1. Charles Davies as a Philosopher of Mathematics Education
Amy Ackerberg-Hastings
Independent Scholar
Charles Davies (1798–1876)

2. Jeremiah Day
(1773–1867)
John Playfair
(1748–1819)
John Farrar
(1779–1853)
Charles Davies
(1798–1876)

3. Davies’s Mathematics Textbooks
Nearly 50 separate titles
Audiences ranged from young children to working adults
7 volumes for US Military Academy
Represent 200+ of approximately 480 total printings
Adopted wherever USMA graduates were instructors
Booklist also included:
15 arithmetics
8 books for secondary schools
10 solution keys
Over 5 million copies sold
School Arithmetic: 1,250,000
“Davies’s Legendre”: 300,000 by 1862

4. Davies’s Academic Employment & Affiliations
1816–1837: United States Military Academy at West Point
Professor of Mathematics, 1823–1837
1839–1841: Trinity College, Hartford, CT
1848–1849: University of New York
1852–1853: President, New York State Teachers’ Association
1857–1865: Columbia College, New York City

5. Questioning Davies’s Reputation
Beginning at West Point, Co-opter Rather than Translator, Editor, or Author
1845 Plagiarism Lawsuit by Frederick Emerson
Susan B. Anthony’s Experience at August Meeting of New York State Teachers’ Association
October 1863 Attempted Nepotism for William Guy Peck at Columbia
J. B. Barnard: Davies had “scientific attainments fit for a head schoolmaster”
G. Kemble: “With all his selfishness and mischief making, [Davies] is, and always was a fool. I have known him from boyhood.”

6. Career Theme:
Major Figure as Textbook Producer and Educator Despite Questions about Reputation
Conference Theme:
Sources and Quality of Knowledge in Circulation
Illustration of Theme:
Davies, Charles. The Logic and Utility of Mathematics, With the Best Methods of Instruction Explained and Illustrated. New York: A. S. Barnes & Co., 1850.

7. Logic & Utility: Structure & Sales
3 Books
Logic (3 chapters, 71 pp.)
Mathematical Science (4 chapters, 193 pp.)
Utility of Mathematics (3 chapters, 48 pp.)
8 Printings
Probably ca 8000 Copies
1873 2nd Edition
New Title: The Nature and Utility of Mathematics
~40 Pages Longer
1 Printing

8. Barnes used reviews to advertise by 1851
Promotion and Legacy
Barnes used reviews to advertise by 1851
Described in 1970 as the “first American book on mathematics teaching methods.”

9. Assessing Originality
Acknowledged Large-Scale Copying in Book I
Richard Whately’s Elements of Logic
John Stuart Mill’s System of Logic

10. Assessing Originality
Acknowledged Large-Scale Copying in Book I
Richard Whately’s Elements of Logic
John Stuart Mill’s System of Logic
More Borrowing in Book III
Edward Deering Mansfield’s “Discourse on the Utility of the Mathematics”
Davies’s Brother-in-law
Also Quotes John Herschel, Locke, Bacon, Barrow

11. Impact and Influence of Logic & Utility’s Content

12. Outline of Book II, “Mathematical Science”
Fundamentals of Quantity and Mathematical Science (16 pp.)
Arithmetic (105 pp.)
Geometry (37 pp.)
Analysis, Algebra, Analytical Geometry, Differential and Integral Calculus (32 pp.)

13. Davies’s Principles of Mathematics Teaching
Mathematics is the Science of Quantity
Valid Mathematical Reasoning Rests on Clear, Unambiguous Definitions
Mathematics is Worth Learning Because It Imparts Mental Discipline
Arithmetic is the Foundation of Civilized Life
Teach Abstract Principles First, Then Applications
Follow a Good Textbook

14. Book III as Contribution to Ongoing American Discussion of Tension between Mental Discipline and Utility
T. M. Post, “Lecture Upon the Study of the Greek and Latin Languages as a Part in the Course of a Liberal Education,” Transactions of the College of Professional Teachers 4 (1834): 63–96.
Thomas Smith Grimké, “Oration, on the Subject ‘That Neither the Classics Nor the Mathematics Should Form a Part of a Scheme of General Education in Our Country,” Transactions of the College of Professional Teachers 4 (1834): 99–137.
Jeremiah Day and James Luce Kingsley, “Original Papers in Relation to a Course of Liberal Education,” American Journal of Science 15 (1829): 297–351.

15. Book I: Employing Logic in Mathematics Teaching
(Plagiarized) Sources:
Richard Whately’s 1826 Elements of Logic
John Stuart Mill’s 1843 System of Logic
Potentially Novel Concept
More Closely Resembles a Theory of Knowledge Than a System of Logic
Assertion that Mathematical Reasoning and Logic are Identical

16. Charles Davies as a Philosopher of Mathematics Education
Amy Ackerberg-Hastings
Independent Scholar
Charles Davies (1798–1876)