Surveyed in historical perspective, the contents of school geometry can be
sorted into the following three stages: intuitive, pre-Euclidean and Euclidean. Geometric topics usually found in primary
school programs constitute the first stage of intuitive geometry. Although this geometry is related to the perception of
the surrounding real world, both the coherence and order in its exposition are equally important. This paper is devoted to
that didactical task.
At this first stage, pairings of the real world appearances (objects and their collections) with geometric models (iconic
signs and their configurations) make the main learning procedures. These pairings are interactive, meaning that the
appearances ``re-animate'' the models and the latter serve to the intelligible conceiving of the former. In order to
discriminate between the two sides of this process of pairing, we consider two levels of intuitive geometry. When
conveyors of geometric meaning are real world appearances, we speak of inherent geometry and when such conveyors are
configurations of iconic signs, we speak of visual geometry. These latter signs (called here ideographs) express the
meaning of geometric concepts and their deliberate use leads to the assimilation of this meaning.
Following Poincaré's views on genesis of geometric ideas, we formulate a cognitive principle stating that perception of
solids in the outer space, in the way when all their physical properties are abstracted (ignored), leads to the creation
of these ideas. In addition, an intelligent ignoring of extension leads, then to the creation of concepts: point, line
In the final didactical analysis, a series of basic geometrical concepts will be discussed (and this paper includes:
point, line, segment, ray and straight line).
Keywords: Intuitive geometry, levels of inherent and visual geometry, principle of creation of
geometric ideas, point, line segment, ray, straight line.