Influence of Context on Greatest Common Divisor Problem Solving: A Qualitative Study

Abstract

This paper presents results from a study about problem solving related to the concept of the greatest common divisor with secondary school students. The perspective of the analysis is the meaningful learning of the constructivist theory. The main objectives are to assess the students’ competence in the resolution of such problems and analyze if the difficulties in the acquisition of this competence are influenced by the kinds of magnitudes or the context of the problem. The results suggest that some contexts generate more difficulties to perform the use of the greatest common divisor. Moreover, some erroneous patterns have been detected. On one hand, students tend to relate and confuse the concepts of greatest common divisor and lowest common multiple. On the other hand, they have a predisposition to simplify problems, performing only the operation to obtain the greatest common divisor, and without thinking that additional arithmetic operations can be performed.

Keywords

• greatest common divisor
• word problems
• secondary school education
• context
• erroneous patterns
• learning difficulties