Analysis of Grade XI Students’ Conceptual Understanding of the Law of Sines and Cosines Based on APOS Theory at SMA Negeri 1 Jayapura
DOI:
https://doi.org/10.59211/mjpjetl.v4i2.400Keywords:
conceptual understanding, APOS theory, law of sines and cosine, think aloudAbstract
This study aimed to describe and analyze students’ conceptual understanding based on APOS theory (Action, Process, Object, Schema) on the topic of the law of sines and cosines in Grade XI of SMA Negeri 1 Jayapura. A descriptive qualitative approach was used. Eight subjects were purposively selected from 35 students of Class XI-7 based on a written test, ensuring representation of two students at each APOS stage. Data were collected through a written test and Think aloud interviews conducted at two different times (TA 1 and TA 2), then analyzed using the Miles and Huberman interactive model and verified through time triangulation. The results showed that students’ conceptual understanding of the law of sines and cosines developed hierarchically across the four APOS stages. At the Action stage, students could only execute procedures mechanically without detecting errors. At the Process stage, students could explain steps sequentially and reverse procedures, but could not yet verify their own results independently. At the Object stage, students consciously integrated triangle properties into their solutions. At the Schema stage, students could connect the laws of sines and cosines with other trigonometric concepts and independently evaluate and select more appropriate approaches. Of the 35 students, the majority (77.1%) remained at the Action stage, indicating that instruction still emphasized procedural mastery over the formation of complete conceptual structures.
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