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This study aims to examine Subject Matter Knowledge (SMK) of pre-service teachers in differential units. There is a notable lack of research focusing on the in-depth knowledge and understanding of pre-service teachers in diffential units. This study, therefore, reconstructed questionnaire items based on previous research surveys and textbooks, containg 12 problems covering the areas of tangents, differentiability, and the properties of derivatives. The questionnaire was administered to pre-service teachers, and the responses were analyzed. The study identifies four key characteristics of pre-service teachers' Common Content Knowledge (CCK) and Specialized Content Knowledge (SCK). Additionally, the types of knowledge reflected in the responses were categorized and explained. Based on this finding, the study concludes that it is essential for pre-service teachers to be aware of the differences between school mathematics and academic mathematics propositions in the domain of differential units. Moreover it emphasizes the need to provide pre-service teachers with opportunities to develop their mathe- matical competence and professional knowledge.
Kim et al. (Sun,) studied this question.