In the early years of the Republic, arithmetic was generally taught to teenaged boys planning careers in commerce, often by private tutors. With the advent of free common or elementary schools established in Northeastern states from the 1820s onward, arithmetic teaching became part of the educational experience of American girls and boys. Such schools gradually spread across the country.
Throughout most of the nineteenth century, students studied mathematics not only because of its practical utility but because educators believed that it promoted general mental discipline. Toward the end of the century, a new breed of university-educated psychologists challenged this view. They found no evidence that study of arithmetic and geometry promoted achievement in other areas. In part as a result, early twentieth century textbooks placed new emphasis on those aspects of arithmetic thought to be of greatest general use. Some topics—such as finding cube roots—which had long been a part of arithmetic teaching disappeared from the curriculum. Some routine drills were also eliminated. Newly introduced standardized tests came to be widely used to diagnosis student difficulties and predict future achievement, encouraging efficient use of school time.
Professional research mathematicians took relatively little interest in elementary education during this period. In the years following World War II, the expansion in the school-aged population, the need to replace mathematicians who had emigrated to the U.S., and fear of the Soviet Union combined to encourage new, more sophisticated mathematical curricula. Advocates of the “New Math,” as this movement was called, encouraged more abstract studies of arithmetic. At the same time, funds from the federal government and private foundations encouraged a variety of experimental approaches to teaching arithmetic and other topics.
The first machines that could perform arithmetic date from the seventeenth century, and commercially successful adding and calculating machines from the nineteenth century. These were far too expensive for general use in the home or the school. However, in the early 1970s, with the advent of the microchip, inexpensive handheld calculators became commonplace. Some manufacturers built new teaching devices using the technology. More generally, the electronic calculator challenged longstanding assumptions about the place of arithmetic in American education.