in the world to teach mathematics-beyond-arithmetic, on a systematic basis, to students aged between 12 and 16. Throughout the book, Ellerton and Clements examine issues through the lens of a lag-time theoretical perspective. From a historiographical perspective, this book emphasizes how the history of RMS can be portrayed in very different ways, depending on the vantage point from which the history is written. The authors write from the vantage point of international developments in school mathematics education and, therefore, their history of RMS differs from all other histories of RMS, most of which were written from the perspective of the history of Christ’s Hospital.
Author: Nerida Ellerton
Publisher: Springer Nature
ISBN: 3030857247
Category : Mathematics
Languages : en
Pages : 462
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Book Description
This book presents a history of mathematic between 1607 and 1865 in that part of mainland North America which is north of Mexico but excludes the present-day Canada and Alaska. Unlike most other histories of mathematics now available, the emphasis is on the gradual emergence of "mathematics for all" programs and associated changes in thinking which drove this emergence. The book takes account of changing ideas about intended, implemented and attained mathematics curricula for learners of all ages. It also pays attention to the mathematics itself, and to how it was taught and learned.
Author: David E. Zitarelli
Publisher: American Mathematical Society
ISBN: 1470472570
Category : Mathematics
Languages : en
Pages : 500
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Book Description
This is the first truly comprehensive and thorough history of the development of mathematics and a mathematical community in the United States and Canada. This first volume of the multi-volume work takes the reader from the European encounters with North America in the fifteenth century up to the emergence of a research community the United States in the last quarter of the nineteenth. In the story of the colonial period, particular emphasis is given to several prominent colonial figures—Jefferson, Franklin, and Rittenhouse—and four important early colleges—Harvard, Québec, William & Mary, and Yale. During the first three-quarters of the nineteenth century, mathematics in North America was largely the occupation of scattered individual pioneers: Bowditch, Farrar, Adrain, B. Peirce. This period is given a fuller treatment here than previously in the literature, including the creation of the first PhD programs and attempts to form organizations and found journals. With the founding of Johns Hopkins in 1876 the American mathematical research community was finally, and firmly, founded. The programs at Hopkins, Chicago, and Clark are detailed as are the influence of major European mathematicians including especially Klein, Hilbert, and Sylvester. Klein's visit to the US and his Evanston Colloquium are extensively detailed. The founding of the American Mathematical Society is thoroughly discussed. David Zitarelli was emeritus Professor of Mathematics at Temple University. A decorated and acclaimed teacher, scholar, and expositor, he was one of the world's leading experts on the development of American mathematics. Author or co-author of over a dozen books, this was his magnum opus—sure to become the leading reference on the topic and essential reading, not just for historians. In clear and compelling prose Zitarelli spins a tale accessible to experts, generalists, and anyone interested in the history of science in North America.
Author: David E. Zitarelli
Publisher: American Mathematical Soc.
ISBN: 1470448297
Category : Education
Languages : en
Pages : 501
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Book Description
This is the first truly comprehensive and thorough history of the development of mathematics and a mathematical community in the United States and Canada. This first volume of the multi-volume work takes the reader from the European encounters with North America in the fifteenth century up to the emergence of a research community the United States in the last quarter of the nineteenth. In the story of the colonial period, particular emphasis is given to several prominent colonial figures—Jefferson, Franklin, and Rittenhouse—and four important early colleges—Harvard, Québec, William & Mary, and Yale. During the first three-quarters of the nineteenth century, mathematics in North America was largely the occupation of scattered individual pioneers: Bowditch, Farrar, Adrain, B. Peirce. This period is given a fuller treatment here than previously in the literature, including the creation of the first PhD programs and attempts to form organizations and found journals. With the founding of Johns Hopkins in 1876 the American mathematical research community was finally, and firmly, founded. The programs at Hopkins, Chicago, and Clark are detailed as are the influence of major European mathematicians including especially Klein, Hilbert, and Sylvester. Klein's visit to the US and his Evanston Colloquium are extensively detailed. The founding of the American Mathematical Society is thoroughly discussed. David Zitarelli was emeritus Professor of Mathematics at Temple University. A decorated and acclaimed teacher, scholar, and expositor, he was one of the world's leading experts on the development of American mathematics. Author or co-author of over a dozen books, this was his magnum opus—sure to become the leading reference on the topic and essential reading, not just for historians. In clear and compelling prose Zitarelli spins a tale accessible to experts, generalists, and anyone interested in the history of science in North America.
Author: Sinan Kanbir
Publisher: Springer
ISBN: 3319592041
Category : Education
Languages : en
Pages : 339
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Book Description
In this well-illustrated book the authors, Sinan Kanbir, Ken Clements, and Nerida Ellerton, tackle a persistent, and universal, problem in school mathematics—why do so many middle-school and secondary-school students find it difficult to learn algebra well? What makes the book important are the unique features which comprise the design-research approach that the authors adopted in seeking a solution to the problem. The first unique feature is that the authors offer an overview of the history of school algebra. Despite the fact that algebra has been an important component of secondary-school mathematics for more than three centuries, there has never been a comprehensive historical analysis of factors influencing the teaching and learning of that component. The authors identify, through historical analysis, six purposes of school algebra: (a) algebra as a body of knowledge essential to higher mathematical and scientific studies, (b) algebra as generalized arithmetic, (c) algebra as a prerequisite for entry to higher studies, (d) algebra as offering a language and set of procedures for modeling real-life problems, (e) algebra as an aid to describing structural properties in elementary mathematics, and (f) algebra as a study of variables. They also raise the question whether school algebra represents a unidimensional trait. Kanbir, Clements and Ellerton offer an unusual hybrid theoretical framework for their intervention study (by which seventh-grade students significantly improved their elementary algebra knowledge and skills). Their theoretical frame combined Charles Sanders Peirce’s triadic signifier-interpretant-signified theory, which is in the realm of semiotics, with Johann Friedrich Herbart’s theory of apperception, and Ken Clements’ and Gina Del Campo’s theory relating to the need to expand modes of communications in mathematics classrooms so that students engage in receptive and expressive modes. Practicing classroom teachers formed part of the research team. This book appears in Springer’s series on the “History of Mathematics Education.” Not only does it include an important analysis of the history of school algebra, but it also adopts a theoretical frame which relies more on “theories from the past,” than on contemporary theories in the field of mathematics education. The results of the well-designed classroom intervention are sufficiently impressive that the study might havecreated and illuminated a pathway for future researchers to take.
Author: Alexander Karp
Publisher: Springer
ISBN: 3319316168
Category : Education
Languages : en
Pages : 47
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Book Description
This work examines the main directions of research conducted on the history of mathematics education. It devotes substantial attention to research methodologies and the connections between this field and other scholarly fields. The results of a survey about academic literature on this subject are accompanied by a discussion of what has yet to be done and problems that remain unsolved. The main topics you will find in “ICME-13 Topical Survey” include: • Discussions of methodological issues in the history of mathematics education and of the relation between this field and other scholarly fields. • The history of the formation and transformation of curricula and textbooks as a reflection of trends in social-economic, cultural and scientific-technological development. • The influence of politics, ideology and economics on the development of mathematics education, from a historical perspective. • The history of the preeminent mathematics education organizations and the work of leading figures in mathematics education. • Mathematics education practices and tools and the preparation of mathematics teachers, from a historical perspective.
Author: David Alan Grier
Publisher: Princeton University Press
ISBN: 1400849365
Category : Science
Languages : en
Pages : 423
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Book Description
Before Palm Pilots and iPods, PCs and laptops, the term "computer" referred to the people who did scientific calculations by hand. These workers were neither calculating geniuses nor idiot savants but knowledgeable people who, in other circumstances, might have become scientists in their own right. When Computers Were Human represents the first in-depth account of this little-known, 200-year epoch in the history of science and technology. Beginning with the story of his own grandmother, who was trained as a human computer, David Alan Grier provides a poignant introduction to the wider world of women and men who did the hard computational labor of science. His grandmother's casual remark, "I wish I'd used my calculus," hinted at a career deferred and an education forgotten, a secret life unappreciated; like many highly educated women of her generation, she studied to become a human computer because nothing else would offer her a place in the scientific world. The book begins with the return of Halley's comet in 1758 and the effort of three French astronomers to compute its orbit. It ends four cycles later, with a UNIVAC electronic computer projecting the 1986 orbit. In between, Grier tells us about the surveyors of the French Revolution, describes the calculating machines of Charles Babbage, and guides the reader through the Great Depression to marvel at the giant computing room of the Works Progress Administration. When Computers Were Human is the sad but lyrical story of workers who gladly did the hard labor of research calculation in the hope that they might be part of the scientific community. In the end, they were rewarded by a new electronic machine that took the place and the name of those who were, once, the computers.
Author: Gilbert Chinard
Publisher: Good Press
ISBN:
Category : Fiction
Languages : en
Pages : 623
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Book Description
This is an informational work on Thomas Jefferson, an American statesman, diplomat, lawyer, architect, philosopher, and Founding Father who served as the third president of the United States from 1801 to 1809. This book comprehensively reviews Thomas Jefferson's education and subsequent political thought. It's not just a biography of Thomas Jefferson but rather an examination of the evolution of his political thought. His views on truth, politics, religion, morality, and the relationships between European entanglements and business are interesting. Moreover, the author intertwines the biography with many quotes from the tremendous volume of letters and journals Jefferson maintained throughout his lifetime.
Author: Charles Lee Coon
Publisher:
ISBN:
Category : Education
Languages : en
Pages : 592
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Book Description
