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## Revista latinoamericana de investigación en matemática educativa

*versão On-line* ISSN 2007-6819*versão impressa* ISSN 1665-2436

#### Resumo

ANDRADE, Jael Miriam e SARAIVA, Manuel Joaquim. **Multiple representations**: **a contribution for the learning of the concept of function**.* Relime* [online]. 2012, vol.15, n.2, pp.137-169.
ISSN 2007-6819.

This article presents a study focused on the understanding of the concept of function by students of 10th grade. It studies the connections that students establish among the various representations of a function, mobilizing and linking his concepts definition and image of a function, when solving problem-solving tasks, exploratory and investigative tasks and using the graphing calculator, oriented by the teacher. It also studies the importance of multiple representations for the development of the learning of the concept of function. It aims to identify and understand, also, the difficulties that students manifest in the learning of functions, knowing better the connections made by students between the various representations of functions considered. It follows the theory defined by Duval *(register of semiotic representation)* and the cognitive theory of Vinner *(concept image and concept definition).* Students worked in classes of mathematics in an environment of problem solving, exploratory and investigative tasks and using the graphing calculator. The research methodology adopted is a qualitative and interpretative. Data collection included an initial questionnaire, reports written by students in classrooms throughout the didactic unit ''functions'' and an interview with a couple of students after the apprentice. The results indicate that the coordination that students make between the various registers of representation of a function and of different functions allows them to achieve different perspectives of a function. The cognitive paradox of mathematical understanding was highlighted by the students through the coordination that they made of the records of semiotic representations (natural language, algebraic, tabular and graphic), which allowed them to stop confusing the mathematical object function with its representation, and also achieve a strong convergence of the concept image to the concept definition of function.

**Palavras-chave
:
**Concept of function; Semiotic representation of a function; Connections between representations; Concept image of a function; Concept definition of a function.