Straight Lines and Angles that Move, Students’ Ideas that Touch and Add

Abstract

Background: Visualisation is a crucial skill for several everyday life activities and conceptual construction and development. Objectives: As it represents a substantial part of Euclidean geometry, this article addresses: the study and analysis of the relationships between angles formed from two parallel lines intersected by a transversal and the role of visualisation in the construction and development of geometric concepts imbricated in the mathematical relationships underlying the theme. Design: The methodological approach adopted was Design Experiments. Settings and participants: A teaching situation is presented, in which students from the 8th grade of elementary school at a state public school in Rio de Janeiro, Brazil, performed manipulations on the smartphone screen while carrying out an activity. Data collection and analysis: To analyse this activity, we selected events from a video obtained from the smartphone used by the students. Results: Through interactions and handlings, students visualised, analysed, and built the concepts of corresponding angles and collateral angles by studying a geometric object on the smartphone screen through the GeoGebra application. Conclusions: The geometric work mediated by mobile devices with touch screens enables the curricular reorganisation of Geometry and the articulation and the breaking of the hierarchy of concepts.