Nerida Ellerton's Books

Rewriting the History of School Mathematics in North America 1607-1861

The Central Role of Cyphering Books

By: Nerida F. Ellerton,M. A. Ken Clements

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Rewriting the History of School Mathematics in North America 1607-1861

The Central Role of Cyphering Books

By: Nerida F. Ellerton,M. A. Ken Clements

The focus of this book is the fundamental influence of the cyphering tradition on mathematics education in North American colleges, schools, and apprenticeship training classes between 1607 and 1861. It is the first book on the history of North American mathematics education to be written from that perspective. The principal data source is a set of 207 handwritten cyphering books that have never previously been subjected to careful historical analysis.

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230

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Springer Science & Business Media

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ISBN 10

9400726384

ISBN 13

9789400726383

Samuel Pepys, Isaac Newton, James Hodgson, and the Beginnings of Secondary School Mathematics

A History of the Royal Mathematical School Within Christ’s Hospital, London 1673–1868

By: Nerida F. Ellerton,M. A. (Ken) Clements

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Samuel Pepys, Isaac Newton, James Hodgson, and the Beginnings of Secondary School Mathematics

A History of the Royal Mathematical School Within Christ’s Hospital, London 1673–1868

By: Nerida F. Ellerton,M. A. (Ken) Clements

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.

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340

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Springer

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ISBN 10

3319466577

ISBN 13

9783319466576

Abraham Lincoln’s Cyphering Book and Ten other Extraordinary Cyphering Books

By: Nerida F. Ellerton,M. A. (Ken) Clements

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Abraham Lincoln’s Cyphering Book and Ten other Extraordinary Cyphering Books

By: Nerida F. Ellerton,M. A. (Ken) Clements

This well-illustrated book provides strong qualitative and comparative support for the main arguments developed by Nerida Ellerton and Ken Clements in their groundbreaking Rewriting this History of School Mathematics in North America 1607–1861: The Central Role of Cyphering Books. Eleven extraordinary handwritten school mathematics manuscripts are carefully analyzed—six were prepared entirely in Great Britain, four entirely in North America, and 1 partly in Great Britain and partly in North America. The earliest of the 11 cyphering books was prepared around 1630, and the latest in 1835. Seven of the manuscripts were arithmetic cyphering books; three were navigation cyphering books, and one was a mensuration/surveying manuscript. One of the cyphering books examined in this book was prepared, over the period 1819–1826, by a young Abraham Lincoln, when he was attending small one-teacher schools in remote Spencer County, Indiana. Chapter 6 in this book provides the first detailed analysis of young Abraham’s cyphering book—which is easily the oldest surviving Lincoln manuscript. Another cyphering book, this one prepared by William Beattie in 1835, could have been prepared as a special gift for the King of England. The analyses make clear the extent of the control which the cyphering tradition had over school mathematics in North America and Great Britain between 1630 and 1840. In their final chapter Ellerton and Clements identify six lessons from their research into the cyphering tradition which relate to present-day circumstances surrounding school mathematics. These lessons are concerned with sharp differences between intended, implemented and attained curricula, the remarkable value that many students placed upon their cyphering books, the ethnomathematical circumstances which surrounded the preparations of the extraordinary cyphering books, and qualitative differences between British and North American school mathematics.

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383

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Springer Science & Business Media

Published Date

ISBN 10

3319025023

ISBN 13

9783319025025

Thomas Jefferson and his Decimals 1775–1810: Neglected Years in the History of U.S. School Mathematics

By: M.A. (Ken) Clements,Nerida F. Ellerton

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Thomas Jefferson and his Decimals 1775–1810: Neglected Years in the History of U.S. School Mathematics

By: M.A. (Ken) Clements,Nerida F. Ellerton

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.

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219

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Springer

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ISBN 10

3319025058

ISBN 13

9783319025056

Toward Mathematics for All

Reinterpreting History of Mathematics in North America 1607-1865

By: Nerida Ellerton,M. A. (Ken) Clements

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Toward Mathematics for All

Reinterpreting History of Mathematics in North America 1607-1865

By: Nerida Ellerton,M. A. (Ken) Clements

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.

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462

Publisher

Springer Nature

Published Date

ISBN 10

3030857247

ISBN 13

9783030857240

Rewriting the History of School Mathematics in North America 1607-1861

The Central Role of Cyphering Books

By: Nerida Ellerton,M.A. (Ken) Clements

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Rewriting the History of School Mathematics in North America 1607-1861

The Central Role of Cyphering Books

By: Nerida Ellerton,M.A. (Ken) Clements

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230

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Springer Science & Business Media

Published Date

ISBN 10

9400726392

ISBN 13

9789400726390

Abraham Lincoln’s Cyphering Book and Ten other Extraordinary Cyphering Books

By: Nerida F. Ellerton,M. A. (Ken) Clements

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Abraham Lincoln’s Cyphering Book and Ten other Extraordinary Cyphering Books

By: Nerida F. Ellerton,M. A. (Ken) Clements

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383

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Springer Science & Business Media

Published Date

ISBN 10

3319025023

ISBN 13

9783319025025

Using Design Research and History to Tackle a Fundamental Problem with School Algebra

By: Sinan Kanbir,M. A. (Ken) Clements,Nerida F. Ellerton

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Using Design Research and History to Tackle a Fundamental Problem with School Algebra

By: Sinan Kanbir,M. A. (Ken) Clements,Nerida F. Ellerton

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.

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339

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Springer

Published Date

ISBN 10

3319592041

ISBN 13

9783319592046

Toward Mathematics for All

Reinterpreting History of Mathematics in North America 1607-1865

By: Nerida Ellerton,M. A. (Ken) Clements

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Toward Mathematics for All

Reinterpreting History of Mathematics in North America 1607-1865

By: Nerida Ellerton,M. A. (Ken) Clements

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462

Publisher

Springer Nature

Published Date

ISBN 10

3030857247

ISBN 13

9783030857240

Thomas Jefferson and his Decimals 1775–1810: Neglected Years in the History of U.S. School Mathematics

By: M.A. (Ken) Clements,Nerida F. Ellerton

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Thomas Jefferson and his Decimals 1775–1810: Neglected Years in the History of U.S. School Mathematics

By: M.A. (Ken) Clements,Nerida F. Ellerton

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219

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Springer

Published Date

ISBN 10

3319025058

ISBN 13

9783319025056

Polya, Krutetskii and the Restaurant Problem

Reflections on Problem Solving in School Mathematics

By: M. A. Clements,Nerida F. Ellerton

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Polya, Krutetskii and the Restaurant Problem

Reflections on Problem Solving in School Mathematics

By: M. A. Clements,Nerida F. Ellerton

Prepared for units ECT405, ECT705 offered by the Faculty of Education in Deakin University's Open Campus Program.

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UNSW Press

Published Date

ISBN 10

0730012530

ISBN 13

9780730012535

Book's by Nerida Ellerton

Rewriting the History of School Mathematics in North America 1607-1861

Rewriting the History of School Mathematics in North America 1607-1861

Samuel Pepys, Isaac Newton, James Hodgson, and the Beginnings of Secondary School Mathematics

Samuel Pepys, Isaac Newton, James Hodgson, and the Beginnings of Secondary School Mathematics

Abraham Lincoln’s Cyphering Book and Ten other Extraordinary Cyphering Books

Abraham Lincoln’s Cyphering Book and Ten other Extraordinary Cyphering Books

Thomas Jefferson and his Decimals 1775–1810: Neglected Years in the History of U.S. School Mathematics

Thomas Jefferson and his Decimals 1775–1810: Neglected Years in the History of U.S. School Mathematics

Toward Mathematics for All

Toward Mathematics for All

Rewriting the History of School Mathematics in North America 1607-1861

Rewriting the History of School Mathematics in North America 1607-1861

Abraham Lincoln’s Cyphering Book and Ten other Extraordinary Cyphering Books

Abraham Lincoln’s Cyphering Book and Ten other Extraordinary Cyphering Books

Using Design Research and History to Tackle a Fundamental Problem with School Algebra

Using Design Research and History to Tackle a Fundamental Problem with School Algebra

Toward Mathematics for All

Toward Mathematics for All

Thomas Jefferson and his Decimals 1775–1810: Neglected Years in the History of U.S. School Mathematics

Thomas Jefferson and his Decimals 1775–1810: Neglected Years in the History of U.S. School Mathematics

Polya, Krutetskii and the Restaurant Problem

Polya, Krutetskii and the Restaurant Problem

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