Abstract:

The aim of this study is to examine the mathematical understanding levels of secondary school mathematics teacher candidates regarding the concept of rational numbers according to the Pirie-Kieren theory. The research was carried out with three pre-service teachers studying in a university in Istanbul's primary school mathematics teaching program. The pre-service teachers were selected from among volunteer pre-service teachers with a high and good level of academic achievement and high communication skills who took the courses "Basics of Mathematics", "Secondary School Mathematics Curriculum", and "Teaching Numbers". The research was designed according to the case study pattern. The data were collected through a rational numbers concept test consisting of four open-ended questions on the concept of rational numbers developed by the researchers and semi-structured interviews. The obtained data were analyzed according to the Pirie-Kieren comprehension layers. The study determined that pre-service teachers were mostly in the "image creation" layer. Considering the process together with the semi-structured interview results, it was determined that the pre-service teachers tried to construct their knowledge by folding back and forth between the layers of "having the image", "noticing the feature", and "abstraction". In addition, pre-service teachers' mind maps were created according to the Pirie-Kieren theoretical model, and the results were discussed. According to the results obtained, suggestions have been developed for researchers in this field.