External Influences on U.S. Undergraduate Mathematics Curricula: 1950-2000 - Universal Mathematics

Edward James McShane (1904-1989) (Photo source: MacTutor Archive. For another photograph, see Convergence's Paul Halmos Photograph Collection.)

William Larkin Duren Jr. (1905-2008) (Photo source: MAA Presidents. For another photograph, see the Paul Halmos Photograph Collection.)

Griffith Baley Price (1905-2006) (Photo source: MAA Presidents. For another photograph, see the Paul Halmos Photograph Collection.)

Albert William Tucker (1905-1995) (Photo source: MacTutor Archive, which has more photos of Tucker)

Universal Mathematics

The post-1950 curricular curtain goes up in the summer of 1954, with a group of six highly respected leaders in undergraduate education, a subgroup of the newly formed Committee for the Undergraduate Program (CUP), meeting to write a two-volume work, Universal Mathematics.  This group soon expanded to 14 participants, four of whom went on to become presidents of MAA:  E. J. McShane (1953-54), W. L. Duren Jr. (1955-56), G. B. Price (1957-58), and A. W. Tucker (1961-62). McShane also was president of the American Mathematical Society (AMS) during 1959-60, and John Kemeny became president of Dartmouth College.  Universal Mathematics was meant for a new course intended to serve all first year college students who had taken intermediate algebra and geometry in high school.  The first semester covered some ideas in precalculus and in calculus.  The second covered discrete topics, including sets, combinatorics, probability, algebraic systems, and applications, including some applications to the social sciences [41].  The course was not a success.  William Duren, chair of the writing committee, said “The book is not yet suitable as a textbook and caused considerable difficulty to students and instructors.  The main trouble is that students cannot read it . . .  .”  [12].

Even in its time, in a unified country flush with victory in World War II and confident of its power, the egalitarian impulse of the eminent leaders of the Universal Mathematics project was ambitious.  Also breathtaking was the enthusiasm and energy expended by the talented and dedicated mathematicians working on the project.  In one summer, operating with scant funding, they wrote a volume for the first semester of the course and drafted one for the second.  The eagerness of the curricular leaders of those years is neatly sketched by G. Baley Price’s account of the first meeting of CUP in 1953 in which the chair, Duren, demonstrated a new tool for productivity:  “He rented a suite of rooms in a hotel and he locked us up in them till our business was finished” [50, p. 4].

Enthusiasm was essential in creating Universal Mathematics because direct financial support was restricted to a small grant of $2,500 – equivalent to $21,701.12 in 2013 dollars, according to the Bureau of Labor Statistics’ inflation calculator – from the privately organized Social Science Research Council.  The NSF had only just come into existence in 1950 and its budget for Education and Human Resources in the year when Universal Mathematics was written was only 1.5% (in constant dollars) of what that budget became by century’s end [47]. 

Bookending the 1950-2000 era at the recent end, we see a set of projects often termed “calculus reform” that offer an interesting contrast to the Universal Mathematics project.  Whereas the latter was an expression of a comparatively small and eminent leadership group, operating with highly uncommon speed and enthusiasm and with meager financial support, calculus reform was different in all these respects:  it was inclusive and deliberate and it enjoyed generous financial support.  NSF supported 127 separate calculus reform projects, stretching from 1988 to 1997, averaging $186,458 per project, for a total of $23,680,000 for all 127 projects [15, p. 22].  It would have been impossible for the Universal Mathematics project to proceed in the way that calculus reform did; the money was not there to do it that way.  It is interesting to speculate whether Universal Mathematics would have been a success if it had enjoyed the financial advantages that calculus reform had.

We return again to the Universal Mathematics project to consider its motivations.  The preface of Universal Mathematics, Part I. Functions and Limits says little about why this novel curricular idea was put forward.  Examining the content of the book, and reading between the lines of the preface, one can see a desire to be more modern, as in the use of Moore-Smith limits for example.  But the only remark about motivation in the preface is the phrase  “. . . because of widespread interest in revision of the elementary courses in mathematics…” [4].  Fortunately, project author Price was more expansive in writing elsewhere:  in [50] Price included the external pressures of manpower and demographics in explaining the reasons for the project.  Ever more students were coming to college but there was a serious shortage of mathematics faculty because of World War II – among other factors, due to the crimping of the pipeline of graduate students.  According to Price, Universal Mathematics was meant, in part, to deal with the numbers economically.  A further goal was to give the high schools targets for improvement.  Finally, Price remarked, it was hoped that Universal Mathematics would get “strong research mathematicians back into contact with the elementary courses.”

In addition to the external influence from demographics and manpower matters, one can infer some external influence on Universal Mathematics from neighboring social science disciplines because significant space is given to recent applications in those disciplines in Volume 2.  For more about the Universal Mathematics project, including forerunner work at the University of Chicago, see [52]. 

The unhappy fate of Universal Mathematics should not be taken to mean that the middle 1950s was not the right time for curricular change, or that much more money would have been essential to achieve change.  As we shall point out next, service courses, such as the wildly successful Finite Mathematics – one of the first notable widespread changes in curriculum of the 1950s – provide a counterexample.