Phillip S. Jones: Mathematician, Historian, Educator - HPM-Americas

Phillip S. Jones 

Phillip S. Jones: Mathematician, Historian, Educator 

Betty Mayfield 

Hood College 

mayfield@hood.edu 

AMS Eastern Section Meeting/ March 17, 2012 

Betty Mayfield (Hood College) 1 / 35


Phillip Sanford Jones 

Born in Elyria, Ohio on February 26, 1912. 

Died in Ann Arbor on June 27, 2002 at the age of 90. 


Education 

Degrees in mathematics from the University of Michigan: 

B.A. (with teacher certification) 1933 

M.A. 1935 

Ph.D. 1948 


Education 


Bulletin of the AMS 1949 

Education 

NOTES 

The following one hundred and seventeen doctorates, with mathematics, 

mathematical physics, or statistics as a major subject, were conferred 

during 1948 in universities in the United States and Canada. The 

university, month in which degree was conferred, minor subject (other than 

mathematics) and the title of the dissertation are given in each case if 

available . . . 

P. S. Jones, Michigan, February, The development of the mathematical 

theory of linear perspective and its connections with projective and 

descriptive geometry with especial emphasis on the contributions of Brook 

Taylor. 


Education 

A Remarkable Class of Ph.D.s 

R. D. Anderson, Texas, June, Concerning upper semi-continuous 

collections of continua. 

T. M. Apostol, California, September, A study of Dedekind sums and 

their generalization. 

R. W. Ball, Illinois, June, minor in philosophy, Dualities of finite 

projective planes. 

F. E. Browder, Princeton, June, The topological fixed point theory 

and its application in functional analysis. 

Herman Chernoff, Brown, June, Studentizalion in testing of 

hypotheses. 

Louise H. Chin, California, June, Distributive and modular laws in 

relation algebras. 


Education 

A Remarkable Class of Ph.D.s 

H. W. Eves, Oregon State, June, minor in physics, A class of 

projective space curves 

P. R. Garabedian, Harvard, June, Schwarz’s Lemma and the Szeg 

kernel function. 

B. R. Gelbaum, Princeton, June, Expansions in Banach spaces. 

I. N. Herstein, Indiana, June, minor in physics, Divisor algebras. 

J. B. Keller, New York, June, minor in physics, Reflection and 

transmission of electro-magnetic waves by thin curved shells. 

Julia B. Robinson, California, June, Definability and decision problems 

in arithmetic. 


University of Michigan 

University of Michigan Department of Mathematics 

Appointed Instructor 1947 

Assistant Professor 1948 

Associate Professor 1953 

Professor 1958 

Retired 1982 








Retired 1982 








Retired 1982 








Retired 1982 








Retired 1982 



Mathematics Education 

Maintained close ties with the U-M School of Education. 

Phil was a member of our department at a time when we prided 

ourselves on abstract research. He excelled in an area that really 

didn’t fit into that mold. – George E. Hay (Chair of the 

Department of Mathematics, 1957-67) 



Mathematics Education 

Maintained close ties with the U-M School of Education. 

Phil was a member of our department at a time when we prided 

ourselves on abstract research. He excelled in an area that really 

didn’t fit into that mold. – George E. Hay (Chair of the 

Department of Mathematics, 1957-67) 



1951: Organized first Mathematics Education Conference at U-M. 

1961-1971: Directed a variety of academic-year, summer, and 

in-service programs for elementary and secondary teachers. 

Jones-Payne-Coxford Award in Mathematics Education. 


NCTM 

History of math for teachers: 1969 NCTM Yearbook 


Preface 

NCTM 

“In response to long-felt-need, a yearbook on ‘the use of the history of 

mathematics in the teaching of mathematics’ was first proposed during the 

NCTM presidency of Phillip S. Jones...” 


NCTM 

NCTM Leadership 

Director (1953-1959) 

Vice president (1959-1960) 

President (1960-1962) 


NCTM 


Director (1953-1959) 




NCTM 


Director (1953-1959) 




NCTM 


Director (1953-1959) 




NCTM 

“Historically Speaking” 

Monthly column in Mathematics Teacher. 

Examples: 

The binary system (1953) 

Angular measure (1953) 

American mathematics (1956) 

“Enough of its history to improve its teaching.” 


NCTM 

NCTM Yearbooks 

The Growth of Mathematical Ideas, Grades K-12, 1959 (Chair of 

editorial committee). 

Historical Topics for the Mathematics Classroom, 1969, reprinted 

1989. 

A History of Mathematics Education in the United States and 

Canada, 1970, reprinted 2002 (Editor). 


NCTM 

The Growth of Mathematical Ideas, 1959 

Preface 

Chapter 1: The Growth and Development of Mathematical Ideas in 

Children, or How and Why to Use This Book 

Co-author of Chapter 2: Number and Operation 

His colleague Joseph Payne also contributed to this volume. 


NCTM 

Historical Topics for the Mathematics Classroom, 1969 

Chapter I: The History of Mathematics as a Teaching Tool. 

Teaching so that students understand the “whys”: 

Chronological whys 

Logical whys 

Pedagogical whys 


NCTM 

Historical Topics for the Mathematics Classroom 

Chapter IV: The History of Geometry: Howard Eves 

Chapter VII: The History of the Calculus: Carl Boyer 

Chapter IX: The Science of Patterns: Lynn Steen 


NCTM 

A History of Mathematics Education in the United States 

and Canada, 1970 

Prepared for the semicentennial celebration of NCTM. 

Editor: Phillip S. Jones 

Associate editor: Arthur F. Coxford, Jr. (colleague from U-M) 

Reform is nothing new. 


NCTM 


and Canada 

Introduction (Jones and Coxford) 

Part One: Mathematics in the Evolving Schools (Jones and Coxford) 

Five chapters, 1492 - present, grammar schools to universities. 

Photocopies of pages from copybooks, early textbooks. 

“Reform, Revolution, Reaction.” 


NCTM 


and Canada 

Issues: 

Part Six: Summary and Forecast (Jones) 

What are the goals of mathematical instruction? 

What should we teach at each grade level? 

How can we organize our content and classroom methods to achieve 

these goals in a rapidly growing and diverse school population? 


MAA 

The Mathematical Association of America 

Michigan Section: 

Secretary-Treasurer, 1949-1953 

Governor, 1953-1956 

Published in the Monthly. 

Reviewed books. 

Chair of the Committee on Films for Classroom Instruction, 1955-59. 


MAA 

Committee on Instructional Films 

Surveyed current films and especially television meant to teach 

mathematics. 

Types of films: Single film? Series? Course? 

Audiences. 

Advantages/disadvantages of using films and television to teach 

mathematics. 


Mathematics on Television 

Listed projects from 1949 to 1958. 

MAA 

1949: The Slide Rule. Six 15-minute lessons by George R. Anderson 

of the Pa. State Teachers College. WGAL-TV, Lancaster, Pa. 

1955: Solid geometry. Summer school course, “noncredit but to fulfill 

college entrance requirements.” Henry C. Cooke, N.C. State College. 

WUNC-TV, Raleigh. 

1955: Fifth Grade Arithmetic. TV teaching for 25 minutes of the 

40-minute arithmetic classes in Pittsburgh Public Schools. Five days 

a week for 178 days. Mrs. Anita Seewald. WQED, Pittsburgh. 

1956-57: Calculus. Closed-circuit at Purdue. Students had 3 hours 

per week television, 1 hour conventional instruction. John 

Dyer-Bennet, Merrill E. Shanks. 

1956-57: Two courses at University of Washington: Intermediate 

Algebra and Plane trigonometry, taught by Carl B. Allendoerfer. For 

credit. 


MAA 

Mathematics on Television 

Phillip Jones projects: 

1952: Mathematics Around Us. Two 27-minute programs (Numbers, 

Geometry). WOOD, Grand Rapids. 

1952: Understanding Numbers: Their History and Use. Seven 

18-minute programs. WWJ-TV, Detroit. 

1954: Kinescopes: Understanding Numbers. Seven 30-minute 

kinescopes made for The Educational Television and Radio 

Programming Center, widely distributed. 


MAA 

Committee on Instructional Films 

Conclusions: 

A topnotch teacher can extend his effectiveness through the use of 

television (or film). 

Pupils often learn at least as much in television classes as with 

conventional instruction. 

In one study, students learned as much but liked the subject less. 


MAA 

Committee on Educational Media 

1966-68: Served on Committee on Educational Media. 

“Mathematics Today” series, 1961. 

Documentary on John von Neumann, 1966. 

“Challenge in the Classroom: the Methods of R.L. Moore,” 1966. 


MAA 

Fiftieth Anniversary Celebration of the MAA, 1965 

Summer meeting at Cornell. 

Series of invited lectures. 

American Mathematical Monthly January 1967. 

Albert A. Bennett, Brief history of the MAA before WWII 

R.A. Rolsenbaum, History of the MAA since WWII 

W.L. Duren, Jr., CUPM, the history of an idea 

Phillip S. Jones, The history of mathematics education 

R.H. Bing, Challenging conjectures 

E.J. McShane, Trends in analysis 

C.W. Curtis, The classical groups as a source of algebraic problems 

Saunders MacLane, The future role of the federal government in 

mathematics 

John W. Tukey, What can mathematicians do for the federal 

government? 


HPM 

History and Pedagogy of Mathematics 

International Study Group on Relations between History and Pedagogy of 

Mathematics, cooperating with the International Commission on 

Mathematical Instruction of the Mathematical Union. 

(HPM) 



History and Pedagogy of Mathematics 

International Study Group on Relations between History and Pedagogy of 

Mathematics, cooperating with the International Commission on 

Mathematical Instruction of the Mathematical Union. 

(HPM) 



History of HPM (Thanks, Florence!) 

1972: International Congress on Mathematical Education (ICME-2). 

Exeter, UK. 

Working Group on ‘History and Pedagogy of Mathematics’ organized by 


Leo Rogers (Roehampton Institute of Higher Education, UK) 



History of HPM 

1976: ICME-3 met in Karlsruhe, Germany. 

Phillip S. Jones and Roland Stowasser chaired three sessions on 

‘History of mathematics as a critical tool for curriculum design.’ 

Resolution sent to ICMI proposing regular sessions at future ICMEs 

on relations between history and pedagogy of mathematics. 

ICMI approved new study group. 



History of HPM 

1983: Phillip Jones organized (with Bruce Meserve and Fred Rickey) an 

HPM workshop in Ann Arbor, immediately preceding the annual NCTM 

meeting held in Detroit. 

Rickey showed a collection of rare mathematics books to the participants. 

1997: Meetings incorporated into regular NCTM meetings. HPM an 

affiliated group of NCTM. 


Learn from the Masters 


1988: ICME-6, Budapest. 

International conference on the history of mathematics, Kristiansand, 

Norway. 

Part I: History in School Mathematics 

2. The Role in the History of Mathematics of Algorithms and Analogies, 

by Phillip S. Jones. 


Vita Mathematica 


1992: ICME-7, Quebec; HPM, Toronto 

Dedicated to Phillip S. Jones, “Scholar-teacher, historian of mathematics, 

and colleague.” 


Thanks 

Many, many thanks to... 

Dave Roberts 

Fred Rickey 

Zal Usiskin 

Jim Fey 

Leo Rogers 

Carol Mead

Phillip S. Jones: Mathematician, Historian, Educator - HPM-Americas

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