Investigating of Different Apprehensions of Secondary school Students When Confronting Geometric Figures

Representation is one of the appropriate tools for displaying the relationship between the components of a concept or a situation. However, any representation cannot completely describe a mathematical concept and can only provide information regarding some aspects of that concept. Solving a geometrical task often requires interaction among these three types of apprehension (perceptual, operative, and discursive) and recognition of their differences. This study aims to investigate middle school students’ apprehensions about confronting geometrical figures when doing geometry homework. Thus, a case study was designed. To this end, a test based on Duval (1998) was given to 305 students of the ninth, tenth, and eleventh grades. Qualitative analysis of the answers based on Duval’s cognitive argument indicated that most of the students use perceptual apprehension more than operative apprehension to solve the problems. Further, teaching geometry regarding cognitive apprehensions can help students to promote from the natural path of looking at a geometrical figure to the mathematical one. Therefore, the findings of this study can shed light on the in-service training of teachers.