The concept of function - Critical aspects induced by teaching and textbook

Although students' understanding of the concept of function has been studied by quite a number of researchers internationally, there has not been a lot of research on the subject in Sweden. This paper is an attempt to analyse what the students are offered to learn about the concept of function both in the classroom and in textbooks and what the students actually learn. The presentation is based on data collected while the same object of learning is treated in two classes, and it includes two teachers and 45 students. Among other things, the data consists of video-recordings of lessons and tests. In the analysis, concepts relating to variation theory have been used as analytical tools. From this perspective a fundamental role of teaching is to bring critical aspects of subject matter into focus. The study focuses on what the individual is doing and expressing in relation to the object of learning. The new way of understanding the relation between learning and teaching made it possible to find that some of the critical aspects in students' learning are induced by teaching and textbook exposés. One of these critical aspects is the argument of the function, namely whether it is presented implicitly (y) or explicitly (fix)).