Construction of the Division Algorithm in Fourth Elementary Year in a Chilean School

Abstract

From a socioepistemological approach, this qualitative study explores the argumentation provided by nine-year-old students to characterize the process of construction of the division algorithm in the natural number system. For this, a didactic situation was designed in which students were able to provide argumentation and to give signification in the process of solving divisions, problems of distribution and grouping. The first findings show that division by grouping was not considered division by the students who only recognized this operation as sharing equally. Besides, students did not consider the result as a single number, but as the product of the quotient with the divisor, adding the remainder.

From a socioepistemological approach, this qualitative study explores the argumentation provided by nine-year-old students to characterize the process of construction of the division algorithm in the natural number system. For this, a didactic situation was designed in which students were able to provide argumentation and to give signification in the process of solving divisions, problems of distribution and grouping. The first findings show that division by grouping was not considered division by the students who only recognized this operation as sharing equally. Besides, students did not consider the result as a single number, but as the product of the quotient with the divisor, adding the remainder.