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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 19^{th} 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.

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## Replica of a Babylonian Clay Tablet - Plimpton 322

- Description
- Both written language and written tables originated in the ancient Middle East. Scribes kept lists of numerical data, such as the number of sheep and goats transferred on different days of the month. A few of the clay tablets on which they wrote survive to this day. A tiny number of these tablets have rows and columns arranged in tables.. The rows may give totals of number of various forms of livestock transferred over time, with a column for the animals that were the responsibility of each person charged with such matters. Such documents date from around 2020 BCE.

- Those learning and teaching mathematics in ancient Iraq rarely displayed information in tabular form. However, in 1922 the American collector George Plimpton purchased such a tablet. This replica of that unusual object was made in 1957 by L. C. Eichner. Plimpton donated the original object to Columbia University in the 1920s. The original dates from about 1800 BCE, and reportedly was excavated in what is now Iraq at the side of the ancient city of Lasra. The portion of the tablet that survives has four columns of numbers written in the sexagesimal (base 60) system of numbers.

- Otto Neugebauer and A. J. Sachs offered a modern mathematical interpretation of the tablet in 1945. They noted that the numbers in the second and third columns of the table might represent the squares of the length of the shortest side and of the hypotenuse of right triangles, and interpreted the table as relating to Pythagorean triples. As the name Pythagorean suggests, such numbers had previously only been associated with later Greek mathematics. Other scholars have suggested that this was a part of a larger table of reciprocal numbers and related geometric figures, compiled by a teacher wishing to have examples of such reciprocals available for use in assignments.

- References:

- A. Aaboe,
*Episodes from the Early History of Mathematics*, New Haven: Yale University Press, 1964, pp. 30–31.

- O. Neugebauer and A. J. Sachs,
*Mathematical Cuneiform Texts*, New Haven: American Oriental Society and American Schools of Oriental Research, 1945.

- O. Neugebauer,
*The Exact Sciences in Antiquity*, Providence, R.I.: Brown University Press,1957, pp. 36–40 and Plate 7a.

- E. Robson, “Neither Sherlock Holmes nor Babylon: A Reassessment of Plimpton 322,”
*Historia Mathematica*, 28 (2001), pp. 167–206.

- E. Robson, “Words and Pictures: New Light on Plimpton 322,” American Mathematical Monthly, 109 (Feb 2002), pp. 105–120.

- E. Robson, “Tables and Tabular Formatting in Babylon and Assyria, 2500 BCE–50 CE,”
*The History of Mathematical Tables from Sumer to Spreadsheets*, eds. M. Campbell-Kelly, M. Croarken, R. Flood and E. Robson, Oxford: Oxford University Press, 2003, pp. 18–47.

- Location
- Currently not on view

- date made
- 1957

- maker
- L. C. Eichner Instruments

- ID Number
- MA*315226

- catalog number
- 315226

- accession number
- 218473

- Data Source
- National Museum of American History, Kenneth E. Behring Center