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Penerapan Learning Trajectory pada Materi Luas Permukaan dan Volume Bola melalui Pendekatan Lingkaran dan Kerucut pada Siswa Kelas IX-1 SMPS Pauly Mandiri Tanjung Morawa Kairuddin Kairuddin; Nurbaiti Nurbaiti; Nur Fadillah Yumna; Nessa Alexandria Br. Sinaga; Yemima Eraninta; Anni Fadillah
Populer: Jurnal Penelitian Mahasiswa Vol. 5 No. 3 (2026): September : Populer: Jurnal Penelitian Mahasiswa
Publisher : Universitas Maritim AMNI Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58192/populer.v5i3.5665

Abstract

Mathematics learning requires students to understand concepts rather than merely memorize formulas. However, students often experience difficulties connecting concrete experiences with formal mathematical representations, particularly when learning the surface area and volume of a sphere. This study aims to describe the implementation of Learning Trajectory in teaching these concepts through circle- and cone-based approaches to IX-1 students at SMPS Pauly Mandiri Tanjung Morawa. This study employed a descriptive qualitative approach involving three student groups. The learning activities were organized into four stages: situational context, model of, model for, and formal mathematics. Concrete learning media, student worksheets, pre-tests, post-tests, classroom observations, and documentation were used to support the learning process and collect data. The activities enabled students to explore the relationship between the surface area of a sphere and the area of a circle, as well as the relationship between the volume of a sphere and the volume of a cone. The findings showed that all groups could solve problems involving direct application of the formulas after the learning activities. However, difficulties remained in problems requiring algebraic manipulation and analysis of the relationship between changes in radius and volume. These findings indicate that Learning Trajectory can support the development of students’ conceptual understanding through concrete experiences, although further learning activities are needed to strengthen mathematical reasoning and problem-solving skills.