Designing area of circle learning trajectory based on “what-if” questions to support students’ higher-order thinking skills

The study material on circle areas is contextually oriented and aids students in comprehending their surrounding environment. Higher-order thinking skills are imperative for the success of circular learning, as they help students grasp concepts holistically and solve concept problems. "What-if" questions can enhance students' higher-order thinking skills through problem-solving activities, fostering critical and creative thinking. However, applying "what-if" questions is limited to serving as problem-posing triggers, resulting in minimal variation in the material. Therefore, this study aims to design a learning trajectory for the area of circles based on "what-if" questions to enhance students' higher-order thinking skills. This research also addresses the gap by utilizing "what-if" questions to construct and evaluate circle area learning activities. We employed design research as the research method, conducted in three stages: preliminary design, experimental design, and retrospective analysis. The results demonstrated that the designed learning trajectory enhanced higher-order thinking skills in various aspects. Students exhibited critical thinking and profound analysis when working on worksheets and addressing the provided problems. Moreover, students showcased creative and divergent thinking abilities, enabling them to generate alternative problem solutions. Furthermore, optimizing technology usage and emphasizing reasoning in learning should be augmented to enhance student motivation and foster innovative learning.