THE LIBER ABACI OF LEONARDO of PISA AND ITS DIDACTIC POTENTIALITIES FOR MATHEMATICS TRAINING TEACHERS
Keywords: division of integers; historical sources; History of Mathematics; Objectification Theory; teaching and learning activity.
This thesis is the result of an investigation developed around the work Liber Abaci, written in the thirteenth century by the Italian Leonardo of Pisa. The Liber Abaci is an encyclopedic work that explains and exemplifies the use of the Indo-Arabic numeral system and contributed to the diffusion of this system in the Western world. The work is composed of 15 chapters that deal with the arithmetic and algebraic knowledge of the time, addressing examples involving practical and recreational problems of a mercantile, commercial and financial nature. Starting from the conception that the History of Mathematics can contribute to the training of mathematics teachers and the hypothesis that the work Liber Abaci is potentially didactic for this training, the investigation was developed from the following question: how can the work Liber Abaci contribute to the training of mathematics teachers? We delimit as a general objective: to identify in the work Liber Abaci potentially didactic elements for the training of mathematics teachers. Throughout the investigation, several potentially didactic elements were identified. One of these elements is the way in which the division of integers is presented and developed in the work. To confirm the didactic potential of the way the division is developed in the work, an eight-hour workshop was held with mathematics teachers linked to a professional master's course in mathematics, during the History of Mathematics classes. The workshop was structured and developed based on the methodology of Luis Radford's Theory of Objectification. In addition to enabling the awareness of another historical-cultural way of thinking about the division of integers, the workshop allowed the participants to reflect on the difference between the concept of number and its symbolic representation, on the possible meanings of division and on the historical-cultural nature of mathematical thinking.