### An Analysis of Errors on Mathematical Symbol as a Metaphor in Linear Programming

Saniyatul Wardah, Dwi Priyo Utomo, Octavina Rizky Utami Putri

#### Abstract

Symbol sense is crucial in the understanding of mathematical problems comprising various symbols. The misuses of symbols happen due to misinterpretation, which is considered the constraint to learn algebra more comprehensively, including in linear programming. The term ‘metaphor’ is defined as a means to carry over symbol sense, and is used to improve mathematical understanding. This present research was aimed at analyzing errors on mathematical symbol as a metaphor in linear programming. This research was conducted by means of descriptive qualitative design, with a test and interview as the instruments. The test was made essay, and its results were analyzed qualitatively. The test, further, was administered to five eleventh graders selected according to highest rates of errors committed. This research has shown that the students committed a number of errors in some cases, such as representing symbols as variables, representing numbers, and interpreting symbols as relational operators. In addition, errors which the students committed in constructing mathematical models covered defining the final value, representing numbers, applying inequality system, and interpreting symbols as operation counts. This present research has provided some ways for symbol sense, and thus the errors on mathematical symbol as a metaphor could be lessened. Next, this research can be further followed up by reviewing the effectiveness of remedial instruction according to the committed errors on mathematical symbols.

#### Keywords

error, representation, mathematical symbol, metaphor

PDF

#### References

Andriyani, A. (2018). Analisis kesalahan siswa dalam menyelesaikan soal cerita pada materi program linear ditinjau dari gaya kognitif siswa. Pendekar: Jurnal Pendidikan Berkarakter, 1(1), 16-22. https://doi.org/10.31764/pendekar.v1i1.252

Arifin, Z., Trapsilasiwi, D., & Fatahillah, A. (2016). Analisis kemampuan komunikasi matematika dalam menyelesaikan masalah pada pokok bahasan sistem persamaan linier dua variabel siswa kelas VIII-C SMP nuris jember. Jurnal Edukasi, 3(2), 9–12. https://doi.org/10.19184/jukasi.v3i2.3522

Aristiyo F.D.N, Rochmad, & Kartono. (2014). Pembelajaran matematika model ikrar berpendekatan RME untuk meningkatkan kemampuan representasi matematika. Unnes Journal of Research Mathematics Education, 3(2), 111–116.

Ayuningsih, R., Setyowati, R. D., & Utami, R. E. (2020). Analisis kesalahan siswa dalam menyelesaikan masalah program linear berdasarkan teori kesalahan kastolan. Imajiner: Jurnal Matematika dan Pendidikan Matematika, 2(6), 510–518. https://doi.org/10.26877/imajiner.v2i6.6790

Fannie, R. D., & Rohati. (2014). Pengembangan lembar kerja siswa (LKS) berbasis POE (predict, observe, explain) pada materi program linear kelas XII SMA. Jurnal Sainmatika, 8(1), 96–109.

Feny, R. F., Budayasa, I. K., & Lukito, A. (2017). Membangun definisi genetis kubus melalui distorsi dan manipulasi objek spasial. Jurnal Elemen, 3(2), 130–137. https://doi.org/10.29408/jel.v3i2.403

Fridgo, T., Yenti, I. N., & Heriyanti, S. (2016). Analisis kesalahan transformasi soal pada kemampuan representasi matematis secara simbolik. Eksakta, 2, 24–30.

Fu’adiah, D. (2018). Pengembangan penalaran kuantitatif di sekolah dasar untuk mengembangkan berpikir aljabar di sekolah menengah pertama. Jurnal Riset Pendidikan dan Inovasi Pembelajaran Matematika (JRPIPM), 1(1), 1–49. https://doi.org/10.26740/jrpipm.v1n1.p19-29

Goldin, G. A. (2020). Mathematical representations. Encyclopedia of Mathematics Education, 566–572.

Herutomo, R. A., & Saputro, T. E. M. (2014). Analisis kesalahan dan miskonsepsi siswa kelas VIII pada materi aljabar. Edusentris, 1(2), 134-145. https://doi.org/10.17509/edusentris.v1i2.140

Hidayah, S. (2016). Analisis kesalahan siswa dalam menyelesaikan soal cerita SPLDV berdasarkan langkah penyelesaian polya. Jurnal Pendidikan, 1(2), 182–190.

Hidayati, R. (2019). Analisis kesalahan dalam menyelesaikan soal persamaan kuadrat siswa SMK kesehatan. Math Didactic: Jurnal Pendidikan Matematika, 5(1), 93–100. https://doi.org/10.33654/math.v5i1.524

Hutami, F. E., Trapsilasiwi, D., & Murtikusuma, R. P. (2020). Analisis kesalahan siswa dalam menyelesaikan soal program linear ditinjau dari adversity quotient. Alifmatika: Jurnal Pendidikan dan Pembelajaran Matematika, 2(1), 1–13. https://doi.org/10.35316/alifmatika.2020.v2i1.1-13

Irfan, M. (2017). Analisis kesalahan siswa dalam pemecahan masalah berdasarkan kecemasan belajar matematika. Kreano, Jurnal Matematika Kreatif-Inovatif, 8(2), 143–149. https://doi.org/10.15294/kreano.v8i2.8779

Kaposi, A., Kovács, A., & Altenkirch, T. (2019). Constructing quotient inductive-inductive types. Proceedings of the ACM on Programming Languages, 3(POPL), 1–24. https://doi.org/10.1145/3290315

Kaput, J. J., Carraher, D. W., & Blanton, M. L. (Eds.). (2017). Algebra in the early grades. Routledge.

Lutfianannisak, L., & Sholihah, U. (2018). Kemampuan komunikasi matematis siswa dalam menyelesaikan soal materi komposisi fungsi ditinjau dari kemampuan matematika. Jurnal Tadris Matematika, 1(1), 1–8. https://doi.org/10.21274/jtm.2018.1.1.1-8

Malihatuddarojah, D., & Prahmana, R. C. I. (2019). Analisis kesalahan siswa dalam menyelesaikan permasalahan operasi bentuk aljabar. Jurnal Pendidikan Matematika, 13(1), 1–8. https://doi.org/10.22342/jpm.13.1.6668.1-8

Malviya, S. (2019). Symbol as metonymy and metaphor: A Sociological perspective on mathematical symbolism. Science, Technology and Society, 24(1), 53–72. https://doi.org/10.1177/0971721818821798

Miftah, R., & Orlando, A. R. (2016). Penggunaan graphic organizer dalam meningkatkan kemampuan representasi matematis siswa. FIBONACCI: Jurnal Pendidikan Matematika dan Matematika, 2(2), 72–90. https://doi.org/10.24853/fbc.2.2.72-89

Presmeg, N. C. (2013). Mathematical reasoning analogies, metaphors, and images. Routledge.

Primayanti, G., Suwu, S. E., & Appulembang, O. D. (2018). Penerapan Metode drill untuk meningkatkan kemampuan komunikasi matematis siswa kelas VIII SMP lentera way pengubuan pada topik persamaan garis lurus [the implementation of the drill method to increase mathematical communication skills of grade 8 students in linear equations topics at SMP Lentera Way Pangubuan]. JOHME: Journal of Holistic Mathematics Education, 1(2), 135–149. https://doi.org/10.19166/johme.v1i2.867

Raharti, A. D., & Yunianta, T. N. H. (2020). Identifikasi kesalahan matematika siswa SMP berdasarkan tahapan kastolan. Journal of Honai Math, 3(1), 77–100. https://doi.org/10.30862/jhm.v3i1.114

Rahmania, L., & Rahmawati, A. (2016). Analisis kesalahan siswa dalam menyelesaikan soal cerita persamaan linier satu variabel. JMPM: Jurnal Matematika dan Pendidikan Matematika, 1(2), 165–174. https://doi.org/10.26594/jmpm.v1i2.639

Rahmawati, D., & Permata, L. D. (2018). Analisis kesalahan siswa dalam menyelesaikan soal cerita program linear dengan prosedur newman. Jurnal Elektronik Pembelajaran Matematika, 5(2), 173–185.

Rini, A. D. P., Hussen, S., Hidayati, H., & Muttaqien, A. (2021, February). Symbol Sense of Mathematics Students in Solving Algebra Problems. In Journal of Physics: Conference Series (Vol. 1764, No. 1, p. 012114). IOP Publishing.

Setiawan, F. (2018). Analisis kesalahan siswa kelas VII B SMP pangudi luhur moyudan dalam menyelesaikan ssoal persamaan dan pertidaksamaan linear satu variabel tahun ajaran 2017/2018. Repository. Usd.Ac.Id, 5(2), 1–139.

Setiawan, Y. B., Hapizah, & Hiltrimartin, C. (2018). Kesalahan siswa dalam menyelesaikan soal Olimpiade SMP konten aljabar Students’ error in solving junior high school Olympiad problem on algebra content. Jurnal Riset Pendidikan Matematika, 5(2), 233-243.

Sulastri, S., Marwan, M., & Duskri, M. (2017). Kemampuan representasi matematis siswa SMP melalui pendekatan pendidikan matematika realistik. Beta Jurnal Tadris Matematika, 10(1), 51–69. https://doi.org/10.20414/betajtm.v10i1.101

Veraksa, A. N. (2013). Symbol as a cognitive tool. Psychology in Russia: State of the Art, 6(1), 57–65. https://doi.org/10.11621/pir.2013.0105

Wagner, R. (2013). A historically and philosophically informed approach to mathematical metaphors. BRISK Binary Robust Invariant Scalable Keypoints, 27(2), 12–19. https://doi.org/10.3929/ethz-a-010782581

Wahbi, A., & Bey, A. (2015). Analisis kesalahan siswa dalam menyelesaikan soal faktorisasi suku aljabar ditinjau dari objek matematika pada siswa kelas VIII SMP negeri 15 kendri. Jurnal Penelitian Pendidikan Matematika, 3(1), 19–30.

Wijaya, A. A., & Masriyah. (2013). Analisis kesalahan siswa dalam menyelesaikan soal cerita materi sistem persamaan linear dua variabel. MATHEdunesa, 2(1).

Yunarni, A. Y. Y. (2015). Profil pemahaman notasi aljabar ditinjau dari kemampuan verbal siswa di kelas V sekolah dasar. Jurnal Daya Matematis, 3(1), 1–9. https://doi.org/10.26858/jds.v3i1.1291

Zukhrufurrohmah, Z., & Putri, O. R. U. (2019). Rekognisi dalam merepresentasikan simbol turunan parsial sebagai metonymy dan metaphor. JINoP (Jurnal Inovasi Pembelajaran), 5(2), 214-226. https://doi.org/10.22219/jinop.v5i2.9659

Zulfah, Z., & Rianti, W. (2018). Kemampuan Representasi matematis peserta didik bangkinang dalam menyelesaikan soal PISA 2015. Jurnal Cendekia : Jurnal Pendidikan Matematika, 2(2), 118–127. https://doi.org/10.31004/cendekia.v2i2.56

DOI: https://doi.org/10.24815/jdm.v8i1.18304

### Refbacks

• There are currently no refbacks.

Copyright (c) 2021 Saniyatul Wardah, Dwi Priyo Utomo, Octavina Rizky Utami Putri

Jurnal Didaktik Matematika

ISSN 2355 – 4185 (print) | 2548 – 8546 (online)

Master Program of Mathematics Education incorporated with Himpunan Matematika Indonesia (Indonesian Mathematical Society/IndoMs)

Faculty of Teacher Training and Education

Universitas Syiah Kuala

Darussalam, Banda Aceh, Indonesia - 23111

Website : http://jurnal.unsyiah.ac.id/DM/
Email     : jurnal.jdm@unsyiah.ac.id