A Hypothetical Learning Trajectory Design for Social Arithmetic to Fostering Computational Thinking and Self-Regulated Learning Abilities

This study aims to design a Hypothetical Learning Trajectory (HLT) on the topic of social arithmetic to address learning obstacles related to students’ computational thinking (CT) and self-regulated learning (SRL) abilities. Employing an Educational Design Research (EDR) approach, the study developed the Missouri Mathematics Open-Ended Problem-Based Learning (MiMOPBL) model supported by an e-module based on the Predict–Observe–Explain (POE) strategy. The HLT integrates CT and SRL by guiding students through prediction, observation, and explanation stages while solving open-ended contextual problems. Validation results confirmed that the instructional tools—including lesson plans, student worksheets, e-modules, CT and SRL instruments—are both valid and reliable. Content validity assessed using Aiken’s V showed values ranging from 0.80 to 0.98, while reliability testing using Cronbach’s Alpha indicated high internal consistency (SRL: α = 0.85; CT: α = 0.89; observation sheet: α = 0.88). These results indicate that the tools are suitable for use in mathematics classrooms. Although limited to the design phase and one topic, the study offers a structured, competency-based learning design that supports student engagement, problem-solving skills, and independent learning. Future research should explore the effectiveness of this learning design across various topics and student groups.