Gymnasieelevers förståelse av enhetscirkeln och trigonometri : en undersökning av elevers förståelse av matematiska begrepp, samt vad lärarna anser att nyblivna matematikstudenter bör kunna när de kommer till högskola eller universitet

Sammanfattning: The aim of my study is to investigate how last year students in upper secondary schoolunderstand certain mathematical concepts, in particular the unit circle and its trigonometry.I have used intentional analysis to interpret student’s actions when they solve certain tasks onthe basis of a cognitive, situated and cultural context.Interviews with four university teachers in mathematics about the unit circle, trigonometry,and mathematical understanding, serve both as background for the study and as basis for adiscussion, where I relate students understanding to what the teachers want new students toknow about these concepts when they begin university studies in mathematics.The students were arranged in three groups with three students in each group. Each group waspresented with two tasks, one in which they were asked to calculate the cosine values for onepointed, one blunt and one straight angle, each located in a separate triangle. They were alsoasked to decide whether the points (0,71; 0,71) and d (1 2 , 3 2 ) are located on the unit circleor not.My conclusion is that students mainly have an operational conception of the unit circle andtrigonometry. The lack of structural conceptions result in difficulties in seeing connectionsbetween the concepts in unfamiliar situations. The students search for known strategies andalgorithms to solve the tasks. They know that the unit circle is a circle with radius 1 andcenter at the origin. They are also familiar with related concepts. One student group showsdeep formal understanding, which is what the university teachers would like the students tohave. The other groups have difficulties separating different concepts and to use themathematical language properly.Further research could include a socio-cultural study with the same empirical material. Itwould also be interesting to study how the language and the graphical calculator influencestudent’s understanding of mathematical concepts.