Geometrical intuition components for designing mathematical tasks

Geometrical intuition is the ability to visualize, construct, and manage geometrical shapes in the mind when solving geometry problems. Geometrical intuition requires four skills: the ability to construct and manage geometrical figures in mind, perceive geometrical properties, connect pictures to concepts and theories in geometry, and determine where and how to begin when solving geometry problems. This geometric intuition ability is important for developing problem-solving. Therefore, we need a task that can be used to identify and develop students' geometric intuition abilities. This research aims to design a geometric intuition task. We employ design research methods to design geometrical intuition tasks by conducting a literature review on geometric intuition and geometry tasks, creating geometrical intuition tasks, and estimating and noting the possible student responses. This study produced three types of tasks based on the four components of geometric intuition. We provide a list of possible responses that junior high school students may provide, as well as practical suggestions for teachers. We recommend research using our developed task to evaluate students' geometrical intuition.