Toward mathematics for all : reinterpreting history of mathematics in North America 1607-1865

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Preface to this Book References Preface to the Series List of Publications in the Springer Nature History of Mathematics Education Series Recent Springer Books on the History of Mathematics Education by Nerida F. Ellerton and M. A. (Ken) Clements Also Note: Contents List of Figures List of Tables Abstracts Abstract for the Book Abstracts for the Nine Individual Chapters Abstract for Chapter 1: ``The Scope of the Book´´ Abstract for Chapter 2: ``Young Children´s Introduction to Mathematics in North America Between 1607 and 1865´´ Abstract for Chapter 3: ``The Influence of the Cyphering Tradition on North American Elementary- and Middle-School Mathematics... Abstract for Chapter 4: ``Mathematics Textbooks and the Gradual Decline in the Use of Middle- to Advanced-Level Abbaco Arithme... Abstract for Chapter 5: ``The Struggle for Algebra´´ Abstract for Chapter 6: ``Pre-College Geometry, Mensuration, Trigonometry, Surveying, and Navigation 1607-1865´´ Abstract for Chapter 7: ``College Mathematics, 1607-1865´´ Abstract for Chapter 8: ``Different Perspectives on Mathematics in North America1607-1865´´ Abstract for Chapter 9: ``Toward Mathematics for All: Answers to Research Questions, Limitations, and Possibilities for Furthe... About the Authors Chapter 1: The Scope of This Book What is Mathematics? Mathematics Studied in North America in the Seventeenth Century Terminology Indigenous Counting Systems and the Coming of the Hindu-Arabic Numeration System Who Used the Hindu-Arabic Numeration System in North America, 1607-1699? The Abbaco Sequence for Arithmetic Differences in the Opportunity to Learn Abbaco Arithmetic in North America, 1607-1865 The Main Aims for This Book The Six Research Questions The Concept of ``School´´ in this Book Outline of Chapters in this Book References Chapter 2: Young Children´s Introduction to Mathematics in North America Between 1607 and 1865 Educating Young Children in North America, 1607-1799 Hornbook Education Florian Cajori´s (1890) Misleading Definition of the Hornbook Use of the Hornbook in Colonial North America A Research Imperative Andrew White Tuer´s Pioneering Work on the History of Hornbooks Hornbooks Currently Held in the United States of America Hornbooks, and the Mathematics Education of Young Children in North America in the Seventeenth and Eighteenth Centuries Dame Schools Battledores Summary: The Influence of the Hornbook Warren Colburn´s Challenge to Those Who Defined Intended and Implemented Mathematics Curricula for Young Children Changes in the Modes of Implementing Mathematics Curricula in U.S. Schools References Chapter 3: The Influence of the Cyphering Tradition on North American Elementary- and Middle-School Mathematics Between 1607 a... Mathematics Studied by Children Aged Between 10 and 16 The Cyphering Tradition Definition of a Cyphering Book Mathematics Content in the Cyphering Books-The Abbaco Sequence Pedagogy, Cyphering, Recitation, and the Cyphering Tradition Educational Rationale for the Cyphering Tradition The Ellerton and Clements Cyphering Book Collection The Extent of the Collection and its Documentation Although Cyphering Books Were Special and Private Creations, They Sometimes Included Important Historical Documents A 1774 protest letter. A Revolutionary War Oath of Allegiance. Some Special Cyphering Books The Oldest Extant North American Cyphering Book The Pine-Chichester (Long Island, New York) Composite Cyphering Book An Early Composite Cyphering Book, Started in England in 1702 and Completed in New Hampshire Between 1720 and 1722 A 1771 Cyphering Book Prepared by a Future Revolutionary War Solder A 1775-1777 Cyphering Book Prepared by a Revolutionary War Solder Apparently ``Ordinary´´ Cyphering Books Which Became Historically Interesting An Early Pennsylvania (1764-1767) Cyphering Book with Links to William Penn, President Theodore Roosevelt, and President John ... Samuel Fay´s (1817) Cyphering Book Elijah Allen Rockefeller´s (1825-1828) Cyphering Book A Teacher´s Cyphering Book, with an Emphasis on Rules and Cases Mathematical Errors or Questionable Procedures in Cyphering Books Intended, Implemented and Attained Curricular Considerations Concluding Comments and Questions Toward a More Coordinated Vision of the History of North American Mathematics References Chapter 4: Mathematics Textbooks and the Gradual Decline in the Use of Middle- to Advanced-Level Abbaco Arithmetic 1607-1865 Leading North American Mathematics Textbook Authors Between 1607 and 1865 Commentary on Mathematics Textbook Authors Whose Books Were Often Used in North American Schools Between 1607 and 1775 Robert Record(e) Edmund Wingate (and John Kersey) Edward Cocker James Hodder Isaac Greenwood Thomas Dilworth Authors from the Federal Period, 1787-1801 Nicolas Pike Benjamin Workman Consider Sterry and John Sterry Zachariah Jess and ``Sundry Teachers in and Near Philadelphia´´ Erastus Root Chauncey Lee Peter Tharp North American Authors from the Period 1800-1820 Nathan Daboll False position problems in Daboll Daniel Adams Michael Walsh Stephen Pike Overview of Middle- to Advanced-Level Abbaco Arithmetic Textbooks, 1776-1820 The Move Away from the Abbaco Sequence, 1820-1850 Warren Colburn´s Fundamental Challenge to Teachers of Mathematics Charles Davies´s Vision of a National Textbook Series Frederick Emerson (1787-1865) and the Concept of Ability in Mathematics Joseph Ray (1807-1855), a Best-Selling Author Benjamin Greenleaf Works Toward a National Curriculum The Abbaco Sequence Loses Popularity References Chapter 5: The Struggle for Algebra The Need for Algebra Mathematics Beyond the Abbaco Sequence: Evidence from Cyphering Books A Dutch-Language Textbook Published in New York in 1730, Which Included Algebra Pieter Venema Historical Errors Made in Commentaries on Pieter Venema Venema´s (1725) Precursor Manuscript Consider Sterry´s and John Sterry´s (1790) 147-Page Text on School Algebra Influence of British Authors Charles Hutton, Samuel Webber and Robert Adrain The Influence of John Bonnycastle on North American Mathematics Education Jeremiah Day´s (1814) Algebra-The First Dedicated Algebra Textbook Published in North America and Written by a U.S. Citizen Colburn´s, Bailey´s and Ray´s ``Inductive´´ Algebras, Written Specifically for Schools Warren Colburn´s (1825) An Introduction to Algebra Ebenezer Bailey´s (1833) An Introduction to Algebra Joseph Ray´s (1848) Elements of Algebra The Influence of French Approaches on Algebra Education in North America Charles Davies and School Algebra, 1818-1865 The Emergence of Normal Schools, and Its Effects on School Algebra The Effect of the Introduction of Written Examinations on Algebra Education Who Should Be Given the Most Credit for Improving School Algebra in North America? Epilogue to Chapter 5 An Alligation Question from Venema´s (c. 1725) Precursor References Chapter 6: Pre-College Geometry, Mensuration, Trigonometry, Surveying, and Navigation 1607-1865 How Much Geometry, Mensuration, Trigonometry, Surveying, and Navigation, Was Studied in Pre-College Education Institutions in ... Thomas Willson´s (1789) Composite Cyphering Book Thomas Willson´s (1789) Section on Gauging Thomas Willson´s (1789) Section on Geometry Thomas Willson´s (1789) Section on Mensuration Thomas Willson´s (1789) Section on Trigonometry Thomas Willson´s (1789) Section on Surveying Thomas Willson´s (1789) Section on Navigation Thomas Willson´s (1789) Log of a Journey Shortage of Teachers for ``Higher´´ Mathematics in Pre-College Schools Robert Lazenby Enoch Lewis Equity Considerations: Opportunity to Learn Opportunity to Learn Gender Considerations Built-in Inequalities Which Threatened to Hold Back Needed Developments Geometry in North American Pre-College Educational Institutions, 1607-1865 The Push for Legendre´s Geometry Trigonometry, Mensuration, Surveying and Navigation in North American Pre-College Educational Institutions 1607-1865 Surveying in Pre-College Curricula Navigation in Pre-College Curricula What Was the Attained Mathematics Curriculum? References Chapter 7: College Mathematics, 1607-1865 The Classics Stranglehold 1607-1865 The European Background The Inherited Bias Toward the Classics Isaac Greenwood´s and John Winthrop IV´s Views on the Nature of Mathematics, 1727-1779 John Winthrop IV Builds on the Work of Isaac Greenwood at Harvard Benjamin Franklin´s and Benjamin Rush´s Attacks on What They Perceived to Be an Over-Emphasis on Classics Maintaining the Status Quo with College Mathematics, 1776-1810 Nicolas Pike´s (1788) Arithmetic Puzzling Events Surrounding Mathematics at Yale College in the 1820s Jeremiah Day´s Textbooks and His Mathematics Program The Extent of French Influence on Mathematics Curricula in North American Colleges Releasing the Education Potential of Recitation Through Blackboards The Yale ``Conic-sections´´ rebellions. The 1828 Yale Report, and Yale College´s Confirmation of the Pre-eminence of the Classics Benjamin Peirce and the ``Functions´´ Breakthrough in U.S. College Mathematics Maintaining a Wider View of Mathematics Education in the New Nation, 1776-1865 Methods of Teaching Mathematics in U.S. Colleges, 1636-1865 The gender factor in college mathematics. Concluding Comments References Chapter 8: Different Perspectives on Mathematics in North America 1607-1865 Applying Mathematics in North America 1607-1865 Benjamin Franklin´s Contributions to Mathematics Thomas Jefferson´s Usage of Mathematics in His Attempts to Improve the Everyday Lives of U.S. Citizens Jefferson and the Declaration of Independence Abraham Lincoln applies Euclidean structure. When preparing key speeches Jefferson and the introduction of a system of decimal currency. Comments on ``Some Thoughts on a Coinage.´´ A Textbook Which Conquered ``the Horn´´ William Cook Pease Seeks ``to Make Himself a Better Man´´ A Young Huguenot Woman´s Incomplete Cyphering Book The Cases of David Rittenhouse (1732-1796), Benjamin Banneker (1731-1806) and Robert Adrain (1775-1843) David Rittenhouse Benjamin Banneker Robert Adrain The Remarkable Mathematical Contributions of Nathaniel Bowditch Nathaniel Bowditch´s Life-A Summary Nathaniel Bowditch´s Work as a Supercargo ``The Bowditch´´ Benjamin Peirce Concluding Comments References Chapter 9: Toward Mathematics for All: Answers to Research Questions, Limitations, and Possibilities for Further Research Answering the Research Questions Limitations and Possibilities for Further Relevant Research Concluding Comments References Combined Reference List (Note that cyphering books mentioned in the text were not considered for the purposes of this list.) Author Index Subject Index