Designing a Hypothetical Learning Trajectory with Open-Ended Tasks: An Approach to Teaching Angle Measurement

Fazri Zuzano (), Edwin Musdi () and Lufri Lufri ()

International Journal of Innovative Research and Scientific Studies, 2025, vol. 8, issue 3, 1563-1572

Abstract: This study aims to examine the effectiveness of integrating the Hypothetical Learning Trajectory (HLT) with an open-ended approach in teaching angle measurement to pre-service elementary school teachers, addressing the passive learning behavior often observed in PGSD (Primary School Teacher Education) students. Using a design research methodology, this study focused on the first phase preparing for the experiment. It involved 30 third-semester PGSD students in the Basic Mathematics Concepts 2 course. The process included a literature review, student needs analysis, and the development of an initial learning trajectory. Data were collected through pretests, posttests, classroom observations, and student reflections. The findings revealed a notable improvement in students’ conceptual understanding, with average test scores increasing from 56.4 (pretest) to 84.7 (posttest). Students also showed enhanced critical thinking, creativity, and confidence in problem-solving. However, some challenges remained, particularly related to disparities in student abilities and initial resistance to the open-ended learning model. The integration of HLT and open-ended approaches effectively fosters deeper mathematical understanding and active engagement among PGSD students, helping transform passive learning behavior into dynamic participation. The results support the implementation of HLT and open-ended learning in teacher education programs to cultivate essential 21st-century skills. Educators are encouraged to receive training in HLT development and explore digital tools to enhance learning experiences and accommodate diverse student needs.

Keywords: Active Learning; Hypothetical Learning Trajectory; Open-Ended Approach; Pre-Service Teachers. (search for similar items in EconPapers)
Date: 2025
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