Dos mínimos quadrados à regressão linear: atividades históricas sobre função afim e estatística usando planilhas eletrônicas

Abstract

This research aims to create guided activities in the History of Mathematics, carried out through Mathematical Investigation, and Information and Communications Technologies, to encompass and contextualize concepts of Affine Function and Statistics in High School. Therefore it is based on the historical context of Adrien-Marie Legendre (1752-1833) and his creation of the Method of Least Squares (1805); and Francis Galton (1822-1911) and his experiments that originated Linear Regression (1875). From this literature research, and from the selected historical moments and results achieved, this study proposes and validates a sequence of activities to be used for students of the first year of High School. This sequence is composed of two historical activities to be supported using an electronic spreadsheet software. The first proposed activity recreates, with the students, Galton’s experiment about the comparative study of the stature of parents and children. The students collected data and analyzed them as they distinguished function from relation, types of variables, linear and angular coefficients and function growth, learning some Basic Statistics concepts while exploring the software. The second activity aims to apply the historical concepts discussed earlier to conduct a comparative study of the body, clothes, shoes and accessories measurements. In this activity, the students investigated, in their real data, situations of Injective, Surjective and Bijective Functions, distinguished domain from image, variables from numeric coefficients, and made estimates of the functions. The use of technology raised motivation to study the addressed mathematical concepts. Furthermore, it reduced the time to create graphs, promoting more space for the students to investigate the presented questions. Combined with the History of Mathematics, it stimulated the students’ interest and creativity to perform the proposed investigative activities. All this qualitative research obtained, as a result, the educational product constituted of activities, with suggestions and tips for the teacher that might wish to apply it in class.