ANALYSIS OF PRE-SERVICE MATHEMATICS TEACHERS' INTERPRETATIONS OF THE SYMBOL dx AND EXPLANATION MODES IN INSTRUCTIONAL SITUATIONS

This study investigates how pre-service mathematics teachers interpret the differential symbol dx and how their interpretations manifest as explanation modes in instructional situations. The symbol dx exemplifies the epistemological discontinuity between school mathematics, where it appears as mere notation, and university mathematics, where it is defined as an infinitesimal or a differential form. Data were collected from 21 first- and second-year undergraduate students in mathematics education, and 16 valid responses were analyzed using data from written surveys, supplemented by follow-up interviews. Analysis revealed five interpretation types ranging from symbol-based view to differential form, and five explanation modes ranging from conventional to reconstructed. Results indicate that while some pre-service teachers possessed Advanced Mathematical Knowledge (AMK) regarding dx, this did not automatically transform into Specialized Content Knowledge (SCK) or Horizon Content Knowledge (HCK). These findings suggest that pre-service teacher education should provide opportunities to transform AMK into pedagogically meaningful forms of knowledge for teaching.