A proposal for an alliance between the history of mathematics and technologies through manipulation of John Hadley's Reflective Octant for teaching geometry in the training of mathematics teachers
History of Mathematics; Digital Technologies; Reflective Octant, Knowledge of geometric nature; Initial teacher training.
This dissertation proposes a notebook of activities based on the alliance between the history of mathematics and digital technologies through the use of instruments in the classroom in the training of teachers in the classroom. From this perspective, the objective of the work is to carry out a historical-mathematical study around the use of the Reflective Octante in order to produce an Educational Product based on the alliance between the history of mathematics and digital technologies through the use of mathematical instruments for training teachers of mathematics, which addresses the manipulation of the Reflective Octant, by the Hadley brothers, in the teaching of geometry. To achieve this, we used a qualitative methodology with a bibliographic and documentary approach for the data collection phase about Octante and the Hadley brothers, in an attempt to contextualize the period in which the instrument was developed and the mathematical knowledge behind its use. Using this methodology, it was possible to understand the influences of the Hadley brothers and The Royal Society on the development of the Octante and, in addition, it was also possible to understand how double reflection works, which depends on the structure of the instrument and knowledge of a mathematical nature to happen, and, an exploratory approach to the application of the Educational Product, in order to validate and refine it during application in the initial training of mathematics teachers.