Hypothetical Learning Trajectory for Ninth Graders’ Understanding of Curved Three-Dimensional Shapes through Javanese Ethno-Realistic Mathematics Education
DOI:
https://doi.org/10.31980/plusminus.v5i2.2906Keywords:
Design Research, Hypothetical Learning Trajectory, Curved Three-dimensional Shapes, Ethno-Realistic Mathematics Education (E-RME), Problem Solving, Penelitian Desain, Hipotesis Lintasan Pembelajaran, Bangun Ruang Sisi Lengkung, Etno-Pendidikan Matematika Realistik, Pemecahan MasalahAbstract
Geometri merupakan aspek penting dalam matematika yang mendukung perkembangan kemampuan kognitif siswa. Meski demikian, pemahaman terhadap konsep-konsep geometri, khususnya yang berkaitan dengan bangun ruang sisi lengkung, sering kali menjadi kendala bagi siswa. Artikel ini bertujuan untuk menyusun dan menyajikan sebuah lintasan pembelajaran hipotetik mengenai bangun ruang sisi lengkung dengan pendekatan Etnomatematika Realistik Jawa. Penelitian dilakukan menggunakan metode design research yang mencakup tiga tahap utama, yaitu perancangan awal, pelaksanaan eksperimen pembelajaran, dan analisis retrospektif. Penelitian ini melibatkan siswa kelas IX di salah satu SMP di kota Semarang. Fokus pembahasan artikel ini berada pada tahap desain awal, yakni pengembangan hipotesis lintasan pembelajaran yang meliputi empat aktivitas utama: (1) mengenali unsur-unsur bangun ruang sisi lengkung melalui pengamatan video berbasis konteks budaya, (2) menyusun pemahaman tentang luas permukaan dan volume tabung, (3) merumuskan luas permukaan dan volume kerucut, dan (4) menemukan rumus luas permukaan serta volume bola. Rangkaian aktivitas dalam lintasan pembelajaran ini dirancang untuk membantu siswa membangun pemahaman yang lebih mendalam terhadap konsep bangun ruang sisi lengkung, sekaligus menumbuhkan apresiasi terhadap budaya lokal dan keragaman dalam berpikir matematis. Lintasan pembelajaran hipotetik ini dirancang untuk diimplementasikan pada kelas eksperimen dan pengajaran berbasis penelitian menggunakan E-RME untuk meningkatkan kemampuan pemecahan masalah matematika siswa yang merupakan novelty dari penelitian ini.
Geometry plays a vital role in mathematics to foster students' cognitive growth. Nevertheless, grasping geometry concepts can be particularly difficult, especially when dealing with three-dimensional shapes with curved surfaces. This paper proposes a Hypothetical Learning Trajectory (HLT) for teaching such shapes, grounded in Javanese Ethno-Realistic Mathematics Education (E-RME). The study adopts a design research methodology comprising three key phases: initial design, experimental teaching design, and retrospective analysis. The participants in this research are ninth-grade students from a junior high school in Semarang. The article focuses on the outcomes of the initial design phase, specifically the development of an HLT that includes four learning activities: (1) recognizing components of curved surface solids through contextual video observation, (2) exploring the surface area and volume of cylinders, (3) deriving formulas for the surface area and volume of cones, and (4) discovering the formulas for the surface area and volume of spheres. This sequence of activities is intended to help students build a meaningful understanding of curved 3D objects, while also fostering an appreciation for their cultural background and encouraging diverse approaches to mathematical reasoning. The HLT developed in this study is intended for implementation in trial classrooms and experimental teaching through E-RME, with the goal of enhancing students’ problem-solving skills, which is the novelty of this research.
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