O problema do xadrez na obra de al-Biruni: uma aliança entre história da matemática e objeto de aprendizagem na formação de professores de matemática

Abstract

We understand that mathematics has been and is being produced in different regions of the planet and at different times. For example, we highlight contributions from Islamic scholars from the medieval period, such as Abu Arrayhan Muhammad ibn Ahmad al- Biruni (973 – 1048). In fact, even living in a context of political instability due to the rise of the Islam religion, al-Biruni developed a vast amount of writings in different fields of knowledge that, in the 21st century, we know as mathematics, physics, geography and others. An example of al-Biruni's contribution is in his work The Chronology of Ancient Nations (prepared in the year 1000). Particularly, a fragment, called The Chess Problem, which became the object of our dissertation research. In this context, we ask ourselves: How can the use of a learning object produced in the light of a historical- mathematical study of al-Biruni's chess problem contribute to the initial training of mathematics teachers? Thus, our research aims to produce a learning object through a historical-mathematical study of the solution to the chess problem proposed by al- Biruni, from the perspective of the alliance between the history of mathematics and digital technologies. To achieve our objective, we adhere to a qualitative methodology with a theoretical and practical phase. To this end, we adopted bibliographic and documentary procedures, starting with a bibliographic survey of sources about al-Biruni, his production and its context, regarding the history of medieval Islamic mathematics, as well as about the alliance between the history of mathematics and digital technology. , particularly, learning objects. After the bibliographic phase, we carried out documentary research with a historical-mathematical study of the text The Chronology of Ancient Nations, by al-Biruni, focusing on the fragment The Problem of Chess, from which we created an educational product of the learning object type. In the practical part, we used experimental research to apply and evaluate the educational product in a class of undergraduate students in mathematics. As a result, in the theoretical phase, we were able to extract elements from the work that, based on understanding the context in which it was created, we identified in the solution to the chess problem proposed by al-Biruni. Furthermore, in the practical phase, we obtain the production of the learning object based on the alliance between the history of mathematics and digital technologies with the content of the fragment, as well as its evaluation obtained through its application in an initial teacher training class. Among 8 the results of the practical phase, we observed that the participants identified, in addition to the mobilization of concepts such as geometric progression, potentiation and multiplication, the alliance between trends in the history of mathematics and digital technologies