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Coordinating Mathematical Structure and Pedagogical Appropriateness: Preschool Teachers’ Problem Posing Across Differently Structured Tasks

Bölükbaş FA, Coşgun AA, Ulutaş İ · 25 Sept 2026

Abstract

Abstract Problem posing is widely recognised as a central mathematical activity, yet little is known about how preschool teachers coordinate the pedagogical and mathematical demands of posing problem situations for young children. This qualitative study examined 15 preschool teachers’ conceptions, reported classroom practices, professional learning needs, and performance across structured, semi-structured, and visually supported open problem-posing tasks. Teachers responded to two visual contexts construction materials and grocery shopping and produced 90 problem situations. Interview data were analysed through descriptive and pattern coding, while task responses were classified as not a problem, non-mathematical, impossible, insufficient, or sufficient. Teachers consistently valued play, concrete materials, everyday-life contexts, and child participation. However, these pedagogical orientations did not always become mathematically explicit and coherent problem situations. Of the 90 responses, 68 were sufficient, 16 insufficient, and 6 were not problems; no response was classified as non-mathematical or impossible. Performance was strongest in structured tasks and became more variable as task structure decreased. All responses classified as not a problem occurred in the open tasks. The two visual contexts yielded the same overall number of sufficient responses but foregrounded different mathematical possibilities. The findings suggest that preschool teachers’ problem-posing competence is best understood as the coordination of pedagogical appropriateness, an explicit mathematical relationship, and a meaningful requirement for children’s action. Open prompts did not automatically produce productively open mathematical problems; instead, they transferred greater responsibility for selecting the mathematical relationship, coordinating information with the requirement, and specifying a meaningful goal. Open task formats may therefore reveal, rather than automatically promote, this coordination. Implications are proposed for practice-based teacher education centred on comparing, revising, and discussing problem situations.