Ways of Thinking Dan Ways of Understanding Siswa Dalam Menyelesaikan Soal Bilangan Rasional Ditinjau Dari Teori Harel

Authors

  • Ahmad Nur Iryanto Saputra Universitas Cenderawasih
  • Bettisari Napitupulu Universitas Cenderawasih
  • Pitriana Tandililing Universitas Cenderawasih
  • Agnes Teresa Panjaitan Universitas Cenderawasih
  • Elsi Sirampun Universitas Cenderawasih

DOI:

https://doi.org/10.58258/jupe.v10i2.8981

Abstract

This research is a descriptive qualitative research that aims to describe students' Ways of Thinking and Ways of Understanding in solving arithmetic operation problems of rational numbers reviewed from Harel's theory. The subjects of this study were 19 students of class VII B SMP YPPK Santu Paulus Abepura. The determination of the subjects was carried out using a purposive sampling technique where there were special criteria so that the research objectives were achieved. The data collection technique in this study was an individual test conducted twice and time triangulation was conducted to ensure the validity of the data. The results of the study were that there were five characteristics of students' ways of thinking and ways of understanding in solving rational number arithmetic operations, namely thinking wrong and understanding right (SB), thinking wrong and understanding wrong (SS), thinking wrong (inconsistent) and understanding right (consistent), thinking wrong (inconsistent) and understanding wrong (consistent), and changes in characteristics where students experienced an increase or decrease in characteristics.

References

Aiyub, A. (2023). Ways of thinking siswa dalam menyelesaikan masalah pola bilangan non rutin: Suatu penelitian fenomenologi hermeneutik. Journal of Didactic Mathematics, 4(2), 65–76. https://doi.org/10.34007/jdm.v4i2.1851

Andriani, P. (2015). PENALARAN ALJABAR DALAM PEMBELAJARAN MATEMATIKA. Beta: Jurnal Tadris Matematika, 8(1), 124–148.

Harel, G. (2008). A DNR perspective on mathematics curriculum and instruction. Part II: With reference to teacher’s knowledge base. ZDM - International Journal on Mathematics Education, 40(5), 893–907. https://doi.org/10.1007/s11858-008-0146-4

Harel, G. (2013). DNR-Based Curricula: The Case of Complex Numbers. Journal of Humanistic Mathematics, 3(2), 2–61. https://doi.org/10.5642/jhummath.201302.03

Herlina Budiarti, Teguh Wibowo, & Puji Nugraheni. (2022). Analisis Berpikir Komputasional Siswa dalam Menyelesaikan Masalah Matematika. Jurnal Pendidikan Mipa, 12(4), 1102–1107. https://doi.org/10.37630/jpm.v12i4.752

Iskandar. (2012). Psikologi Pendidikan (Sebuah Orientasi Baru) (Pertama). Jakarta Selatan: REFERENSI.

Novrini, Siagian, P., & Surya, E. (2015). PENGEMBANGAN PERANGKAT PEMBELAJARAN BERORIENTASI PROBLEM BASED LEARNING UNTUK MENINGKATKAN KEMAMPUAN VISUAL THINKING DALAM PEMECAHAN MASALAH MATEMATIS SISWA KELAS VIII SMP. Jurnal Paradikma, 8. https://doi.org/https://doi.org/10.24114/paradikma.v8i3.3364

Nurhanurawati. (2019). BERPIKIR MATEMATIS DALAM PEMECAHAN MASALAH. Yogyakarta: GRAHA ILMU.

Nurhasanah, H., Turmudi, & Jupri, A. (2021). Karakteristik Ways of Thinking (WoT) dan Ways of Understanding (WoU) siswa berdasarkan teori Harel. Journal of Authentic Research on Mathematics Education (JARME), 3(1), 105–113. https://jurnal.unsil.ac.id/index.php/jarme/article/view/2449/1588

Parwadi, P., Susanta, A., & Muchlis, E. E. (2020). Analisis Kesalahan Siswa Dalam Menyelesaikan Soal Matematika Materi Pecahan Kelas Vii Smp Negeri 16 Kota Bengkulu. Jurnal Penelitian Pembelajaran Matematika Sekolah (JP2MS), 4(3), 442–454. https://doi.org/10.33369/jp2ms.4.3.442-454

Purwati, P., Taha, I., Bakar, M. T., Lanani, K., & Malik, R. P. (2022). Analisis Kemampuan Berpikir Kritis Matematis Siswa Dalam Memecahkan Masalah Matematika. Matrix: Jurnal Pendidikan Matematika, 1(1), 25–35. https://doi.org/10.62522/mjpm.v1i1.8

Sintawati, M., & Mardati, A. (2023). Kemampuan Berpikir dalam Pembelajaran Matematika. K-Media.

Subroto, T., & Sholihah, W. (2018). Analisis Hambatan Belajar Pada Materi Trigonometri Dalam Kemampuan Pemahaman Matematis Siswa. IndoMath: Indonesia Mathematics Education, 1(2), 109. https://doi.org/10.30738/indomath.v1i2.2624

Syavira, V. F., & Novtiar, C. (2021). Analisis Kesalahan Pemecahan Masalah Matematis Siswa dalam Menyelesaikan Soal Operasi Hitung Campuran Bilangan Cacah dan Pecahan. JPMI (Jurnal Pendidikan Matematika Indonesia), 4(6), 1671–1678. https://doi.org/10.22460/jpmi.v4i6.1671-1678

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Published

2025-06-30

Issue

Vol 10, No 2 (2025): JUPE : Jurnal Pendidikan Mandala (Juni)

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How to Cite

Ways of Thinking Dan Ways of Understanding Siswa Dalam Menyelesaikan Soal Bilangan Rasional Ditinjau Dari Teori Harel. (2025). JUPE : Jurnal Pendidikan Mandala, 10(2), 832-841. https://doi.org/10.58258/jupe.v10i2.8981