Teaching Mathematics with Ephemera: Teaching the Prospectus

The themes that emerge from the projected lecture topics are one of the most notable features of Prospectus. For example, Playfair emphasized the use of mathematical instruments throughout the document. In the astronomy lectures, he planned to recommend the use of the telescope, astronomical quadrant, Hadley's quadrant, micrometer, gnomon, sundial, clock, and transit telescope. Under physical geography, he referred to the barometer, hygrometer, and themometer, which were all instruments that early geologists were taking into the field for making measurements. In the sections dealing with navigation, he mentioned the log, mariner's compass, rhumb-line, and compass, and he again intended to discuss Hadley's quadrant.

Another theme that ran through both the Prospectus and Playfair's entire career was his interest in the history of science and mathematics. Specifically, he planned in the lectures to talk about some of the secondary sources he was reading about mathematics and astronomy in India. He also intended to introduce the general subject of geography with a review of its history. A third theme is the large number of recent or open questions Playfair expected to share with his audience, including: parallax, adjustments for differences between real and apparent motion, the dimensions of the solar system, the figure of the Earth, and determination of longitude. Major research achievements explaining many of these phenomena, such as Laplace's Mécanique céleste, remained a few years in the future when Playfair put together his outline in 1793. Staff at the Dibner Library, Smithsonian Institution Libraries, have digitized their copy of Prospectus so that you may explore the pamphlet yourself and develop additional themes of relevance to your own students and subjects.

Considering how the content of a piece of ephemera relates to the topics you teach is one way to bring an example such as Prospectus into a mathematics classroom. The format of Prospectus and similar documents, an extended outline, suggests additional possibilities for classroom use:

• Students may evaluate the overall structure, content, and approach represented by a course outline. How effective do they think it might have been at promoting teaching and learning? How could they apply what they found in their analysis to planning out a class period or entire course that they might teach? How might they design a curriculum or articulate standards?
• Instructors might pull out a specific definition from an outline and ask students to research whether that definition remains in use or whether understandings of the term being defined have changed over time.
• As with any historical document, an extended outline reflects the values of its creator. According to Prospectus, what mattered to Playfair? How do his beliefs about which subjects and concepts were essential compare to the values we assume are widespread in the present? Are the convictions we accept as universal truly as widespread as we think they are?

These sorts of activities might be most useful in mathematics education classes, upper-level courses that orient students to particular fields within the mathematics major, and senior capstones. This category of material, though, is only one form of the wide range of mathematical ephemera that exist and thus represents only one set of opportunities among the many possible classroom applications of these primary sources. As you review all of the sections of this article, feel free to let your imagination roam!