Abstract

In this paper, we split into all intermediate steps and illustrate algorithms of vertical addition and subtraction of two-digit and three-digit numbers. We consider the relating of symbolic codes of arithmetic to their iconic representations to be a basic way of supplying them with meaning. Hence, our didactical maxim is: I see, therefore I understand. Writing this paper, our intension is deepening of teachers' understanding of these classical algorithms of arithmetic and, as our analysis shows it clearly, a right understanding is more a matter of good knowledge of didactics of mathematics than of mathematics itself.

Keywords: Decimal notation; decimal grouping; algorithms of vertical addition and subtraction; regrouping and the Cantor Principle of Invariance of Number.

Pages:  57$-$72     

Volume  XII ,  Issue  2 ,  2009