The Depth of Problem Definition: Evaluating Pre-Service Mathematics Teachers’ Initial PCK through Post-Case Study Diagnosis

Source abstract

This qualitative embedded single-case study examined how pre-service mathematics teachers in Eastern Indonesia define pedagogical problems after school-based case studies and how the depth of those definitions differs across initial pedagogical content knowledge (PCK) categories. Six purposively selected sixth-semester students, two each in low, moderate, and high initial-PCK groups, were selected from 44 questionnaire respondents. Data comprised post-case-study reports, an initial-PCK questionnaire, and semi-structured interviews. The data were analyzed through a reflexive thematic procedure involving data condensation, coding, theme development, and cross-category comparison, with triangulation, peer debriefing, member checking, and an audit trail. All participants identified conceptual and procedural difficulties, prerequisite gaps, and modeling obstacles. However, low-PCK participants predominantly described surface symptoms; moderate-PCK participants mapped error patterns and prerequisite weaknesses using evidence; and high-PCK participants constructed precise, evidence-based, multidimensional diagnoses spanning cognitive, affective, and metacognitive dimensions. Topic complexity was treated as an analytic condition rather than a basis for causal inference by comparing the structure and evidential quality of definitions within each case and then across PCK categories. The findings position problem definition as an observable expression of pedagogical reasoning and support explicit, scaffolded diagnostic-competence learning in mathematics teacher education, especially in resource-constrained and diverse educational settings. Keywords: pre-service mathematics teachers, problem definition, initial pedagogical content knowledge, eastern indonesia.