The concept of proportion present in the handling of the Two Rules for Calculation by William Oughtred under the view of graduates in mathematics from UECE

Abstract

Debates about the contributions of the insertion of the history of mathematics in teacher training have gained prominence in scientific research in Brazil during the first two decades of the 21st century. Among these studies, we highlight those carried out by the Education and History of Mathematics Research Group (GPEHM), which look at scientific/mathematical instruments developed between the 16th and 17th centuries. With this in mind, among these instruments are the Two Rulers for Calculation by William Oughtred (1574-1660), used to solve arithmetic questions, trigonometric and astronomical calculations. Thus, based on a study of the contextual, historiographical and epistemological aspects surrounding the Two Calculating Rulers, we realized that some mathematical knowledge emerged from their construction, use and application, including the concept of proportionality, which was included in their use. With the aim of understanding this idea through the instrument and inserting the history of mathematics into initial teacher training, we designed an extension course entitled "Performing multiplications through the manipulation of William Oughtred's Two Rulers for Calculation", given in April and May 2023 at the State University of Ceará, from which we used one of the proposed activities to discuss in this article. That said, we realized that the participants were able to understand the concept of proportionality through the mathematical instrument, and also related it to the current concept of proportion, bringing the idea of a possible reframing of the mathematical knowledge addressed.