摘要：The purpose of this study is to draw attention to the concepts of “formula” and “rule” in mathematics, thereby revealing the views of pre-service teachers relating to these concepts by exploring their knowledge in, and their capacity to exemplify these concepts. The study is important in that it would reveal how pre-service teachers see the concepts of “formula” and “rule”, and to what extent they associate these concepts with mathematics, and further contribute to the field as there is currently no similar study in the literature. For this purpose, researchers prepared a diagnostic test consisting of ten questions. Nine (9) of the questions were open-ended, and 1 was multiple-choice. With this diagnostic test, pre-service teachers were expected to explain the concepts of formula and rule, reveal the formula and rule that first come to their mind, express the formulas and rules they learned during secondary and high education, describe what sort of a mathematics without formula and rules would be, and finally answer the question “is mathematics without formula and rules possible?”. The sample of the research was composed of a total of 159 pre-service mathematics teachers including Grades 1, 2 and 3 students in Kars. The data were analysed by qualitative analysis and results were tabulated to indicate frequency and percentage values. It has been concluded that pre-service teachers associate the concepts of formula and rule with mathematics, they mathematically internalize and correctly interpret these concepts, they are accustomed to and familiarized with these concepts, and they believe mathematics without formulas and rules is not possible. Mathematics without formula and rule would be meaningless and difficult, take long time to study, and would not be possible, and mathematics can only be implemented through solving with individually proven concrete concepts and describing the rationale behind them.
