'In these numbers we use no fractions': A Classroom Module on Stevin's Decimal Fractions - Evolution and Elements of the Task

Evolution of the Task

The design of this classroom task was prompted by an innocent question that I posed to PSMTs at the beginning of a “Using History in the Teaching of Mathematics” course. In particular, I thought I would begin with a question about a pre-secondary mathematics topic, to investigate how well their responses would address the “how” or “why” a particular mathematical process worked (in this case, the multiplication of two decimal numbers). Ultimately, the PSMTs’ responses were not only disappointing but a little disturbing. The majority of their responses correctly explained that the result of multiplying say, 5.674 by 13.799, was determined by finding the product of the whole numbers 5674 and 13799, and then “moving” the decimal point to the left six places since the total number of decimal places in the two factors is six. Unfortunately, very few of the PSMTs in the class could explain why this was the case. It was then that I decided that an episode from the historical development of decimal fractions could contribute a great deal to the mathematical knowledge for teaching of these PSMTs. In order to address additional course objectives, however, I also needed to include the historical and humanistic elements related to Simon Stevin’s mathematical contribution.

Elements of the Task

I. Identifying a Strategy for Using History

II. Applying the Wilson & Chauvot (2000) Strategy

III. Concentrating on the Mathematics, or Clarifying Conceptions of Decimal Fractions