Purpose: This study examined the influence of metacognitive awareness, epistemological beliefs, and mathematical resilience on university students’ perceived mathematical problem-solving ability and explored the cognitive and affective processes students employ when solving mathematical problems. Design/methodology/approach: An explanatory mixed-methods design was employed. Quantitative data were collected from 350 undergraduate Mathematics Education students at a public university in Ghana using a structured questionnaire and analyzed using exploratory factor analysis, confirmatory factor analysis, and structural equation modeling. Qualitative data were obtained from 10 purposively selected students and analysed thematically to provide further insight into students’ problem-solving processes. Findings: Metacognitive awareness (β = .247, p < .001) and epistemological beliefs (β = .273, p < .001) significantly predicted perceived mathematical problem-solving ability, whereas mathematical resilience did not significantly predict perceived mathematical problem-solving ability (β = .105, p = .163). The qualitative findings indicated that students engaged in problem interpretation and strategy planning, monitoring and evaluation, persistence and strategy adjustment, and experienced varied emotional responses during problem solving. Practical implications: Mathematics instruction should incorporate activities that strengthen students’ metacognitive regulation and productive epistemological beliefs while developing resilience alongside mathematical knowledge and problem-solving strategies. Originality/value: The study combines structural evidence on cognitive and epistemological predictors of mathematical problem-solving with qualitative accounts of students’ cognitive and affective experiences, providing a more comprehensive account of problem-solving among university mathematics education students.

Binary classifications of teaching as transmission or constructivism obscure how participation, authority, knowledge practices, and conceptual work can vary within one lesson. This article introduces the social, procedural, epistemic, and conceptual (SPEC) framework for episode-level lesson analysis. SPEC was developed through a structured purposive theory synthesis rather than an exhaustive systematic review. A documented corpus of foundational traditions, observation systems, and targeted verification sources was compared using explicit inclusion, boundary, and disposition rules. Candidate constructs were assigned by observable target; three indicators per dimension were retained as a parsimonious authorial proposal; and qualitative descriptors were generated from theoretically warranted adjacent distinctions checked against cross-dimensional counterexamples. The dimensions are analytically distinguishable but potentially related. Their descriptor codes form non-additive, non-normative profiles rather than composite scores or judgments of teaching quality. An instructional episode is the primary unit; a hypothetical transcript illustrates indicator coding, opportunity/evidence flags, and rejection of nearby alternatives. SPEC is an initial conceptual proposal requiring operationalization, reliability examination, and validity testing. Ordering, thresholds, and cross-domain use require study before evaluative application.