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Mathematics and Primary Sources: Measurement, History, and the English Language

The following is a guest post by Michael Apfeldorf of the Library of Congress.

Analyzing primary sources with a mathematics focus can help students develop their math skills in a real-world context, while also giving them fresh insights into history and other disciplines.

One intriguing example from the Library of Congress is Arithmetical Tables – For Schools By Miss D. A. Hadley (c. 1855), a piece of ephemera that offers a way for students to reflect on measurement from the combined perspectives of mathematics, history, and the English language.  Not much is known about the origins of this piece, apart from the fact that it was apparently used to help instruct school children in the mid-1800s.

Students can begin by engaging the chart from a purely mathematical perspective, practicing conversions and reflecting on the structure of measurement systems generally.  Sample questions you might ask include:

• How many gills are in 3 hogsheads of molasses?
• How many pints are in one chaldron? Can you write an equation for the conversion of pints into chaldrons?

Next challenge students to look deeper into the measurement system by directing them to areas where conversion is more difficult.  For example:

• Using the table, can you convert between Troy weight, Avoirdupois weight, and Apothecaries’ weight? Why or why not? Now imagine you have a single scale and exactly one ounce of each type of weight. Could you then develop a table to convert from one type of weight to the other?  Can you identify any other areas in the chart that are hard to use?
• In 1790, Thomas Jefferson recommended a nationally, standardized system of weights and measures based on factors of 10. What are the pros and cons of implementing such a proposal?  Why do you think it was not accepted?

For further enrichment, Hadley’s tables may also be used for interdisciplinary connections related to history and the English language.  For example, students may:

• Examine the language of the table, identifying measurement terms they recognize, as well as ones that seem foreign.
• Research connections between measurement terms found in the table and historical meanings of such words as: “grains,” “gills,” “hogsheads,” and “scruples,” a word with a non-measurement usage as well.  A visit to a dictionary that provides word etymologies could provide useful.  (For instance, a “scruple” could potentially be a little bit of weight or a little bit of “conscience” that’s keeping you back!)

Such investigations can be fun for students who enjoy language, while also serving to highlight the interaction that exists between mathematics, the English language and history, further helping students to see mathematics in a real-world, applied context.