Errors associated with additive operations with fractions: An exploratory study with high school students
Main Article Content
Keywords
Rationals, Addition and subtraction of fractions, Errors, Prior knowledge
Abstract
This is an exploratory case study of qualitative and descriptive nature located in an interpretative paradigm, whose purpose was to identify the errors associated with the additive operations with fractions, of students between 11 and 16 years old, who are in the seventh grade of secondary school in a public educational institution in the municipality of Quibdó. The sample consisted of one hundred and ninety-fve students who underwent a diagnostic evaluation to verify their level of understanding of this topic. It is assumed that the Basic Learning Rights in Colombia state that, in this grade, students can solve problems involving various operations with rationals in diferent contexts. The results show that students add numerators and denominators as if they were two independent whole numbers, and it was also identifed that when fractions have the same numerator, students keep it and add the denominators. Likewise, mistakes are made when using algorithms, since they do not consider whether the fractions are homogeneous or heterogeneous and an irreducible fraction is not ofered as an answer. It is concluded that students make mistakes that allow inferring a lack of understanding of how to solve operations that involve adding or subtracting fractions, as well as a difculty in understanding the meaning of the concept of fraction according to the situation.
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Wilmer Ríos-Cuesta, University of the Valley, Colombia
Doctor (c) in Education from the Universidad del Valle
Omar Harry Asprilla-Mena, University of Medellin, Colombia
Magister in Education from the University of Medellín. Faculty of Social and Human Sciences, University of Medellín