# RIEMANN SUM: A COMPUTATIONAL EXPLORATION

C. Cargnin^{1},

R.M. de Oliveira Barros^{2},

A. Mognon^{3}^{ 1}Universidade Tecnológica Federal do Paraná (BRAZIL)

^{ 2}Universidade Estadual de Maringá (UEM) (BRAZIL)

^{ 3}Universidade Tecnológica Federal do Paraná (UTFPR) (BRAZIL)

The Differential and Integral Calculus has been the subject of study by several researches. In recent years, there has been an increase in research related to the integral object, in particular, definite integrals, whose definition is supported in the Riemann sum. Some textbooks used for reference in Differential and Integral Calculus I classes present this setting as if it were something simple to understand. In practice, in the classroom, it is perceived that such simplicity does not exist.This article introduces part of an didactical sequence applied to 1st. period students of several undergraduate courses on the geometric mean of the Riemann Sum. Using the theory of Didactic Situations and theory of Semiotic Representation Register, activities that required the calculation of areas under a curve in a given range were prepared. The students used the Software Geogebra as support to exploration. The proposed tasks became the concept of Riemann Sum easier to understand , however, they had difficulties in writing the formula for the Riemann sum based on the resolution procedures of the tasks, but know how to explain the meanings of all the steps used in this resolution, which indicated the contribution of discourse in natural language for the learning of concepts the Integral Calculus of students.