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AUTOUR DU CONCEPT DE FRACTION À l'ECOLE PRIMAIRE EN FRANCE : Étude exploratoire des significations de la fraction au travers des manuels scolaires, des représentations et des connaissances des élèves de cycle III.

Abstract : This study concerns the fraction mathematical concept, mainly in its teaching-learning in the cycle 3 of French primary school. This concept is often difficult to be understood by pupils; it is formally introduced in the CM1 class of the cycle 3 in primary school.The object of this research was, firstly, the study of fractions’ teaching. To do that, we analyzed learning situations that offer activities bearing on fractions in five math textbooks of CM1 and five math textbooks of CM2, all from the same collection ; the goal is to know the different meanings of the fraction present in these books.In a second time, the object of this research was to find out what pupils remain after they studied fractions. For that, a sample of 275 subjects, 160 from CM1 and 115 from CM2, answered to a written questionnaire bearing on fractions. The goal is to study conceptions and representations that pupils have in respect of the concept of fraction, particularly in respect of different meanings of fraction given by these pupils.In a third time, we wanted to know the opinions of a few teachers about the way in which they approach fractions at school. To do that, 8 teachers among the 12 teachers of the classes concerned participated in the study.The analysis conducted on the books was made with the help of an analysis grid; the results of this analysis point out that the activities or learning situations offered in selected books are not equally distributed between the various meanings of fraction.Moreover, the most present meanings of fraction in CM1 books through the activities analyzed are respectively the following: Part of a whole, Measurement and Number; in CM2 books, the most present meanings are respectively the following: Number, Part of a whole and Measurement. However, the activities related to the other meanings are generally present, but with a reduced frequency.To treat fractions’ learning by pupils, the analysis was made around of the knowledge and the representations of the pupils of CM1 and CM2 relative to different meanings of fraction. This analysis, performed on the pupils' answers on the questionnaire, shows that the meaning of fraction the most used by the students of CM1 and CM2, is that of Part of a whole (continuous quantity). The meanings Number, Measure, Part of a whole (discrete quantity) and Number on a number line are present in pupils' answers. However, the other meanings are those who are the less used by the pupils. Moreover, in regards to the manifested meanings of fraction, pupils of both school levels do not differ much. Finally, our study shows that pupils use the most fraction’s meanings found in books. It gives us a light on the subject of the influence of fractions’ teaching in pupils’ training.To know the epistemological and pedagogical conceptions of teachers in their approach to fraction’s teaching, we built the data by a sample survey with 8 teachers. The answers were analyzed using two perspectives, pedagogic and mathematic. For the pedagogical character analysis, a grid was built around the privileged modes of representation by the teachers and around the respective roles reserved to teacher and pupils. In parallel, we verified the mathematical value of the answers provided by the teachers. To introduce the concept of fraction, the teachers say that they give a large place to concrete or graphical representations. Also, the teachers have an important role throughout teaching and learning approaches.
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https://halshs.archives-ouvertes.fr/tel-01302152
Contributor : Abdul Aziz Alahmadati Connect in order to contact the contributor
Submitted on : Wednesday, April 13, 2016 - 3:47:47 PM
Last modification on : Monday, October 19, 2020 - 11:09:13 AM
Long-term archiving on: : Thursday, July 14, 2016 - 5:35:30 PM

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• HAL Id : tel-01302152, version 1

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Abdul Aziz Alahmadati. AUTOUR DU CONCEPT DE FRACTION À l'ECOLE PRIMAIRE EN FRANCE : Étude exploratoire des significations de la fraction au travers des manuels scolaires, des représentations et des connaissances des élèves de cycle III.. Education. Univ. Lyon 2, 2016. Français. ⟨tel-01302152⟩

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