Exploring secondary school students’ geometrical figure apprehension: cognitive structure and levels of geometrical ability

The present study examines secondary school students’ geometrical figure apprehension based on Duval’s theoretical framework regarding perceptual, operative, and discursive apprehension. The aim is to explore the cognitive structure of the geometrical figure apprehension dimensions (operative, discursive, and perceptual) in three grades of secondary school students. The tasks in the present study were completed by a sample of 881 students attending public secondary education in Cyprus. Confirmatory factor analysis indicated the stability of the structure of the model concerning secondary school students’ geometrical figure apprehension. However, differences were found in the interrelations among the three main aspects of the model in the examined grades (9, 10, and 11). Moreover, it was observed that students find it easier to solve tasks involving perceptual apprehension compared to discursive apprehension tasks, indicating a possible hierarchical structure of figure apprehension. The present study acts as a pilot study of the constructed instrument. Finally, the results are interpreted in relation to the type of geometrical paradigm in which students work at each hierarchical level.