O ensino da função afim a partir dos registros de representação semiótica - Delgado, Carlos José Borges (2010)
This case study aims to evaluate the difficulties in teaching and learning of the affine function for students of the 1st year of state high schools in Rio de Janeiro – RJ. The work was developed through activities prepared by the teacher and applied to three classes, being effective participants a total of one hundred and thirteen students. Ten activities were done but some of them were split, which resulted in a total of twenty-five items. The main objective was to verify from which changes on conversion among different registers of representation of the affine function (natural language, algebraic expressions, tables, and graphical form) students have more difficulties and facilities. To do so, the teacher included at least two different forms of representation in the activities, following the guidelines of the National Curriculum Parameters (NCP's) to High School. The theoretical framework was based on the "study of registers of semiotic representation for learning math," developed by Raymond Duval, and they were also a basis for the proposal to diversify the methodological procedures used in teaching linear functions. We tried to answer the following question: Has the use of registers of semiotic representations helped the teaching and understanding of their various representations? The theme affine function was chosen rather than the other types of mathematical function studied in the 1st year of high school because this is the first function taught to students, which allows us to observe more clearly the difficulties in teaching and learning this subject. In conducting this study we explored the variety of representations of the affine function, so that students could perform tasks that required conversion between registers with changes from: a) natural language to algebraic, tabular, graphic forms, b) algebraic form to the tabular form and vice versa; c) algebraic form to the graphical form and vice versa, and d) tabular form to the graphic form and vice versa.