MATH EDUCATION

Analysis of pre-service mathematics teachers' interpretations of the symbol 𝑑⁢𝑥 and explanation modes in instructional situations  [Journal]
(Joint with Jihun Kwak and Kyeong-Hwa Lee)

Abstract : This study investigates how pre-service mathematics teachers interpret the differential symbol 𝑑⁢𝑥 and how their interpretations manifest as explanation modes in instructional situations. The symbol 𝑑⁢𝑥 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 𝑑⁢𝑥, 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.