<![CDATA[General Background: Critical thinking is a fundamental competence in 21st-century education and a core skill for elementary students to solve mathematical problems logically and responsibly. Specific Background: In mathematics learning, especially on Greatest Common Factor (GCF) topics, students are expected to interpret information, select appropriate procedures, and justify solutions using sound reasoning. Knowledge Gap: Previous studies have examined critical thinking in elementary contexts, yet detailed profiling of fifth-grade students’ critical thinking across all Facione indicators in GCF problem solving without instructional intervention remains limited. Aims: This study aims to describe the critical thinking profile of a fifth-grade student in solving GCF story problems using Facione’s six indicators: interpretation, analysis, evaluation, inference, explanation, and self-regulation. Results: Using a descriptive qualitative design with one purposively selected high-ability student, data from tests, structured interviews, and written work show that the student successfully identified key information, justified the selection of solution methods, evaluated alternatives, produced consistent conclusions, explained procedures logically, and verified answers reflectively. Novelty: The study integrates Facione’s framework with Peirce’s semiotic analysis to examine the relationship between students’ reasoning processes and problem-solving representations. Implications: The findings provide evidence that detailed critical thinking profiling can inform the design of elementary mathematics instruction that supports higher-order reasoning in GCF learning. Highlights: The participant demonstrated full attainment of all six assessed reasoning indicators. Factor tree procedure was chosen with explicit justification and comparison to alternatives. Reflective checking confirmed answer consistency across different solution approaches. Keywords:Critical Thinking Skills; Elementary Education; Greatest Common Factor; Mathematics Problem Solving; Facione Framework]]>
