Étude exploratoire des représentations de la fraction chez les élèves de 6è : cas des élèves du Lycée Bilingue d’Application

Abstract

This study focuses on the teaching and learning of fractions in 6e, and on student's representations of fractions.The fraction is one of the concepts whose importance is directly seen in the student's immediate environment; it is a very difficult concept for students, comprising a multifaceted notion encompassing several interdependent meanings. Given that, in the competency-based approach recommended for teaching, the student must be able to deploy mathematical reasoning and solve problems relating to life situations, the student must be able to appropriate all the meanings of the fraction in order to solve problems. There is a lack of conceptual understanding of the fraction among students of 6e; these students memorize rules "to get by" because the basic principles have not been acquired, and they often don't understand the meaning of what is given to them. Our aim was to identify the representations of the fraction concept held by 6th graders, and to see how these representations are constructed on the basis of teaching practices. Our theoretical frameworks and literature review have helped us to clarify these points. The meanings of fraction retained from the literature are: part of a whole, part of a set (discrete case), operator, ratio, quotient, measure, number on a number line and number. To carry out our research, we first analyzed the textbook to see what representations of the fraction were present and how fractions were approached. We then drew up a questionnaire for teachers to see how they approach fractions. We devised a questionnaire for pupils to find out how they represent fractions. The results show that the fraction most present in the pupils' minds is that of part of a whole, and they have great difficulty in illustrating the other meanings. The link was established between the students' representations and the results of our analysis of the textbook and teaching practices. At the end, we have made recommendations that we hope will benefit teachers in the field and inform future research.