Visualization processes in a task that requires generating and representing solids of revolution

Abstract

In this work we analyzed the visualization processes involved in a mathematical task that requires generating and representing solids of revolution. The task was administered to four hundred university students from the Bachelor's Degree in Primary Education. We adopted the Ontosemiotic Approach to Mathematical Instruction and Knowledge as a theoretical framework, using the configuration notion as an analytical tool in both its epistemic and cognitive aspects. For the data analysis, we used a mixed method approach: A qualitative dimension evaluating the primary objects categories, and a quantitative dimension categorizing the answers' success degree. The visualization processes analysis was done via the nine cognitive configurations identified from the students' solutions. The resolution errors focused more on the visual processing than on the interpreting figurative information processing. The majority of these errors were due to difficulties in mobilizing the recognition's abilities of spatial relations and positions, observing a correspondence between the effectiveness of cognitive configurations and the external representation of the generated solids.