Empirical Didactical Design Using the Zone of Proximal Development to Address Learning Obstacles in Social Arithmetic
Keywords:
Didactical Design Research, Empirical Didactical Design, Learning Obstacles, Social Arithmetic, Zone of Proximal DevelopmentAbstract
This study is motivated by the persistent learning obstacles students face in mastering social arithmetic, which hinder conceptual understanding and the ability to apply mathematical concepts to real-life contexts. The study aims to (1) identify students' learning obstacles in social arithmetic, (2) develop a didactical design based on the zone of proximal development that aligns with students' learning trajectories and obstacles, and (3) analyze the implementation of the design to produce an empirical didactical design that optimizes students' potential. The research was conducted at a public junior high school (SMP) in Indonesia and employed a didactical design research approach comprising three phases. The first phase, prospective analysis, involved identifying learning obstacles among 33 eighth-grade students and developing a Hypothetical Learning Trajectory (HLT) and an Analytical Design Plan (ADP). The second phase, meta-didactical analysis, consisted of implementing the didactical design with 29 seventh-grade students and analyzing their responses. The third phase, retrospective analysis, connected the findings from the implementation with the initial design hypothesis to develop an empirical didactical design. Data were collected through diagnostic tests, interviews, observations, and documentation. The results indicate that the developed didactical design effectively reduced students' learning obstacles, with a decrease of 0.51 in the obstacle score (moderate category). Some aspects require refinement, particularly in managing instructional duration. The design also enabled students to reach the actual development stage, fostered constructive social interactions, and facilitated the application of social arithmetic concepts in realistic contexts. These findings imply that didactical designs grounded in the zone of proximal development can serve as an effective strategy to enhance students' conceptual understanding and socio-mathematical skills, while providing a flexible framework that adapts to individual learning obstacles in Indonesian junior high schools
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