O ensino da função afim a partir dos registros de representação semiótica

Abstract

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.