Visualization of Multivariable Calculus: Learning Needs Analysis for GeoGebra-Assisted Teaching Material Development
DOI:
https://doi.org/10.15294/kreano.v16i2.33904Keywords:
Multivariable Calculus, GeoGebra, Learning Needs, Learning Design, Design ResearchAbstract
Students often struggle to visualize multivariable functions, interpret partial derivatives, and apply extrema, yet systematic needs analyses for designing meaningful Multivariable Calculus learning environments remain limited. This study aims to identify students’ learning needs as a foundation for developing GeoGebra-assisted materials. Using a qualitative descriptive approach within the Gravemeijer and Cobb design research framework, data were collected through a needs-analysis questionnaire administered to eight purposively selected university students who had completed the course. Results show that six of the eight students experienced moderate to high levels of difficulty, especially in visualizing multivariable functions and understanding partial derivatives. Students also reported that videos and lecturer explanations were helpful, and all expressed readiness to use GeoGebra-based materials. The findings indicate the importance of designing structured learning environments that integrate dynamic visualizations. This study provides the groundwork for subsequent teaching experiment and retrospective analysis cycles in developing valid and generalizable instructional designs.
Abstrak
Mahasiswa sering mengalami kesulitan dalam memvisualisasikan fungsi multivariabel, menafsirkan turunan parsial, dan menerapkan konsep nilai ekstrem, namun analisis kebutuhan yang sistematis untuk merancang lingkungan belajar Kalkulus Peubah Banyak masih terbatas. Penelitian ini bertujuan mengidentifikasi kebutuhan belajar mahasiswa sebagai dasar pengembangan bahan ajar berbantuan GeoGebra. Dengan pendekatan deskriptif kualitatif dalam kerangka penelitian desain Gravemeijer dan Cobb, data dikumpulkan melalui angket analisis kebutuhan yang diberikan kepada delapan mahasiswa terpilih yang telah menyelesaikan mata kuliah tersebut. Hasil menunjukkan bahwa enam dari delapan mahasiswa mengalami tingkat kesulitan sedang hingga tinggi, terutama dalam visualisasi fungsi multivariabel dan pemahaman turunan parsial. Mahasiswa juga menyatakan bahwa video dan penjelasan dosen membantu pemahaman, dan seluruhnya siap menggunakan bahan ajar berbasis GeoGebra. Temuan ini menjadi dasar bagi pelaksanaan teaching experiment dan analisis retrospektif untuk menghasilkan desain pembelajaran yang valid dan tergeneralisasi.
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