Geodesic
Algebra as a tool for structuring number systems
The Teaching of Mathematics, XVI (2013) no. 2, p. 47 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Numbers in their natural dependence on sets of visible things are abstract products which result from ignoring nature of elements of these sets and any kind of their organization (the way how they are arranged, grouped, etc). We call formulation of this way of cognition {ı Cantor principle of invariance of number\/} and, in this paper, we apply it to a coherent exposition of the first grade arithmetic. Reacting to the way how the elements of a set are grouped, one expression is written, regrouping these elements, another expression is written. Then, such two expressions are equated since they denote one and the same number. Thus, this interplay between meaning and symbolic expressing is the ground upon which the range of numbers up to 20 is structured. Two disjoint sets together with their union make an additive scheme to which an addition or a subtraction task may be attached. Dependently on such a task, sums and differences are written as expressions denoting numbers. To reach the unique decimal (in digits) denotation of a number some steps of transforming the corresponding expressions are made. Displaying these intermediate steps leads to a thorough understanding of the arithmetic procedures, which should precede their suppressing which leads to automatic performance. In particular, methods of adding and subtracting when the ten-line is crossed are treated in detail.
Classification : 1MSC97H20 2MathEducH22
Keywords: Invariance of number, additive scheme, addition and subtraction tasks, number system up to 20. 
@article{TM2_2013_XVI_2_a0,
     author = {Milosav M. Marjanovi\'c and Marijana Zelji\'c},
     title = {Algebra as a tool for structuring number systems},
     journal = {The Teaching of Mathematics},
     pages = {47 },
     publisher = {mathdoc},
     volume = {XVI},
     number = {2},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM2_2013_XVI_2_a0/}
}
TY  - JOUR
AU  - Milosav M. Marjanović
AU  - Marijana Zeljić
TI  - Algebra as a tool for structuring number systems
JO  - The Teaching of Mathematics
PY  - 2013
SP  - 47 
VL  - XVI
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM2_2013_XVI_2_a0/
LA  - en
ID  - TM2_2013_XVI_2_a0
ER  - 
%0 Journal Article
%A Milosav M. Marjanović
%A Marijana Zeljić
%T Algebra as a tool for structuring number systems
%J The Teaching of Mathematics
%D 2013
%P 47 
%V XVI
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM2_2013_XVI_2_a0/
%G en
%F TM2_2013_XVI_2_a0
Milosav M. Marjanović; Marijana Zeljić. Algebra as a tool for structuring number systems. The Teaching of Mathematics, XVI (2013) no. 2, p. 47 . http://geodesic.mathdoc.fr/item/TM2_2013_XVI_2_a0/