Illusion of linearity: Examining the content knowledge of mathematics teacher candidates

The illusion of linearity has been defined as the tendency to perceive mathematical relationships or problems as always linear. This illusion constitutes a significant obstacle in learning and teaching concepts, especially in the mathematics education process. It is important for prospective mathematics teachers to be aware of illusions and to be able to convey their knowledge to students accurately without falling into illusions in order to improve the efficiency of the teaching process and students' mathematical understanding. In this study, prospective mathematics teachers' field knowledge regarding the illusion of linearity was examined. The phenomenology model, one of the qualitative research designs, was used. A total of 41 primary school mathematics teaching senior students, 14 of whom were male and 27 of whom were female, participated in the research in a province in Turkey. The sample group was determined by the criterion sampling method. 10 mathematics teacher candidates who had the illusion of linearity were identified and data were collected through individual interviews with these candidates. The findings show that prospective teachers have the illusion of linearity in function and proportion. These illusions are divided into eight subcategories regarding function and one subcategory regarding proportionality.