Jurnal Riset Pendidikan Matematika
Keywords
Penalaran, level penalaran proporsional, missing value problem, reasoning, proportional reasoning level
Document Type
Article
Abstract
Tujuan penelitian deskriptif kualitatif ini adalah untuk mendeskripsikan level penalaran proporsional siswa kelas VIII SMP dalam memecahkan masalah satu nilai yang tidak diketahui (missing value problem). Instrumen penelitian ini berupa lembar tugas tentang masalah satu nilai yang tidak diketahui yang telah di validasi. Subjek penelitian ini adalah siswa kelas VIII SMP Negeri 1 Kalipare Malang dengan jumlah 33 siswa. Prosedur pengambilan data diawali dengan siswa diminta mengerjakan instrumen penelitian. Setelah mendapat data hasil pekerjaan siswa, dipilih tiga siswa sebagai subjek penelitian untuk dilakukan wawancara dengan tingkat penalaran proporsional yang berbeda. Hasil penelitian menunjukkan bahwa penalaran proporsional siswa berada pada level 0, level transisi 0 ke 2, dan level 4. Pada level 0, siswa memecahkan masalah satu nilai yang tidak diketahui menggunakan selisih dan sembarang operasi. Pada level transisi dari 0 ke 2, siswa memecahkan masalah satu nilai yang tidak diketahui menggunakan selisih kemudian beralih menggunakan cara membangun kedua ukuran (building both measure). Pada level 4, siswa memecahkan masalah satu nilai yang tidak diketahui hanya menggunakan aturan perkalian silang.
Level of student's proportional reasoning in solving missing value problem
Abstract
The purpose of this qualitative descriptive study was to describe the level of proportional reasoning eighth-grade students in solving the problem of the unknown values. This research instrument was an assignment sheet about a missing value problem that validated. The subjects of this research were students of class VIII of SMP Negeri 1 (State Junior High School) Kalipare, Malang, Indonesia, with a total of 33 students. Data collection procedures begin with students being asked to do research instruments. After obtaining data on student work, three students selected as research subjects for interviews with different proportional levels of reasoning. The results showed that students' proportional reasoning was at level 0, transition level 0 to 2, and level 4. At level 0, students solved the problem of missing value problem using differences and arbitrary operations. At the transition level from 0 to 2, students solve the problem of missing value problem using the difference and then switch to using building both measure methods. At level 4, students solve the problem of one unknown value using only the rules of cross multiplication.
Page Range
177-187
Issue
2
Volume
6
Digital Object Identifier (DOI)
10.21831/jrpm.v6i2.19728
Source
https://journal.uny.ac.id/index.php/jrpm/article/view/19728
Recommended Citation
Prayitno, A., Rossa, A., & Widayanti, F. D. (2019). Level penalaran proporsional siswa dalam memecahkan missing value problem. Jurnal Riset Pendidikan Matematika, 6(2), 177-187. https://doi.org/10.21831/jrpm.v6i2.19728
References
Bakker, A., Groenveld, D., Wijers, M., Akkerman, S. F., & Gravemeijer, K. P. E. (2014). Proportional reasoning in the laboratory: An intervention study in vocational education. Educational Studies in Mathematics. doi: https://doi.org/10.1007/s10649-012-9393-y
Brodie, K. (2010). Teaching mathematical reasoning in secondary school classrooms. New York, NY: Springer.
Creswell, J. W. (2009). Research design qualitative, quantitative, and mixed approaches (3rd ed). London, UK: Sage Publication.
Eka, R., & Susanah, S. (2013). Penalaran proporsional siswa kelas VII SMP Negeri II Beji Pasuruan berdasarkan tingkat kemampuan matematika. MATHEdunesa, 2(1), 15-21. Retrieved from https://jurnalmahasiswa.unesa.ac.id/index.php/mathedunesa/article/view/1209
Febriani, C., & Rosyidi, A. H. (2013). Identifikasi penalaran induktif siswa dalam memecahkan masalah matematika. Mathedunesa, 2(1), 1-6. Retrieved from https://jurnalmahasiswa.unesa.ac.id/index.php/mathedunesa/article/view/1448/pdf
Hackenberg, A. J. (2010). Students' reasoning with reversible multiplicative relationships. Cognition and Instruction, 28(4), 383-432. doi: https://doi.org/10.1080/07370008.2010.511565
Hilton, A., Hilton, G., Dole, S., & Goos, M. (2016). Promoting middle school students' proportional reasoning skills through an ongoing professional development programme for teachers. Educational Studies in Mathematics, 92(2), 193-219. doi: https://doi.org/10.1007/s10649-016-9694-7
Howe, C., Nunes, T., & Bryant, P. (2011). Rational number and proportional reasoning: Using intensive quantities to promote achievement in mathematics and science. International Journal of Science and Mathematics Education, 9, 391-417. doi: https://doi.org/10.1007/s10763-010-9249-9
Irawati, T. N. (2015). Mengembangkan kemampuan guru matematika dalam membuat soal penalaran proporsional siswa SMP. Prosiding Seminar Nasional Matematika dan Pendidikan Matematika, FMIPA UNY (pp.1101-1106). Retrieved from http://seminar.uny.ac.id/semnasmatematika/sites/seminar.uny.ac.id.semnasmatematika/files/banner/PM-155.pdf
Irpan, S. (2010). Proses terjadinya kesalahan dalam penalaran proposional berdasarkan kerangka kerja asimilasi dan akomodasi. Beta Jurnal Tadris Matematika, 3(2), 100-117. Retrieved from https://jurnalbeta.ac.id/index.php/betaJTM/article/view/94
Kemdikbud. (2013). Kurikulum 2013: Kompetensi dasar sekolah menengah pertama (SMP)/madrasah tsanawiyah (MTs). Jakarta: Kemdikbud.
Krulick, S., & Rudnick, J. A. (1995). The new sourcebook for teaching and problem solving in elementary school (6th ed.). Boston, MA: Allyn & Bacon.
Lagrall, C. W., & Swafford, J. (2000). Three balloons for two dollars: Developing proportional reasoning. Mathematics Teaching In the Middle School, 6(4), 254-261.
Lamon, S. J. (2018). Teaching fractions and ratios for understanding. New York, NY: Routledge. doi: https://doi.org/10.4324/9780203803165-5
Mullis, I. V. S., Martin, M. O., Foy, P., & Arora, A. (2012). TIMSS 2011 international results in mathematics. Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Boston College.
Nabors, W. K. (2003). From fractions to proportional reasoning: A cognitive schemes of operation approach. Journal of Mathematical Behavior, 22(2), 133-179. doi: https://doi.org/10.1016/S0732-3123(03)00018-X
NCTM. (2000). Principles and standards for school mathematics. Reston, VA: Author.
Norton, S. J. (2005). The construction of proportional reasoning. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th conference of the international group for the psychology of mathematics education (Vol. 4, pp.17-24). Melbourne: PME.
Nugraha, Y., Sujadi, I., & Pangadi, P. (2016). Penalaran proporsional siswa kelas VII. Beta Jurnal Tadris Matematika, 9(1), 34-47. doi: https://doi.org/10.20414/betajtm.v9i1.2
OECD. (2016). PISA 2015 results (Volume I): Excellence and equity in education. Paris: OECD Publishing. doi: https://doi.org/10.1787/9789264266490-en
Prayitno, A. (2015). Proses berpikir refraktif mahasiswa dalam menyelesaikan masalah matematika. (Unpublished doctoral dissertation, Universitas Negeri Malang, Malang).
Prayitno, A., Rossa, A., Widayanti, F. D., Rahayuningsih, S., Hamid, A., & Baidawi, M. (2018). Characteristics of students' proportional reasoning in solving missing value problem. Journal of Physics: Conference Series, 1114, 1-6.doi: https://doi.org/10.1088/1742-6596/1114/1/012021
Van de Walle, J. (2007). Elementary and middle school mathematics. Boston, MA: Pearson Education.