Özet:

In recent years, the emphasis on concept teaching and conceptual understanding has played a central role in mathematics education curricula. The conceptualization of number systems is important to understand all areas of mathematics. Considering the difficulties experienced in the conceptualization of real numbers, it is seen that students have difficulty in understanding the relationship between real numbers and other number systems. This study aims to investigate pre-service mathematics teachers' conceptions of the property of completeness, which is the most basic element that distinguishes a real number set from other number systems. To this end, the APOS theory, which reveals the mental structures and mechanisms of the individual regarding a concept, was used. Data were collected via semi-structured interviews with three pre-service teachers. The data were analyzed using the descriptive analysis method, and the findings were presented under two themes, which are the epistemology of the concept of the property of completeness of real numbers and the mental structures in the schemas related to the property of completeness of real numbers. The findings revealed that the pre-service teachers' conceptions of the property of completeness of real numbers was mostly at the action level. The study found some mental structures such as the representation of rational numbers on a line, which should be included in the genetic decomposition to be created in the context of the APOS theory regarding the completeness of real numbers.

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