# Les fonctions sinus et cosinus dans le secondaire en France et au Cambodge

Abstract : The themes “Trigonometry” and “Trigonometric Functions” are interesting but not very well covered in mathematics didactic, especially in the French context. However, they have long been present in French and Cambodian curricula. We are interested in students’ learning of these mathematical themes in secondary education, as well as the difficulties of understanding related to them. The study objects of secondary school, namely “cosine and sine of a geometric angle”, “cosine and sine of a real number”, “cosine and sine of an oriented angle” and “usual cosine and sine functions of a real variable”, constitute both mathematical and didactical difficulties: there are changes in settings, changes in mathematical objects (quantities “angle” and “length” – and their measurements – real numbers) with the same signs “ ” and “ ” used to designate different study objects. We focus on transitions between different settings, on students’ difficulties in learning, and in particular on the switch between the trigonometry of the trigonometric circle and the cosine and sine functions of a real variable, in French Terminale Scientifique (grade 12) (corresponding to the Première (grade 11) “Spécialité Mathématiques” curriculum in force for the new school year in September 2019) and in grade 11 in Cambodia (corresponding to the Première in France). For our study, we mainly rely on the praxeological organization of the Anthropological Theory of the Didactic. We determine three local mathematical organizations (LMO) corresponding to the trigonometry of the triangle, the trigonometry of the circle and the trigonometric functions. These LMOs arise from the study of French and Cambodian curricula pertaining to trigonometry, sine and cosine functions in secondary school, along with analyzes of a selection of textbooks. We present a mathematical theory to justify, construct and rigorously coordinate the three LMOs. Then, using the task analysis tools of the didactic/ergonomic Double Approach, we elaborate a questionnaire on the three determined LMOs. This is intended for grade 12 students, in order to evaluate the effects of the teaching trigonometry, sine and cosine functions in secondary school. The curricula study, the mathematical study and the questionnaire, in the French and Cambodian contexts, lead us to conceive, using the milieus structuration analysis tools from the Theory of Didactic Situations, a didactical situation focusing on the notion of periodicity aiming to discover the notions of sine and cosine functions via a graphical register, both in grade 12 in France and in grade 11 in Cambodia. The results on the whole research show students’ difficulties in understanding these two themes via the three LMOs and reveal both a didactical and an epistemological obstacle in the teaching and learning of the cosine and sine objects as well as the mathematical objects that accompany them. Carrying out targeted research by focusing on the mentioned abode obstacle, on the students’ side and on the teachers’ side, will lead to a didactical organization allowing to avoid the teaching and learning didactical obstacle of the two themes in secondary school.
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https://tel.archives-ouvertes.fr/tel-02983421
Contributor : Abes Star :  Contact
Submitted on : Thursday, November 5, 2020 - 12:46:10 PM
Last modification on : Thursday, November 5, 2020 - 12:46:11 PM

### Files

LOENG_Ratha_vd2.pdf
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### Identifiers

• HAL Id : tel-02983421, version 1

### Citation

Ratha Loeng. Les fonctions sinus et cosinus dans le secondaire en France et au Cambodge. Education. Université de Paris, 2019. Français. ⟨NNT : 2019UNIP7020⟩. ⟨tel-02983421⟩

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