Number Sense and Mental Arithmetic in Terms of Mathematical Ability: A Case Study on Elementary School Students
DOI:
https://doi.org/10.17977/um009v35i12026p100-118Keywords:
mathematical abilities, mental arithmetic, number sense, kemampuan matematika, aritmatika mental, intuisi bilangan, sekolah dasar, elementary schoolAbstract
Abstract: This descriptive qualitative case study examines the number-sense and mental-arithmetic profiles of six fifth-grade students across varying mathematical ability levels. Data were collected through written tests, semi-structured interviews, and work documentation, then analyzed using data reduction, display, and verification. Findings revealed that high-ability students demonstrated mastery through flexibility, accuracy, and efficiency. Moderate-ability students met most criteria but showed inconsistencies with complex tasks, while low-ability students faced substantial difficulties and displayed unstable strategies. These results emphasize the necessity of differentiated instruction. To foster foundational numerical competencies, teachers should implement regular mental math activities, such as daily number discussions, to practice flexible estimation. Furthermore, providing scaffolded support—such as gradually reducing the use of scratch paper—is essential for low-ability students to alleviate mental strain and strengthen memory for mental calculations. This structured approach ensures effective development of mathematical proficiency across all student profiles. This approach ensures foundational numerical competencies are developed effectively across all student profiles.
Abstrak: Studi kasus kualitatif deskriptif ini mengkaji profil pemahaman bilangan dan perhitungan mental pada enam siswa kelas lima dengan tingkat kemampuan matematika yang beragam. Data dikumpulkan melalui tes tertulis, wawancara semi-terstruktur, dan dokumentasi hasil pekerjaan, kemudian dianalisis dengan metode reduksi, penyajian, dan verifikasi data. Temuan menunjukkan bahwa siswa dengan kemampuan tinggi menunjukkan penguasaan melalui fleksibilitas, akurasi, dan efisiensi. Siswa dengan kemampuan sedang memenuhi sebagian besar kriteria namun menunjukkan ketidakkonsistenan dalam mengerjakan tugas-tugas kompleks, sementara siswa dengan kemampuan rendah menghadapi kesulitan yang cukup besar dan menerapkan strategi yang tidak konsisten. Hasil ini menekankan pentingnya penerapan pembelajaran diferensiasi. Untuk mengembangkan kompetensi numerik dasar, guru sebaiknya menerapkan latihan rutin berhitung di luar kepala tanpa menggunakan alat bantu, seperti diskusi seputar angka, guna melatih kemampuan memperkirakan angka secara fleksibel. Selain itu, pemberian dukungan bertahap—seperti secara bertahap mengurangi penggunaan kertas coretan untuk berhitung—sangat penting bagi siswa dengan kemampuan rendah untuk mengurangi beban mental dan memperkuat daya ingat dalam melakukan perhitungan mental. Pendekatan terstruktur ini memastikan pengembangan kemampuan matematika yang efektif pada semua profil siswa. Pendekatan ini memastikan kompetensi numerik dasar dikembangkan secara efektif pada semua profil siswa.
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