As a basis for treatment of elementary school mathematical
themas, a phenomenological scheme representing concepts as three component
entities is given. Three related components: class of examples, mental image
and name, serve very well as a piece of general language used in subject
analysis. With regard to iconic representation of concepts, ``leaf'' used in
that representation is considered as being a premodel of geometric plane. To
underline that idea and hence, to avoid some often encountered discrepancies,
the following rule which governs such representation is formulated: two icons
occupying different places are different.
At the end, the first topic ``Sets and Counting'' is sketched, setting forth
the way how the meaning of words ``set'' and ``element'' can be assimilated at
the initial stage.