Do We Teach Too Much Mathematics . . . ? History Tells Us Much

Frank J. Swetz (The Pennsylvania State University)

One of the earliest extant mathematical texts on problem solving is prefaced with the inducement that accurate reckoning as explained in the book will provide the user with: “The entrance into the knowledge of all existing things and all obscure secrets.” The text is the Egyptian Rhind Mathematical Papyrus, composed about 1650 BCE (Chace 1979, p. 27). What reader could resist the power promised by learning numbers and how to compute with them? Over two thousand years later, we find the Chinese master scholar Sun Zi exhorting the readers of his arithmetic book, Sun Zi suanjing with similar claims:

Mathematics [governs] the length and breadth of the heavens; [it affects] the lives of all creatures. ... [Mathematics] has prevailed for thousands of years and has been used extensively without limitations. If one neglects its study, one will not be able to achieve excellence and thoroughness (Lam and Ang 1992, pp. 151–152).

The scope and comprehensiveness of Zi’s claim impacted the Mandarins or court officials on whose knowledge the existence and harmony of their Celestial Empire depended.

In 1543, Robert Recorde, an English physician, wrote one of the first English-language mathematics texts for the common folk of his country: The Ground of Artes, Teachyng the Worke and Practice of Arithmetk. As a motivation, he noted: “yf nombre be lackynge, it maketh men dumme, so that to most questions, they must answer mum” (Wilde 2014). The readable, nonacademic Ground of Artes became so popular that it went through 47 printings by 1699. Its text, written as a dialogue between a teacher and his pupil, devoted much of its effort to promoting the value and usefulness of mathematics.

In a somewhat similar manner, it was a common practice for 19th-century mathematics textbooks in the United States to carry an endorsement by some prominent citizens as to the value and worth of the material about to be studied. Additionally, many arithmetic texts of this period, both in Europe and North America, bore the word “commercial” in their titles. Even those not so named emphasized business applications in their word problems. There was little confusion about where and how the mathematics would be employed. (See Figure 1.) Thus, from ancient times up to the 20th century, the learning of mathematics was highly motivated and directed. Its contemporary relevance and usefulness was stressed. Mathematics was a powerful tool, whether in the pursuit of magical ponderings, bureaucratic administration, or the earning of a living. It had an important, recognizable, and appreciated human value.

Title page of Jonas Moore's 1681 A New System of the Mathematics.

Figure 1. Text written by Jonas Moore for his students at the Royal School of Mathematics, London, 1681. This was one of the first British institutions devoted to the teaching of mathematics to the common working-class man. The applications of mathematics are clearly stated on the title page and developed within.

In our modern period, education has been homogenized in the service of making it more accessible. It may be questionable whether a particular status can or should be ascribed to any particular subject in the common curriculum by authorities. However, at the discretion of the individual classroom teacher, and as needed by the students, a promotional effort could be applied to certain subjects. Due to its continuing stigma, I believe strongly that mathematics is one of these teaching areas that requires still better answers to the questions “What?” “How?” and “Why?”