How to construct theorems of parallelism condition? A study of learning obstacles and GeoGebra-based didactical design

Abstrak

In Euclidean geometry, parallelism constitutes a foundational concept from which numerous geometric ideas are derived. Despite its fundamental role in geometry and its importance in developing deductive and logical reasoning, research on the concept of parallelism—particularly concerning students’ learning obstacles and corresponding didactical approaches—remains limited, especially in higher education contexts. This study investigates the construction of theorems related to parallelism conditions by examining learning obstacles and implementing a GeoGebra-based didactical design within the framework of the Theory of Didactical Situations. Employing a qualitative approach with a phenomenological hermeneutic design, the study involved 64 undergraduate students from the Mathematics Education Department of a public university in Aceh, Indonesia, to identify the learning obstacles, and 35 students who participated in the implementation of the designed instructional intervention. Data were collected through document analysis, interviews, classroom observations, and audio–video recordings. The data analysis followed the three stages proposed by Miles and Huberman: data reduction, data display, and conclusion drawing. The findings revealed that students’ understanding of the theorems concerning parallelism conditions was impeded by three primary types of learning obstacles: epistemological, didactical, and ontogenic. To address these challenges, a GeoGebra-based didactical design was developed and implemented. The results demonstrated that this design effectively mitigated the identified obstacles and facilitated students’ construction of the theorems of parallelism conditions. Furthermore, the implementation appeared to foster a gradual shift in students’ learning orientation from procedural toward conceptual understanding, although this transition was not entirely uniform. Finally, the study highlights the pedagogical significance of integrating didactical situation theory into the learning process and employing dynamic visualization tools such as GeoGebra to support the transition from empirical to deductive mathematical reasoning.