Mathematical Charts and TablesCharts and Tables for Instruction
Charts and Tables for Instruction
Ancient Babylonian scribes learned to record numerical tables on clay tablets. If a schoolroom or library burned, the tablets baked hard, and might survive for millennia. Several such tablets are preserved in libraries today, and the replica of one of these at the Smithsonian reminds us of the long history of these objects.
In the 19th century, new European ideas about teaching arithmetic to very young children reached the United States. In 1831, the Boston firm of Munroe & Francis published a series of some fifty “infant school cards,” designed to teach subjects ranging from arithmetic to reading to natural history. Teachers were to use the arithmetic cards in conjunction with another piece of apparatus newly introduced in Western Europe and then in the United States, the teaching abacus or numeral frame.
Charts also were used to teach about weights and measures. In the wake of the French Revolution of 1789, the French developed an entirely new system of measuring distance, area, volume, temperature, and even time. By the 1860s, several European countries had adopted a revised version of this metric system, and metric weights and measures were legalized in the United States. An organization known as the American Metric Bureau began to distribute metric demonstration apparatus for the classroom. In the 1890s, the American Metric Bureau began to sell a metric chart for educational use.
Within the decade, the metric system was but one of several topics illustrated in a set of charts copyrighted by R. O. Evans of Chicago. Evans’ set of twenty charts illustrated such wide ranging topics as counting and writing numbers, arithmetic operations, fractions, the area of surfaces and the volumes of solid, business methods, and surveying.
In the first half of the 20th century, machines that could do ordinary arithmetic became common in the store and the office, and inexpensive adders were available for consumers. In the years following World War II, educators placed new emphasis on understanding the principles underlying arithmetic. Charts such as number lines sold for classroom use.
"Mathematical Charts and Tables - Charts and Tables for Instruction" showing 1 items.
- From the time of Descartes (1596–1650), mathematicians have described positive and negative integers as evenly spaced points on a line, now called the number line, that extends infinitely in both directions. This usage had made it into some school textbooks by the early 20th century. Particularly at the time of the development of the New Math in the 1950s and 1960s, number lines became part of the school classroom. This example of a number line was developed by Loraine McMillan and sold by Houghton Mifflin Company to accompany the 1972 edition of the textbook Modern School Mathematics. McMillan also prepared a leaflet describing how the number line should be used and a
that sold separately.
- The device consists of eleven cards. Ten of these can be placed end to end to show a number line with the integers from 0 to 100 written in red. The eleventh card is divided into segments but has no numbers marked on it. Each card, unfolded, measures 89 cm. w. x 11 cm. d. The cards were coated with clear plastic so that teachers could mark them with crayons or felt tip markers. The teacher’s guide is printed on blue paper. A mark on it reads: Teacher’s number line; teacher’s guide(/) by (/) Loraine McMillan. Another mark on it reads: houghton (/) mifflin (/) company. A third mark reads: 1972 .
- This example appears unused. It was received in 2012, and had been the property of Harvard University mathematician Andrew Gleason.
- P. A. Kidwell, A. Ackerberg-Hastings, and D. L. Roberts, Tools of American Mathematics Teaching, Baltimore: Johns Hopkins University Press (2008), pp. 202-203.
- Max Beberman and Bruce Meserve, “The Concept of a Literal Number Symbol,” Mathematics Teacher; 48, 1955, pp. 198–202.
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