About the concept of angle in elementary school: Misconceptions and teaching sequences

This paper reports classroom research dealing with the difficulties encountered by schoolchildren in the acquisition of angle concept. Two obstacles were pointed out in previous studies: the side-length obstacle and the salience of the prototypical right angle. The first aim of the present study is to determine the extent to which a teaching sequence based on a concrete situation in the meso-space can enable pupils to progress in their conceptualization of angles. This problem situation is based on the notion of visual field. The angle appears in real space between two infinite directions that correspond to two lines of sight. The specificity of this situation is to confront pupils with an angle between two infinite directions in space. The second goal of this research is to study the links between the two obstacles. To answer these research questions, we compared two versions of the teaching sequence, one dynamic (the angle varies) and one static (the angle does not vary) in 3rd and 4th grade classes. The unfolding of the sequence was analyzed and pupils were tested individually before and after the sequence. They were requested to draw angles and angle variations. The results showed that (1) the sequence helped the pupils progress (2) the obstacle of side-length is not the only difficulty faced by pupils; the salience of the prototypical right angle constitutes a real learning obstacle and (3) the type of angle produced and the ability to change its size are linked. In conclusion, the implications for teaching are presented.