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

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