Levels of knowledge for the function topic in High School

Abstract

The van Hiele theory for the development of geometric thinking has been considered as a guide for geometry teaching/learning. This model is based on two main principles: the description of cognitive structure, characterized by hierarchical mental levels to be achieved by the students and the teaching methodology for these levels beeing achieved, in order to guide educators concerning teaching decisions related to the leaning. From a study of the development models of thought on language of functions, this paper aims to report the process of testing and validating a model of levels of development for the acquisition of the concept of function, based on Van Hiele’s model. For this, activities were applied to high school students. The results prove the validity of the proposed scale, since the students’ classification in the sample was distributed at all levels, obeying the hierarchy.

Keywords

• function
• van hiele theory
• levels of knowledge.
• levels of understanding
• pupils’ classification
• didactic intervention