'In these numbers we use no fractions': A Classroom Module on Stevin's Decimal Fractions - Element II. Applying the Wilson & Chauvot Strategy

The PSMTs in my course were given selected pages of George Sarton’s (1935) discussion, “The First Explanation of Decimal Fractions and Measures (1585)…”, as well as access to the entire 93-page article from JSTOR through our university library system. In this article, Sarton situated the development of Stevin’s invention (and even examined what occurred after 1585), provided numerous facsimiles of Stevin’s work, and published the entire pamphlet of De Thiende.

If you do not have access to JSTOR or Sarton’s article, other resources are available that may be used with PSMTs, such as the Schultz website referenced here. Perhaps a more thorough resource than Schultz is found on the Digitale Bibliotheek voor de Nederlandse Letteren (DBNL) website. Through this digital initiative, we can access an account of Stevin’s mathematical life, an analysis of the content of De Thiende (from the Dutch, 1585), a transcription of De Thiende, and a scanned copy of the original work. Additionally, English translations of De Thiende (or La Disme) are available through a variety of sources, including the translation offered by Schultz (complete only up to Stevin’s third proposition on multiplication), via the Digital Library of the History of Science and Scholarship in The Netherlands (Struik, 1958), and in David E. Smith’s A Source Book in Mathematics (1929), available on Google Books – though your library may have a copy of this text. The Sarton article, however, provides a wealth of information all in one place.

This part of the task included the following assignment:

Read and reflect:

Read the following excerpts from Sarton (1935):

*page 156 – mid-page 158;

*title pages on page 219;

*bottom of page 159 – mid-page 162;

*a few excerpts of the French edition of Stevin’s work (pp. 233 – 234); and

*pages 174 – 176.

You may want to stop after each chunk and either put in your own words what you read, or discuss it with your peers.

Apply the strategy:

The various paragraphs/pages of reading should alert you to think about the various parts of Wilson & Chauvot’s strategy. Consequently, what I would like for you to do is to imagine that you have decided to include something about the historical development of the decimal fraction notation in teaching decimals to middle grades students. Your motivation for this stems from the idea that you experienced difficulty with students in the past who could “read” a decimal value such as 8.749 as “eight point seven four nine” – yet when you asked them for the number of hundredths in this value you often heard “seven” (7). Thus, you are searching for a way to develop students’ mathematical knowledge in a way that may connect to other aspects of learning. Please use your study of Stevin’s contribution to prepare answers to the following questions:

1. Who is doing the mathematics described? Specifically, what does Sarton tell us about Simon Stevin that enables us to know who he was beyond being a person who worked on mathematics?

2. How is mathematics done? In what ways was Stevin’s contribution (even by his own account) to be used? Do you think it “facilitated or restricted advancement in certain areas of mathematics” (Wilson & Chauvot, 2000, p. 644)? In what ways?

3. What is mathematics? How would you characterize Stevin’s contribution, in terms of a branch of mathematics? (Or, if you want to think in terms of the National Council of Teachers of Mathematics (NCTM) content standards – that’s fine too!) Can you use his definitions and notation to describe how students can “break down” the value 8.749? Although Stevin’s notation is not entirely efficient (it was still 1585!), does it at least make sense? If Stevin did not introduce this notation and these definitions until 1585, does it make you wonder what we did for the previous centuries? Alternatively, given the particular time, does it seem feasible that the world was ready for such notation?

Quick Reflection II

The application of Wilson and Chauvot’s strategy required the PSMTs to consider contributing factors to the development of mathematical ideas over time. For example, in Stevin’s introduction to his own work, we read:

To Astrologers, Surveyors, Measurers of Tapestry, Gaugers, Stereometers in General, Mint-masters, and to all Merchants Simon Stevin sends Greeting[.] (Sanford, 1929, p. 20)

Thus, we can begin to answer the question, Who does mathematics?, by describing Stevin to some degree (i.e., from biographical information available) and also by describing the users of such mathematics. Additionally, great opportunities abound to discuss what an “Astrologer” does within the context of the sixteenth century, as well as the job descriptions of “Gaugers” and “Stereometers”.