Geometry learning trajectories: A systematic review and the development of the GEO-INTECH framework

Abstract

Mathematics learning faces challenges in bridging abstract concepts through concrete experiences, requiring instructional designs that support the gradual development of conceptual understanding. This study systematically synthesizes research on geometry learning trajectories, focusing on conceptual development and technology integration. Specifically, it examines the characteristics of Design Research and Design-Based Research, trends in theoretical framework, the design of learning activities, the role of technology, and evidence of the effectiveness. A systematic literature review following the PRISMA 2020 guidelines was conducted, and 31 studies were synthesized using thematic analysis. The findings reveal two complementary design architectures: Design Research, characterized by structured learning trajectories grounded in Realistic Mathematics Education, and Design-Based Research, which adopts a dynamic and exploratory approach by integrating multiple theoretical perspectives and digital technologies. Learning activities progress from contextual and manipulative experiences to representational exploration and conceptual generalization, supporting students' abstraction and conceptual development. Technology serves different pedagogical roles, functioning as a supporting tool in Design Research and as a learning environment and an object-to-think-with in Design-Based Research. Evidence of effectiveness is reflected through process-oriented indicators, including the alignment between Hypothetical Learning Trajectories and students' responses, the development of geometric thinking, and conceptual generalization. Based on these findings, this study proposes the GEO-INTECH framework, which integrates design architectures, learning activities, technology roles, and evidence-based evaluation to support the design of technology-enhanced geometry learning trajectories and guide future research.