Visual patterns and the development of creativity and functional reasoning

Abstract

Creativity has been recently recognized as an important factor of progress. However, its development has not been a priority of the school and, in particular, of Mathematics. Also, it has not been a topic greatly studied, especially in what concerns ‘normally’ (not gifted) students. On the other hand, students often reveal many difficulties in functional reasoning. Some studies have concluded that an adequate exploration of visual patterns may contribute to overcoming these difficulties. However, they suggest that we should continue to study their impact on other publics and in other contexts. Thus, we developed a qualitative (exploratory) case study aiming to find out to what extent the exploitation of tasks focused on visual patterns contributed to the development of creativity and functional reasoning in students of the 8th grade. Participant observation, inquiry and documental analysis were the main sources of data collection, supported by various instruments. The data collected were submitted to content analysis, guided by categories. Some of them emerged from the research questions and others were defined during the analysis. Generally, it was found that students improved their performance in tasks which resolution required the mobilization of functional reasoning. There was also a remarkable improvement of creativity in what concerns fluency, flexibility and originality. Some of the representations about creativity also evolved positively