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