Abstract. This study examines developing concepts of geometric shapes in 6 to
9 years old children. We use the notions of Duval’s perceptual, operative and
discursive apprehensions and Fischbein’s figural concept to analyse the students’
understanding of shapes and how they completed sorting tasks. We interviewed
30 children ages 6 to 9 and analysed how they recognized and associated figure
attributes so as to classify them. Findings indicate that (a) There is a mismatch
between the term used to name prototypical figures and the way in which they
are understood; (b) That the recognition of attributes to classify figures is not a
uniform process and depends on which attribute is considered (c) The prototypical
figures condition the understanding of the notion of geometrical figure class.
These findings give us new knowledge about how elementary school students
establish relations between perceptual and conceptual approaches in understanding
the progression of the geometrical shapes.
Keywords: Understanding of shapes, figural concept, clinical task-based interview,
geometrical thinking, geometric shapes.