<![CDATA[Algebra is one of the fundamental subjects in secondary school mathematics education, but various studies show that students still often experience misconceptions, particularly in root form operations, which tend to persist even after formal instruction. One ability that is considered to have the potential to help students respond to these misconceptions is cognitive flexibility, which is the ability to use, compare, and switch between strategies adaptively. This case study aims to identify the characteristics of students' misconceptions in algebraic root operations and describe the role of cognitive flexibility in terms of variety, shifting, and justification/reflection. The study uses a qualitative approach with a contrastive case study design. Data were collected through a written test containing 12 root questions and semi-structured interviews based on stimulated recall. The analysis was conducted by combining mathematical correctness and cognitive flexibility scores with within-case and cross-case qualitative analysis. The results show that cognitive flexibility plays a role in responding to misconceptions, but its role is conditional. The novelty of this study lies in the finding that cognitive flexibility only contributes to the revision of misconceptions when supported by a strong conceptual understanding. Without this foundation, flexibility tends to produce procedural variations without meaningful conceptual change. The implication is that mathematics teachers need to design root form learning that not only encourages the use of various strategies but also emphasizes strategy comparison and conceptual reflection to help students reconstruct their understanding.]]>
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