Abstract Researchers in Mathematics Education have consistently found that the concept of angle poses a persistent challenge for students. This study examines how combining physical navigation with its simulation through programming supports the conceptualization of angles as turns and measures. Employing design-based research methodology, we engaged a class of 12-year-old primary students in two navigational activities. Initially, they physically navigated their school’s neighborhood while tracking their paths using a Global Positioning System application. They later recreated these paths in a programmable digital environment, using simple directional commands to move a digital entity simulating their prior navigation. The data collected included audio and screen recordings. In the thematic analysis critical episodes were identified, indicating how embodied schemas provided by physical locomotion were re-enacted, supporting the construction of definitional metaphors about angles as measurable spatial relationships between two directions. The findings indicate that large scale embodied activities such as navigation in physical spaces in combination with simulation activities support students’ understanding of angles as spatial relationships between two directions turns and angle measurement, contributing actionable knowledge for the design of learning environments that serve as scaffolding metaphorical domains for students to transform embodied experience into mathematical understanding and expression.
Gkreka et al. (Fri,) studied this question.