Trigonometry in upper secondary school context: identities and functions
IND's studenterserie nr. 90, 2020. Specialerapport. Matematik.
Vejleder: Carl Winsløw
In the last years of secondary school in Denmark, students transfer from triangle Trigonometry, to unit circle Trigonometry. To this transition, constructing and interpreting graphs of trigonometric functions is also added. The purpose of this thesis is to observe how students transfer between these trigonometric settings, which setting do they mostly work with and to investigate students’ misconceptions related to sin(x) and cos(x).
The results of this thesis are based on observations of lessons and students' interviews in an upper secondary school in Denmark. It was found that some students encountered didactical obstacles when they tried to combine the old knowledge of the triangle setting, to the new knowledge of the unit circle or function setting. Moreover, most students found it challenging to convert between these settings. A main factor for this difficulty was the lack of prerequisite knowledge regarding functions. The results also revealed some misconceptions related to sin(x) and cos(x), such as identifying them to the y-axis and the x-axis respectively, when the students were working in the unit circle setting.