GENERALISASI DALAM PENALARAN KUANTITATIF SISWA MELALUI PEMECAHAN MASALAH PECAHAN

Syarifuddin Syarifuddin(1*),

(1) 
(*) Corresponding Author


Abstract


Tujuan penelitian ini adalah mendeskripsikan penalaran kuantitatif dalam proses generalisasi dan cara siswa dalam menghubungkan kuantitas. Jenis penelitian ini adalah penelitian kualitatif dengan pendekatan deskriptif eksploratif. Penelitian dilakukan pada siswa sekolah menengah (kelas 9) di daerah kabupaten Bima, Nusa Tenggara Barat. Penelitian ini melibatkan 35 orang siswa yang telah memperoleh materi pecahan sebagai subjek penelitian. Subjek yang deskripsikan pada hasil penelitian sebanyak 2 orang yang merepresentasikan dari subjek penelitian dan dilakukan proses seleksi dengan memberikan tes berupa soal pemecahan masalah pecahan sebanyak 2 nomor. Siswa yang terpilih berdasarkan representasi pemecahan masalah dan atas rekomendasi dari guru matematika terhadap siswa yang memiliki kemampuan menjelaskan secara lisan. Data penelitian dikumpulkan dari hasil representasi siswa dan hasil wawancara, kemudian dianalisis secara komprehensif untuk mengidentifikasi penalaran kuantitatif siswa. Hasil penelitian menunjukan: 1) penalaran kuantitatif siswa dapat menghasilkan generalisasi pola bilangan; 2) siswa menghubungkan kuantitas dengan menggunakan rasio ekuivalen; 3) siswa merepresentasikan masalah pecahan dapat menggunakan bentuk kesetaraan. Penelitian ini menemukan bahwa kuantitas atau unit dari pecahan matematika dapat membentuk suatu pola bilangan melalui proses perbandingan kuantitas.

Keywords


Pecahan; pemecahan masalah; penalaran kuantitatif

References


Abdullah, A. H., Abidin, N. L. Z., & Mokhtar, M. (2017). Using Thinking Blocks to Encourage the Use of Higher Order Thinking Skills among Students When Solving Problems on Fractions. International Journal of Educational and Pedagogical Sciences. https://doi.org/scholar.waset.org/1999.10/10006278

Atagi, N., DeWolf, M., Stigler, J. W., & Johnson, S. P. (2016). The role of visual representations in college students’ understanding of mathematical notation. Journal of Experimental Psychology: Applied. https://doi.org/10.1037/xap0000090

Atmarita, A., & Syarifuddin, S. (2021). Visual Processing Assessment on Children: A Pilot Study. Jurnal Pendidikan Dan Pembelajaran Indonesia (JPPI), 1(1), 1–9. https://doi.org/10.53299/jppi.v1i1.18

Blanton, M., Stephens, A., Knuth, E., Gardiner, A. M., Isler, I., & Kim, J. S. (2015). The development of children’s algebrai thinking: The impact of a comprehensive early algebra intervention in third grade. Journal for Research in Mathematics Education, 4(1), 39–87. https://doi.org/10.5951/jresematheduc.46.1.0039

Depdiknas no. 22. (2006). Standar Isi untuk Satuan Pendidikan Dasar dan Menengah. Peraturan Menteri Pendidikan Nasional Republik Indonesia, Nomor 22, Tahun 2006.

Ellis, A. B. (2011). Algebra in the Middle School: Developing Functional Relationships Through Quantitative Reasoning. In Cai Jinfa & E. and Knuth (Ed.), Early Algebraization: A Global Dialogue from Multiple Perspectives (pp. 215–238). Berlin, Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-17735-4_13

Empson, S. B., Levi, L., & Carpenter, T. P. (2011). The Algebraic Nature of Fractions: Developing Relational Thinking in Elementary School. In J. Cai & E. Knuth (Eds.), Early Algebraization: A Global Dialogue from Multiple Perspectives (pp. 409–428). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-17735-4_22

Fadhilah, N., Budiarto, M. T., & Rahaju, E. B. (2019). Mathematical Representation of Middle School Students in Solving Fractional Problems Based on Sex Difference. Journal of Physics: Conference Series. https://doi.org/10.1088/1742-6596/1417/1/012048

Hackenberg, A. J., & Lee, M. Y. (2015). Relationships Between Students’ Fractional Knowledge and Equation Writing. Journal for Research in Mathematics Education, 46(2), 196–243.

Lewis, K. E. (2016). Beyond Error Patterns: A Sociocultural View of Fraction Comparison Errors in Students with Mathematical Learning Disabilities. Learning Disability Quarterly. https://doi.org/10.1177/0731948716658063

Lewis, K. E. (2017). Designing a Bridging Discourse: Re-Mediation of a Mathematical Learning Disability. Journal of the Learning Sciences. https://doi.org/10.1080/10508406.2016.1256810

Moore, K. C. (2014). Quantitative reasoning and the sine function: The case of Zac. Journal for Research in Mathematics Education, 45(1), 102–138. https://doi.org/10.5951/jresematheduc.45.1.0102

Murniasih, T. R., Sadijah, C., Muksar, M., Susiswo, S., & Suwanti, V. (2020). Kesalahan Representasi Pecahan pada Garis Bilangan. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 9(2), 316–325.

NCTM. (2000). Principles and Standards for School Mathematics. The National Council of Teachers of Mathematics.

Palpialy, J. J., & Nurlaelah, E. (2015). Pengembangan Desain Didaktis Materi Pecahan pada Sekolah Menengah Pertama (SMP). Jurnal Matematika Integratif, 11(2), 127–136. https://doi.org/https://doi.org/10.24198/jmi.v11.n2.9425.127-136

Sa’dijah, C., Handayani, U. F., Sisworo, Sudirman, Susiswo, Cahyowati, E. T. D., & Sa’Diyah, M. (2019). The Profile of Junior High School Students’ Mathematical Creative Thinking Skills in Solving Problem through Contextual Teaching. Journal of Physics: Conference Series. https://doi.org/10.1088/1742-6596/1397/1/012081

Sa’diyah, M., Sa’dijah, C., Sisworo, & Handayani, U. F. (2019). How Students Build Their Mathematical Dispositions towards Solving Contextual and Abstract Mathematics Problems. Journal of Physics: Conference Series. https://doi.org/10.1088/1742-6596/1397/1/012090

Sutarto, S., Nusantara, T., Subanji, S., Dwi Hastuti, I., & Dafik, D. (2018). Global conjecturing process in pattern generalization problem. Journal of Physics: Conference Series. https://doi.org/10.1088/1742-6596/1008/1/012060

Syarifuddin, Nusantara, T., Qohar, A., & Muksar, M. (2019a). Quantitative reasoning process in mathematics problem solving: A case on covariation problems reviewed from Apos theory. Universal Journal of Educational Research, 7(10), 2133–2142. https://doi.org/10.13189/ujer.2019.071011

Syarifuddin, Nusantara, T., Qohar, A., & Muksar, M. (2019b). The Identification Difficulty of Quantitative Reasoning Process toward the Calculus Students’ Covariation Problem. Journal of Physics: Conference Series, 1254(1). https://doi.org/10.1088/1742-6596/1254/1/012075

Syarifuddin, S. (2018). Representasi Penalaran Kuantitatif Siswa dalam Pemecahan Masalah Matematika. Dalam Prosiding Seminar Nasional Lembaga Penelitian Dan Pendidikan (LPP) Mandala, (pp. 434-438).

Syarifuddin, S., Nusantara, T., Qohar, A., & Muksar, M. (2020). Students’ Thinking Processes Connecting Quantities in Solving Covariation Mathematical Problems in High School Students of Indonesia. Participatory Educational Research, 7(3), 59–78. https://doi.org/10.17275/per.20.35.7.3

Syarifuddin, S. (2019). Identifikasi Kesulitan Representasi Matematis Siswa SMP pada Pemecahan Masalah Pecahan. Supermat (Jurnal Pendidikan Matematika), 3(1), 34–42. https://doi.org/10.33627/sm.v3i1.174

Syarifuddin, S., Nugroho, P. B., Mutmainah, M., Hadi, A. M., & Sriaryaningsyih, S. (2020). The connecting quantities process to solve fraction mathematical problems of middle school students. Humanities and Social Sciences Reviews, 8(5), 121–131. https://doi.org/10.18510/hssr.2020.8512

Weber, E., Ellis, A., Kulow, T., & Ozgur, Z. (2014). Six Principles for Quantitative Reasoning and Modeling. The Mathematics Teacher, 108(1), 24–30. https://doi.org/10.5951/mathteacher.108.1.0024

Zulaini, Z., Sutarto, S., & Juliangkary, E. (2019). Analisis Koneksi Matematis Siswa pada Proses Conjecturing dalam Menggeneralisasi pada Pola. JPIn: Jurnal Pendidik Indonesia, 2(2), 68–76. https://doi.org/10.47165/jpin.v2i2.79




DOI: http://dx.doi.org/10.24127/ajpm.v10i2.3255

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