Middle School Students’ Proportional Reasoning Ability in Solving Proportional and Non-proportional Problem
DOI:
https://doi.org/10.35194/jp.v13i1.3841Kata Kunci:
missing-value, numerical comparison, problem types, proportional reasoning, qualitative comparisonAbstrak
The objective of this descriptive qualitative study is to describe students' proportional reasoning ability in solving each type of proportional problem, namely missing-value problem, numerical comparison problem, and qualitative comparison problem. A non-proportional problem was also included in this study to assess students' ability in one of the indicators used to measure proportional reasoning ability. The instrument used in this study consists of mathematical word problems on the proportion concept. The participants involved nine eighth-grade students, who were chosen from a total of 49 eighth-grade students at a school in Bandung City. These students were selected using a technique known as purposive sampling, by looking at the answers of students who best represent the answers of other students. The gathered data were analyzed using content analysis and narrative analysis techniques. According to the results, students appeared to have difficulty solving proportional problems of all types using proportional reasoning. Students are still struggling with distinguishing between proportional and non-proportional situations, as well as direct and inverse proportions. Furthermore, students often encounter difficulties when attempting to solve numerical comparison and qualitative comparison problems. This might be a consequence of students' lack of experience in solving these types of problems. Another tendency is the use of the cross-multiplication algorithm in solving missing-value problems without knowing the purpose of using the algorithm.
Referensi
A
yan, R., & Isiksal-Bostan, M. (2019). Middle school students’ proportional reasoning in real life contexts in the domain of geometry and measurement. International Journal of Mathematical Education in Science and Technology, 50(1), 65–81. https://doi.org/10.1080/0020739X.2018.1468042
Beckmann, S., & Izsák, A. (2015). Two perspectives on proportional relationships: Extending complementary origins of multiplication in terms of quantities. Journal for Research in Mathematics Education, 46(1), 17–38. https://doi.org/10.5951/jresematheduc.46.1.0017
Ben-Chaim, D., Fey, J. T., Fitzgerald, W. M., Benedetto, C., & Miller, J. (1998). Proportional reasoning among 7th grade students with different curricular experiences. Educational Studies in Mathematics, 36(3), 247–273. https://doi.org/10.1023/A:1003235712092
Fadilla, D. M. N., & Siswono, T. Y. E. (2022). Penalaran Proporsional Siswa Bergaya Kognitif Sistematis dan Intuitif Dalam Menyelesaikan Masalah Numerasi. MATHEdunesa, 11(3), 630–643. https://doi.org/10.26740/mathedunesa.v11n3.p630-643
Gläser, K., & Riegler, P. (2015). Beginning students may be less capable of proportional reasoning than they appear to be. Teaching Mathematics and Its Applications, 34(1), 26–34. https://doi.org/10.1093/teamat/hru025
Gündogdu, N., & Tunç, M. (2022). Improving middle school students ’ proportional reasoning through STEM activities. Journal of Pedagogical Research, 6(2), 164–185.
Im, S.-H., & Jitendra, A. K. (2020). Analysis of proportional reasoning and misconceptions among students with mathematical learning disabilities. Journal of Mathematical Behavior, 57. https://doi.org/10.1016/j.jmathb.2019.100753
Johar, R., Yusniarti, S., & Saminan. (2018). The analysis of proportional reasoning problem in the Indonesian mathematics textbook for the junior high school. Journal on Mathematics Education, 9(1), 55–68.
Karli, M. G., & Yildiz, E. (2022). Incorrect Strategies Developed by Seventh- Grade Students to Solve Proportional Reasoning Problems. Journal of Qualitative Research in Education, 22(29), 111–148. https://doi.org/10.14689/enad.29.5
Khotimah, K., & Shodikin, A. (2021). An Analysis of Proportional Reasoning Ability of Secondary School Students on Opportunity Material Viewed from Gender Perspective. Hipotenusa?: Journal of Mathematical Society, 2(1), 111–128. https://doi.org/10.18326/hipotenusa.v3i1.111-128
Khumairoh, B., Amin, S. M., & Wijayanti, P. (2020). Penalaran Proporsional Siswa Kelas Menengah dalam Menyelesaikan Masalah Matematika Ditinjau dari Adversity Quotient. Pedagogia?: Jurnal Pendidikan, 9(1), 67–80. https://doi.org/10.21070/pedagogia.v9i1.259
Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. National Academy Press.
Lamon, S. J. (2020). Teaching Fractions and Ratios for Understanding. In Teaching Fractions and Ratios for Understanding. https://doi.org/10.4324/9781410617132
Langrall, C. W., & Swafford, J. (2000). Three balloons for two dollars: Developing proportional reasoning. Mathematics Teaching in the Middle School, 6(4), 254–261.
Lobato, J., & Ellis, A. (2010). Developing Essential Understanding of Ratios, Proportions, and Proportional Reasoning for Teaching Mathematics: Grades 6-8. NCTM.
Mardika, F., & Mahmudi, A. (2021). An analysis of proportional reasoning ability of junior high school students. Jurnal Riset Pendidikan Matematika, 8(1), 22–32.
https://doi.org/10.21831/jrpm.v8i1.14995
NCTM. (2000). Principles and Standards for School Mathematics. In School Science and Mathematics (Vol. 47, Issue 8). www.nctm.org
NCTM. (2016). Reasoning and Sense Making in the Mathematics Classroom: Pre-K-Grade 2. NCTM.
Nur, I. M., & Sari, P. (2022). Penalaran Proporsional Siswa SMP dalam Menyelesaikan Masalah Missing Value dan Comparison Berdasarkan Gaya Kognitif Sistematis. Jurnal Ilmiah Wahana Pendidikan, 8(21), 467–482.
Nurlela, N., Sumarni, S., Riyadi, M., Adiastuty, N., & Syafari, R. (2022). Proportional Reasoning Level Based on Student Self-Efficacy Review. https://doi.org/10.4108/eai.2-12-2021.2320311
Ontario Education Ministry. (2012). Paying Attention to Proportional Reasoning K-12: Supporting Document for Paying Attention to Mathematical Education. Education Ministry.
Orrill, C. H., & Burke, J. P. (2013). Fine-grained Analysis of Teacher Knowledge: Proportion and Geometry. In M.V. Martinez & A.C. Superfine (Eds.), Proceedings of the 35th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 605–612). University of Illinois.
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
Prayitno, A., Rossa, A., Widayanti, F. D., Rahayuningsih, S., Hamid B, A., & Baidawi, M. (2018). Characteristics of students’ proportional reasoning in solving missing value problem. Journal of Physics: Conference Series, 1114(012021).
Putra, A., Tensa, Y., & Erita, S. (2020). Analisis Penalaran Proporsional Siswa dengan Gaya Belajar Auditori dalam Menyelesaikan Soal Perbandingan. Journal on Education, 2(4), 323–330. https://doi.org/10.31004/joe.v2i4.326
Rohmah, W. N., Septian, A., & Inayah, S. (2020). Analisis Kemampuan Penalaran Matematis pada Materi Bangun Ruang Ditinjau dari Gaya Kognitif Siswa. Prisma, 9(2), 179–191.
Septian, A., Fahrisyal, M. L., & Jusniani, N. (2022). Pengembangan GeoGebra Classroom Pada Materi Transformasi Geometri. PRISMA, 11(2), 504–514. https://doi.org/10.35194/jp.v11i2.2483
Sumartini, T. S., & Utami, I. E. (2023). Analisis Kemampuan Penalaran Matematis Siswa pada Materi Relasi dan Fungsi. Prisma, 12(2), 333. https://doi.org/10.35194/jp.v12i2.3062
Supriyadi, E., Septian, A., Dahlan, J. A., & Juandi, D. (2022). GeoGebra Research in Indonesia: A Bibliometric Analysis. PRISMA, 11(2), 559–575. https://doi.org/10.35194/jp.v11i2.2572
Taufik, A. (2021). Kemampuan Penalaran Proporsional Matematis Siswa Dengan Gaya Belajar Field Independent. Jurnal Edukasi Dan Sains Matematika (JES-MAT), 7(2), 85–100. https://doi.org/10.25134/jes-mat.v7i2.4213
Taufik, A., Nurhayati, N., Prayitno, A., Tresnawati, B., & Syafari, R. (2021). Analysis of Mathematical Proportional Reasoning Ability Based on Field Dependent and Field Independent Cognitive Style. https://doi.org/10.4108/eai.12-12-2020.2304996
Van Dooren, W., Vamvakoussi, X., & Verschafel, L. (2018). Educational Practices Series 30: Proportional Reasoning. UNESCO International Bureau of Education.
Weiland, T., Orrill, C. H., Nagar, G. G., Brown, R. E., & Burke, J. (2021). Framing a robust understanding of proportional reasoning for teachers. Journal of Mathematics Teacher Education, 24(2), 179–202. https://doi.org/10.1007/s10857-019-09453-0
Widayanti, M., Jumiah, Y., & Ijuddin, R. (2020). Penalaran Proporsional Siswa SMP Negeri 18 Pontianak. Jurnal Pendidikan Dan Pembelajaran Khatulistiwa, 9(10), 1–9.
Unduhan
Diterbitkan
Terbitan
Bagian
Lisensi
As a journal Author, you have rights for a large range of uses of your article, including use by your employing institute or company. These Author rights can be exercised without the need to obtain specific permission.
Authors and readers can copy and redistribute the material in any medium or format, as well as remix, transform, and build upon the material for any purpose, even commercially, but they must give appropriate credit (cite to the article or content), provide a link to the license, and indicate if changes were made. If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original.
The Authors submitting a manuscript do so on the understanding that if accepted for publication, copyright of the article shall be assigned to PRISMA as publisher of the journal.
PRISMA by UNIVERSITAS SURYAKANCANA is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Based on a work at https://jurnal.unsur.ac.id/prisma.
