The concept of Riemann's integral from the viewpoint of semantic congruence

Authors

  • Claudete Cargnin UTFPR
  • Rui Marcos de Oliveira Barros UEM

DOI:

https://doi.org/10.5007/1981-1322.2016v11n1p16

Abstract

This article discusses the semantic congruence between representations of concepts components of the concept of Riemann integral and the role of conversion in their understanding. Analyses are made of congruence, based on criteria established by Duval, for the summation notation, the concept of convergence and the calculation of the area of a region bounded by definite integral. We conclude that the concept of Riemann integral is full of non-congruence in their composition and requires more attention and care to be introduced to students in Calculus I.

Author Biographies

Claudete Cargnin, UTFPR

Professora do Departamento de Matemática da UTFPR, Câmpus Campo Mourão e do Programa de Pós-Graduação  Mestrado Profissional em Ensino de Matemática da UTFPR - câmpus de Londrina/Cornélio Procópio.

Rui Marcos de Oliveira Barros, UEM

Professor do Departamento de Matemática e do Programa de Pós-Graduação em Educação para a Ciência e a Matemática da Universidade Estadual de Maringá.

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Published

2016-07-07

Issue

Vol. 11 No. 1 (2016)

Section

Artigos

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