Geodesic
A Broader way Through Themas of Elementary School Mathematics, IV
The Teaching of Mathematics, V (2002) no. 1, p. 47 .

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Continuing with the didactical analysis of main topics of school arithmetic, first we cover the technique of using place holders as an indispensable device for realization of aims and objectives present in the contemporary process of learning and teaching arithmetic. To ensure the enforcement of correct responses and clear goals of calculation, we insist on the function of these graphical signs as being holders of blank spaces (and it means that a numerical value should never be assigned to such signs). Though an ongoing idea of ``early algebra'' has not yet got its clear contours, it puts forward a more extensive use of numerical expressions in the elaboration of arithmetical topics. In this frame, we consider meaning-based equating of different numerical expressions and establishing of the main rules of arithmetic on that same base. The manner of expressing these rules is of three kinds: procedural (example by example), rhetoric (in words) and symbolic (using letters in the role of variables). The order in which these three manners have just been mentioned is the natural one to be followed in school practice. The procedural manner is also one which is inevitably connected with the use of place holder technique and we treat it here with scrupulous attention to detail.
Classification : 00A35
Keywords: Place holders, manners of expressing arithmetical rules 
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Milosav M. Marjanović. A Broader way Through Themas of Elementary School Mathematics, IV. The Teaching of Mathematics, V (2002) no. 1, p. 47 . http://geodesic.mathdoc.fr/item/TM2_2002_V_1_a2/