Semiotic problem framing: a new framework to guide students and teachers in conceptual understanding and teaching of physics

Problem solving in physics requires more than applying formulas: it involves describing and modeling phenomena, connecting mathematics with physics, and justifying reasoning choices. This process, known as problem framing, has been extensively studied in its cognitive and epistemic dimensions, but its semiotic aspects - how visuals, symbols, language, and metaphors shape understanding - remain underexplored. Physics relies on multiple representational modes that must be coordinated to construct meaning, and semiotics plays a central role in this integration. In this theoretical paper, we propose a new framework - the Semiotic Problem Framing - that explicitly incorporates semiotics into existing problem framing in physics. SPF highlights how students mobilize and shift across linguistic, visual, symbolic, and metaphorical resources in problem solving. For students, it offers a guide to structure reasoning and develop representational fluency; for teachers, it provides a diagnostic tool to scaffold and monitor learning processes. SPF enables analysis of reasoning patterns and error types not captured in previous frameworks, and suggests new directions for instructional design in physics education.