Learning Obstacles in Understanding Pyramid Volume: An Epistemological and Didactical Analysis within the Didactical Design Research Framework

Vallieskha Nurmanita Dhaffah; Septiani Yugni Maudy; Mulia Putra

doi:10.31949/dm.v8i2.18713

Authors

Vallieskha Nurmanita Dhaffah Universitas Singaperbangsa Karawang, Indonesia
Septiani Yugni Maudy Universitas Singaperbangsa Karawang, Indonesia
Mulia Putra Universitas Singaperbangsa Karawang, Indonesia

DOI:

https://doi.org/10.31949/dm.v8i2.18713

Abstract

Understanding the concept of pyramid volume remains challenging for many students, even after prior study. These difficulties indicate learning obstacles that need to be identified before designing effective instructional interventions. This study aimed to identify students’ learning obstacles related to the concept of pyramid volume within the prospective analysis phase of Didactical Design Research (DDR). A qualitative approach was employed involving 35 ninth-grade students from SMP Negeri 13 Tambun Selatan who completed a diagnostic test consisting of six validated items. Based on variations in students’ response patterns, six students were purposively selected for in-depth interviews. To strengthen the credibility of the findings, interviews with a mathematics teacher were also conducted. Data were analyzed using the Miles and Huberman interactive model, including data reduction, data display, and conclusion drawing. The findings revealed seven learning obstacles, comprising four epistemological and three didactical. The epistemological obstacles included difficulties in understanding relationships among pyramid elements, distinguishing points and planes in identifying pyramid bases, recognizing two-dimensional properties as prerequisites for determining pyramid bases, and understanding the meaning of one-third in the pyramid volume formula. The didactical obstacles were associated with procedurally oriented instruction, insufficient reinforcement of prerequisite concepts, and limited opportunities for independent learning. These findings demonstrate that students’ conceptual difficulties are closely related to instructional practices experienced during learning. Therefore, the identified obstacles provide an important foundation for designing learning trajectories and didactical situations that support meaningful understanding of pyramid volume concepts.

Keywords:

Didactical Design Research, Learning Obstacle, Mathematics Education, Pyramid Volume, Learning Trajectory

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