Examining the pedagogical content knowledge of in-service mathematics teachers on the permutations and combinations in the context of student mistakes

Permutations and combinations are generally taught by requiring students to memorize formulas solve problems using the appropriate formula. Students who learn these topics may succeed in gaining high scores on end-of-chapter exams textbooks, while lacking conceptual understanding required deal with real world. Therefore, this study aimed examine in-service mathematics teachers' pedagogical content knowledge (PCK) determine students’ mistakes solving permutations problem their teaching strategies eliminate errors. Data were collected distributing vignettes, CoRe, PaP-eRs thirteen teachers from ten provinces Indonesia after they finished an online professional teacher education program PCK combinations. The data analyzed qualitatively a analysis approach obtain categories inductively. result showed that of was observed identifying student conceptually procedurally, even though some could not permutations. On other hand, instructional can engage all active learning, but most them only give general answers. Furthermore, in-depth topic is needed support development teachers’ pedagogic competencies sustainably. contribution research will be interest curriculum educators.