This article is aimed at integrating the Technological Pedagogical Content Knowledge (TPACK) system with the Didactic Suitability Criteria (DSC) of the Didactic-Mathematical Knowledge and Competences (DMKC) system to improve the reflection of prospective mathematics teachers on online classes. Thirteen prospective teachers, divided into two subgroups, participated in a training cycle that addressed both models. Each participant used and created indicators of reflection of the assigned model to analyze an online class on functions, and subgroups exchanged reflections to examine the class from the other model’s perspective. It was noted that the DMKC model allows for a broad analysis of the class but has limitations in assessing technology and the teacher's technological knowledge, while TPACK’s emphasis is on technology and teacher knowledge but does not explicitly address mathematical interaction or affective aspects. It is concluded that combining the TPACK model and the DSC of the DMKC model can generate more complete tools to reflect on online math classes and consequently allow for a comprehensive evaluation that covers both the mathematical content and the technological and pedagogical skills of the teacher.

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.