The "VLOKS" Geometrical Thinking Model of Students in Relation to Meaningful Learning Processes and Teacher Pedagogy

Abstract

Understanding geometry is an essential aspect of mathematics learning as it plays a central role in developing students’ spatial, visual, and logical reasoning abilities. However, previous studies indicate that students often encounter difficulties in comprehending geometric concepts deeply due to learning approaches that remain largely procedural and insufficiently emphasize visualization or conceptual connections. This study aims to explore students’ geometric thinking profiles through the VLOKS model (Visual, Literational, Operational, Correlational, Spatial), examine their perceptions of meaningful learning, and analyze the relationship between geometric thinking abilities and teachers’ pedagogical competence. A mixed-methods approach was employed using a sequential explanatory design, beginning with quantitative data collection through a VLOKS-based geometric thinking test and a meaningful learning questionnaire, followed by qualitative data through classroom observations of teachers’ pedagogy and in-depth interviews. The research subjects consisted of 33 tenth-grade students at SMAN 7 Pontianak and 31 students at SMAN 2 Teluk Keramat, along with mathematics teachers applying meaningful learning approaches. The findings reveal that students at SMAN 7 Pontianak achieved a moderate average score (70.4%), with their strongest performance in the literational dimension (79%), while their weaknesses were found in the operational (67%) and correlational dimensions, partly due to technical aspects of the test items. In contrast, students at SMAN 2 Teluk Keramat attained a relatively low average score (31.6%) across all VLOKS dimensions without significant dominance in any particular aspect. Qualitative data further indicate that teachers in both schools attempted to implement meaningful learning through contextual approaches, problem-based learning, and remedial strategies, though the implementation proved more effective at SMAN 7 than at SMAN 2. This study concludes that integrating the VLOKS model, meaningful learning processes, and teachers’ pedagogical competence significantly strengthens students’ understanding of geometry, highlighting the need for contextual, reflective, and adaptive instructional designs aligned with students’ thinking processes within the framework of the Merdeka Curriculum.

Model Berpikir Geometris “VLOKS” Siswa Dikaitkan Dengan Proses Pembelajaran Bermakna Dan Pedagogis Guru

ABSTRAK
Pemahaman terhadap geometri merupakan aspek penting dalam pembelajaran matematika karena berperan dalam mengembangkan kemampuan spasial, visual, serta berpikir logis siswa, namun berbagai penelitian menunjukkan bahwa siswa kerap mengalami kesulitan dalam memahami konsep-konsep geometri secara mendalam akibat pendekatan pembelajaran yang masih dominan bersifat prosedural dan kurang menekankan visualisasi maupun koneksi antar konsep. Penelitian ini bertujuan untuk mengeksplorasi profil berpikir geometris siswa melalui model VLOKS (Visual, Literasional, Operasional, Korelasional, Spasial), mengkaji persepsi siswa terhadap pembelajaran bermakna, serta menganalisis hubungan antara kemampuan berpikir geometris dengan kompetensi pedagogis guru. Metode penelitian yang digunakan adalah mixed methods dengan desain eksplanatoris sekuensial, dimulai dari pengumpulan data kuantitatif melalui tes kemampuan berpikir geometris berbasis VLOKS dan kuesioner pembelajaran bermakna, kemudian dilanjutkan dengan data kualitatif berupa observasi pedagogis guru dan wawancara mendalam. Subjek penelitian adalah siswa kelas X di SMAN 7 Pontianak (33 siswa) dan SMAN 2 Teluk Keramat (31 siswa), serta guru matematika yang menerapkan pendekatan pembelajaran bermakna. Hasil penelitian menunjukkan bahwa siswa SMAN 7 Pontianak memiliki capaian rata-rata cukup baik (70,4%), dengan kekuatan utama pada dimensi literasional (79%), sementara kelemahan terdapat pada dimensi operasional (67%) dan korelasional akibat faktor teknis soal. Sebaliknya, siswa SMAN 2 Teluk Keramat memperoleh rata-rata skor rendah (31,6%) pada seluruh dimensi VLOKS tanpa ada dominasi yang signifikan. Data kualitatif mengungkap bahwa guru di kedua sekolah telah berupaya menerapkan pembelajaran bermakna melalui pendekatan kontekstual, problem-based learning, serta strategi remedial, namun implementasinya lebih efektif di SMAN 7 dibandingkan di SMAN 2 Teluk Keramat. Simpulan penelitian ini menegaskan bahwa integrasi antara VLOKS, pembelajaran bermakna, dan kompetensi pedagogis guru berkontribusi penting terhadap penguatan pemahaman geometri siswa, serta menekankan perlunya pengembangan desain pembelajaran yang kontekstual, reflektif, dan adaptif terhadap cara berpikir siswa dalam kerangka Kurikulum Merdeka.

Kata Kunci :
Model Berpikir Geometris “VLOKS”; Proses Pembelajaran Bermakna; Pedagogis Guru