Abstract:

In Mathematics Education, a representation is a configuration that can replace an entity of any form. In mathematical activity a tendency towards abstraction uses essentially symbolic and verbal representations. However visualization, image processes and visual representations can add something important to teaching and learning. A visual representation is a collection of graphical symbols of any kind which represents something concrete or abstract. Multiple representations (and transformations inside and of one into another) of a given mathematical object/concept are one of the biggest difficulties encountered by students.

The objective of this study is to determine the interest of the utilization of visual representations in teaching and learning, particularly in the problem solving. To do so, the following research question is made: If we consider the transformation of representations in problem solving, what is the impact if the teacher values multiple representations (verbal, symbolic and visual) instead of one that values a tendency towards abstraction (verbal and symbolic representations)?

This study involved two groups of students (group A with 18 students and group B with 17), aged between ten and 13. The trial of the experiment was made in a similar number of classes but in two different ways: group A explored those contents using verbal and symbolic representations (tendency towards abstraction) and group B added visualization and image processes (multiple representations). Results showed that students of group B diversified the representations and performed a bigger number and a variety of transformations comparing with group A. At the end of the experiment the number of right answers of group B students increased, compared with group A students, in which the number of No answer increased. And this was due to carrying out transformations introduced by visual representations.

Keywords:

Problem solving, multiple representations, transformations, visual representation.