From its inception the Mathematical Association of America (MAA) has sought to improve education in collegiate mathematics. For the past forty years, the natural MAA vehicle for interest in mathematics for general education has been its Committee on the Undergraduate Program in Mathematics (CUPM). Indeed, one of the first fruits of CUPM (then still called CUP) was some material produced under its sponsorship in 1954-1958 under the title Universal Mathematics, in two parts. According to the preface to Part I, "Universal Mathematics" has been designed as a course for all first-year college and university students with normal high school preparation in mathematics. Normal preparation includes at least two, and preferably two and one-half, units of high school mathematics ..." (p. iii). The goal, presumably, was a kind of quantitative literacy, but that term was not yet used.
There was some pilot-testing of Universal Mathematics, but, especially for some years after receiving its first NSF grant in 1960, CUPM concentrated almost all of its efforts on problems related to more narrowly defined clienteles, and indeed treated "quantitative literacy" in a somewhat gingerly manner. For example, the CUPM booklet A General Curriculum in Mathematics for Colleges (1965), which was in some ways a synthesis of the CUPM recommendations that had by then appeared, included an interesting but inconclusive discussion (pp. 25-26) of the issue, punctuated with disclaimers like "These remarks do not have the force of a recommendation, since CUPM has not yet considered in detail this important curricular problem" (p. 25).
It was not until January, 1978, the CUPM formed a panel (subcommittee) to consider the quantitative literacy problem straight on, and this panel published a brief, worthwhile, thoughtful, but also somewhat inconclusive report, "Minimal Mathematical Competencies for College Graduates" in The American Mathematical Monthly in April, 1982. A reprint of that report appears in the 1989 MAA Notes volume, #13.
In the last ten years mathematics education in American schools and in colleges has received widespread attention. In response to claims of weaknesses in mathematics education nationwide, a coordinated effort is being made by the mathematical community to set standards for curriculum and teaching, as well as to develop better procedures for determining the extent to which the established standards are being met. In this context the National Council of Teachers of Mathematics has produced two major and influential reports regarding mathematics education for students from kindergarten through grade twelve: Curriculum and Evaluation Standards for School Mathematics (1989) and Professional Standards for Teaching Mathematics (1991).
The present report is concerned with quantitative literacy requirements that should be established for all students who receive a bachelor's degree. It has been prepared by a CUPM Subcommittee on Quantitative Literacy Requirements which was formed in late 1989 and has worked since then to frame recommendations which both mesh with the new pre-college standards and are realistically achievable in the college years. Implementation of this report's recommendations and ideas can help develop graduates who are quantitatively more literate, with important benefits to themselves and to the society in which they live.
It is no secret that too many educated people exhibit (even flaunt) great deficiencies in basic mathematical knowledge and skills -- they are quantitatively illiterate! How concerned are our colleges and universities about this form of illiteracy? In the last ten years national report after national report has confirmed this fact. What can, or indeed will, the mathematical community do about it? The Mathematical Association of American (MAA), through CUPM, decided to take up the challenge and offer recommendations which could lead to the acquisition of quantitative literacy by a larger proportion of the nation's college graduates. Hence the present report, which is addressed to provosts and deans at colleges and universities, to members of the mathematical community, and to those who serve on general education committees within colleges and universities or are in other ways concerned about the quantitative literacy of college graduates.
The CUPM Subcommittee on Quantitative Literacy Requirements has wrestled with many complex problems that surround quantitative literacy for all college graduates. This report is the product of many lengthy discussions, a focus group conference on the subject sponsored by the National Science Foundation, presentations on quantitative literacy and reactions to them at national and state professional meetings, in-depth study of national reports and data, and much input by individual mathematicians, scientists, teachers, college administrators, and staff members of state boards of higher education. It attempts to provide workable solutions to many complex problems and guidance toward attainment of those solutions.
The report is visionary in that it does NOT represent a distillation of current national practice in supplying college students with mathematical training. Rather it sets a standard for a quantitatively literate college graduate and suggests reasonable means for the achievement of that standard.
The Subcommittee looked at the problem of too few college graduates being quantitatively literate by asking: why should college graduates be quantitatively literate? what should a quantitatively literate college graduate be able to do? what mathematical topics and experiences would support development of these capabilities? how can colleges and universities realistically proceed from their current curricular programming to provide ways for their college graduates to become quantitatively literate? and what procedures can be used by colleges and universities to assess the extent to which they are accomplishing their goals? The Subcommittee has summarized its conclusions in the present report, which presents a challenge to the will and dedication of those in the mathematical community as well as other faculty and administrators at colleges and universities across the nation.
The report makes four major points which are set forth in detail.
They are:
The cardinal recommendation among these four is the establishment of a quantitative literacy program -- not a course! Many colleges and universities have mathematics requirements in their general education programs. Often this requirement is a choice of one course from a list of possible entry level courses at that institution. No rationale is given for the course and nothing is said about its relationships with other courses or with the remainder of the student's program at the college or university. Students are naturally led to the idea that the course is merely a hurdle to jump, and then its content might as well be forgotten.
Basic quantitative literacy depends on students being introduced to the foundations of quantitative reasoning and then given reinforcement experiences which develop and deepen in the student the habits of thinking which the student has been encouraged to develop. Taking one course is not enough to endow a student with a habit of mind, but completing a carefully devised program can provide sufficient practice to make a pattern of thought part of the student's intellectual tools. The construction of such a program requires leadership from the mathematics faculty and other faculty as well as commitment to the three other major points of this report.
Many factors need to be considered in determining the degree of quantitative literacy appropriate for all college graduates. Among them are the increasing complexity of the society, the desire to improve opportunities for all citizens to participate more fully in their society, current efforts to improve the standards of school mathematics, and the pressures on colleges and universities for accountability regarding undergraduate education. All of these factors influenced the creation of this report.
Part I summarizes published opinion on the importance of quantitative literacy, discusses some of the reasons for it, and emphasizes that this report's concern is with quantitative literacy specifically for college graduates. Part II explores the elements of quantitative literacy. Part III elaborates on facets of Part II and is concerned especially with the practical problem of developing programs of teaching for quantitative literacy. Part IV deals with the important issue of assessing the effectiveness of quantitative literacy programs. The report concludes with a brief bibliography and some other supporting material.