The aim of this study was to evaluate preservice primary mathematics teachers' ability to discuss and investigate students' thinking process about the concepts of variable, equality and equation, to analyse their ability to predict student difficulties and misconceptions and, in this respect, to present their subject-matter knowledge and possible misconceptions on the related topics. The participants were 130 preservice primary mathematics teachers in their fourth year of university education. The data were collected through a questionnaire consisting of open-ended questions and clinical interviews and analysed qualitatively. The results showed that, in general, the preservice teachers were inadequate in terms of knowledge of students about algebraic concepts, they had insufficient subject-matter knowledge and they had misconceptions. (Contains 1 table and 3 figures.)