Radian riddles: semiotic challenges in students’ understanding of the semantic role of π in trigonometry

Date

2026-01-01

Author

Sahin, Zulal
Erbaş, Ayhan Kürşat

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This study investigates how high school students understand the semantic role of π in trigonometry, using the lens of semiotic representational systems and task-based clinical interviews. Specifically, it examines conceptual problems and ambiguities in students’ initial understanding of π and other real numbers as sine and cosine arguments, immediately after school trigonometry, following the convention for representing radians with π notation and degrees without it. Results reveal that students associated π in different representations with multiple real values (e.g. associating π with 180 or –1, and 2π with 1 or 0). These results highlight the vital role of understanding semiotic conventions (e.g. representing radians with π) as a customary choice among equally-valid-alternatives (e.g., with or without π) for recognising invariant mathematical actions behind signs-and-symbols representing mathematical entities. Based on the findings, we propose a model for coherent understanding of the set of real numbers as domains of sinusoidal functions.

Subject Keywords

Cognitive conflict factor, domains of sinusoidal functions, semiotic convention, the number pi

URI

https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=105031138712&origin=inward
https://hdl.handle.net/11511/118885

Collections

Department of Mathematics and Science Education, Article