The purpose of this study is to apply the Five Practices to high school mathematics instruction as a means of implementing competency-based education and to analyze the reflective knowledge gained by the teacher through the instructional process. The researcher conducted four lessons with a first-year class at a general high school, repeatedly engaging in a cyclical process of planning, implementation, and reflection while applying the Five Practices, and analyzed the patterns of practice implementation as well as the teacher’s reflective knowledge. The findings indicate that the Five Practices served as a useful instructional guide for enacting teaching and learning methods aligned with the 2022 Revised Mathematics Curriculum, which emphasizes the development of key mathematical competencies. The study identified differences in the improvement patterns depending on the nature of each practice, interdependencies among the practices, and the characteristic of repeated implementation of certain practices within individual classroom activities rather than across whole lessons. Furthermore, the teacher’s continuous reflection and repeated lesson implementation played a significant role in enhancing the application of the Five Practices. This study confirmed that the Five Practices can serve as detailed instructional guidance for implementing competency-based lessons, and it is expected to offer practical implications especially for teachers seeking concrete strategies to enhance subject-specific competencies.
Yoon et al. (Mon,) studied this question.