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L'histoire des mathématiques au service d'une nouvelle didactique de la discipline dans les cursus scolaires au Sénégal : approches théoriques et applications

Abstract : Our experience as a mathematics teacher has led us to explore a way that is still underused in Senegal, introducing a historical perspective into mathematics education, to check if it could interest students and motivate them to scientific studies.This thesis, which consists of seven chapters; the first five of which deal with the state of the art and the theoretical approaches. The last two describe and analyze the experimentation carried out in class of “Quatrième” at a College in the suburbs of Dakar.Chapter I is devoted on the one hand to the nature and specificity of mathematics to better understand the difficulties related to its teaching, and on the other hand to a review of the literature on the introduction of a historical perspective into teaching of mathematics, which clarified the use of history in the mathematics classroom. In this chapter are also defined the didactic framework of the thesis and the methodology used to carry out an experimentation in class of “Quatrième”.The context of our research was then detailed in Chapter II through a thorough description of the Senegalese educational system characterized by good results in the construction of classrooms and new scientific and technical blocks (BST), the parity index favorable to girls in primary school and high schools, but also by insufficiencies with the plethoric numbers of students, the weakness of the pedagogic supervision, the desertion of the scientific disciplines, the poor results in examinations certifications and external evaluations in mathematics.The presence of the History of Mathematics in curricula, textbooks and teacher training schemes is examined in Chapter III and compared to France, which has enormous potential in the field.These historical informations served as the subject for the didactic analysis proposed in Chapter IV, which also contains another input to the analysis: the illustrated description of the different types of use of the History of Mathematics. The didactic analysis inspired us in the development of a repertoire integrating the History of Mathematics, proposed to evolve the Senegalese programs.Chapter V, quizzes mathematics students and teachers, prior to the experiment, to collect and analyze their opinions and practices regarding the introduction of a historical perspective. The President of the National Commission of Mathematics (CNM) of Senegal is also put to contribution, through an interview, to give his opinion on the question and to bring us clarifications on some options of the program.The experimentation that we have done is discussed in Chapter VI and concerns six sessions in class of "Quatrième" which relate to the intersection of a circle and a line, the condition of existence of a triangle, the history of numbers, the equation modelling, the resolution of equations of the type ax + b = 0, and the theorem of Pythagoras. We have conceived their didactic engineering. They were then tested by a teacher in our presence. The sequences in the classroom were filmed and transcribed.The last chapter focuses on the analysis of experimentation, which was based on Chevallard’s Anthropological Theory of Didactics (TAD) through praxeology and didactical moments to study students’tasks and filmed sequences. Barbin’s three hypothetical arguments, namely replacement, disorientation, and cultural understanding, were also used in this chapter, along with the analysis of questionnaire responses and interviews submitted to students one year after the experiment, to measure positive effects of experimentation on students.The general conclusion provides information on the results of the experiment which are on the whole very promising in the framework of the improvement of the teaching lessons of the mathematics in Senegal despite the difficulties noted in the management of the time and related to the large number of students in the class where the experiment took place.
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Oumar Sagna. L'histoire des mathématiques au service d'une nouvelle didactique de la discipline dans les cursus scolaires au Sénégal : approches théoriques et applications. Education. COMUE Université Côte d'Azur (2015 - 2019), 2019. Français. ⟨NNT : 2019AZUR2035⟩. ⟨tel-02862767⟩

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