Investigating students' critical thinking in solving fractional problems based on Higher Order Thinking Skills (HOTS) viewed from self-efficacy and FRISCO model

Background: Critical thinking is recognised as the highest level of thinking, essential for exploring knowledge and generating new ideas. In the context of mathematics education, particularly at the elementary level, understanding how students engage in critical thinking when solving Higher Order Thinking Skills (HOTS) problems is particularly important. Objective: This study investigates students’ critical thinking processes in relation to their self-efficacy levels using the FRISCO framework—Focus, Reason, Inference, Situation, Clarity, and Overview—during the HOTS mathematical problem-solving process. Method: An exploratory case study design was conducted with 45 elementary school students. Data were gathered through a self-efficacy questionnaire, written tests, interviews, and content analysis of documentation to identify patterns and characteristics of students’ critical thinking processes. Results: Not all components of the FRISCO framework were fully demonstrated by the students. However, they were able to perform mathematical reasoning to formulate ideas and devise problem-solving strategies based on conceptual understanding. In interviews, they frequently used visual representations to clarify their thinking, especially in the 'Clarity' component. Additionally, elements of metacognition emerged spontaneously during the 'Overview' stage, suggesting self-initiated reflection without external intervention. Conclusion: Although elementary students do not consistently exhibit all components of the FRISCO framework, their demonstrated abilities in reasoning, use of visual clarification, and spontaneous metacognitive behaviours highlight a developing capacity for critical thinking. Unique Contribution: This study provides empirical insights into how young learners engage in higher-order thinking through the FRISCO lens, illustrating a novel application of the framework in elementary mathematics education and examining the moderating influence of self-efficacy. Key Recommendations: Educators should cultivate learning environments that foster metacognitive development and encourage the use of visual tools to aid conceptual clarity. Future research should investigate scaffolding strategies to strengthen each FRISCO component across varying levels of self-efficacy.

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