How preservice mathematics teachers construct criteria for worthwhile mathematical activities from written reflections

This qualitative study examines how 81 pre-service mathematics teachers articulate and justify criteria for judging whether a mathematical activity is worthwhile. Using post-module written reflections and reflexive thematic analysis, we trace how participants construct inclusionary and exclusionary criteria and the boundaries they draw around quality. Five themes organize their evaluative reasoning: cognitive demand and depth, student engagement and agency, contextual relevance, clarity and structure, and curricular alignment and feasibility. The findings show that participants do not merely list features; they negotiate tensions (e.g., depth versus accessibility, agency versus control, authenticity versus contrivance) and use these tensions to justify acceptance, rejection, and principled adaptation ideas. The study contributes an empirically grounded account of criteria construction as an element of emerging instructional vision and offers design implications for methods coursework that aims to cultivate principled, task-centered judgment. Claims about classroom enactment are intentionally cautious because the dataset consists exclusively of written reflections collected immediately after the module.