The algorithm of division in the teaching of elementary arithmetic

Abstract

The algorithm of division, as a work tool and didactic resource towards the achievement of significant and relevant learning in students and in the process of knowledge development, has applications in the structuring and teaching of elementary arithmetic: The polynomial representation of the Natural numbers, the calculation of the greatest common divisor of whole numbers, the decimal representation of fractional numbers, etc. Therefore, the mathematics teacher for the initial levels of basic education must know, with breadth and depth, the process of its structuring and its usefulness or applications, initiated in the development of the division as a particular case of subtraction and with applications of heuristic activities, oriented to the process of rediscovery with applications of previous concepts and properties. Taking the set ℕ, in the context of the set theory and with representation of its elements by numerals, follow the basic operations and the approach and solution of equations in ℕ with applications of properties, reaching the division with remainder as formalization of processes of distributing objects in equal quantities, which leads to the formulation of the Division Algorithm and is completed with applications to the calculations of the greatest common divisor and least common multiple of two numbers and the decimal expression of a fraction of numbers in ℕ, presenting properties keys with illustrations of particular cases.