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

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.