Triadic Semiotic Representations and Didactic Engineering: An Articulation for Teaching School Physics in Secondary Education

The teaching of school physics in secondary education faces a structural semiotic challenge: its phenomena are inaccessible to direct perception, so that all learning depends on the quality of the representations used to make them intelligible. This article analyzes seven didactic sequences designed and implemented by pre-service teachers from the Universidad de Sucre under the methodology of didactic engineering (Artigue, 1988, 1995), with approximately 240 secondary students in Sincelejo, Sucre, across two semesters (November 2025 and May 2026). The analytical lens was the theory of registers of semiotic representation (Duval, 1993, 2006). The results show a mean normalized Hake gain of ⟨g⟩ = 0.643 (range: 0.328–0.810); three of the seven cases reach high gain (⟨g⟩ ≥ 0.70). The semiotic route R3 Analogical → R2 Figural → R1 Verbal proves the most productive for conceptual understanding; R5 Symbolic-algebraic is resisted when introduced without that prior route and successful when it follows it. The concept of semiotic a priori analysis is proposed as a tool that integrates both frameworks for designing school physics sequences.

Didactic Engineering · Semiotic Representations · School Physics · Secondary Education · Teacher Training · Hake Gain

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