PROSES TRANSLASI PERMASALAHAN REALISTIK MENJADI REPRESENTASI MATEMATIS MAHASISWA TEKNIK INFORMATIKA

Octavina Rizky Utami Putri(1*), Zukhrufurrohmah Zukhrufurrohmah(2),

(1) Universitas Muhammadiyah Malang
(2) Universitas Muhammadiyah Malang
(*) Corresponding Author


Abstract


Representasi matematis diperlukan dalam menyelesaikan masalah realistik, yakni sebagai mediator penyelesaian permasalahan sehari-hari. Translasi representasi dari suatu permasalahan realistik menjadi model matematis diperlukan sebagai pemahaman terhadap permasalahan yang diberikan untuk ditentukan solusi permasalahannya. Penelitian ini bertujuan untuk mendeskripsikan proses translasi permasalahan realistik menjadi representasi matematis pada Mahasiswa Teknik Informatika. Penugasan penyelesaian masalah realistik dan tanya jawab pada perkuliahan Aljabar Linear dan Matriks digunakan untuk memperoleh deskripsi proses translasi. Data dianalisis berdasarkan tahapan translasi representasi matematis yaitu mengeksplorasi sumber, menyusun pengetahuan awal, membangun target representasi, dan menentukan kesesuaian hasil representasi dengan sumber. Hasilnya adalah mahasiswa mengeksplorasi sumber dengan membaca informasi sumber, selanjutnya menguraikan informasi sumber dengan bahasa alami, membuat kode berdasarkan informasi sumber dan mengaitkannya dengan konsep matematika, mengaitkan konsep matematika dari representasi sumber ke representasi target, serta mengevaluasi representasi target. Temuan-temuan ini dapat digunakan dosen sebagai dasar mendesain pembelajaran pada mahasiswa non-program studi matematika guna mengurangi peluang kesalahan dalam menyelesaikan masalah realistik.

 Kata kunci: Masalah realistik; representasi matematis; translasi.

Mathematical representation is needed in solving realistic problems, namely as a mediator in solving realistic problems. Mathematical representation translation of a realistic problem into a mathematical model that is needed as an understanding of the given problem to determine the problem solution. This study aims to describe the process of translation of realistic problems into mathematical representations for Informatics Engineering Students. Realistic problem solving assignments and interviews in Linear Algebra and Matrix lecture is used to obtain a description of the translation process. Data were analyzed based on the stages of translation of mathematical representations, namely unpacking the source, preliminary coordination, constructing the target, and determining equivalence. The result is that students unpacking the source by reading source information, then describe source information in natural language, code based on source information and relate it to mathematical concepts, link mathematical concepts from source representation to target representation, and evaluate target representations. These findings can be used by lecturers as a basis for designing learning for students non-departement of Mathematics in order to reduce the chance of errors in solving realistic problems.

 Keywords: Mathematical representation; realistic problem; translation


Keywords


Masalah realistik; representasi matematis; translasi

References


Adu-Gyamfi, K., & Bossé, M. J. (2014). Processes And Reasoning in Representations of Linear Functions. International Journal of Science and Mathematics Education, 12(1), 167–192. https://doi.org/10.1007/s10763-013-9416-x

Adu-Gyamfi, K., Stiff, L. V., & Bossé, M. J. (2012). Lost in Translation: Examining Translation Errors Associated With Mathematical Representations. School Science and Mathematics, 112(3), 159–170. https://doi.org/10.1111/j.1949-8594.2011.00129.x

Anwar, R. B., & Rahmawati, D. (2017). Symbolic and Verbal Representation Process of Student in Solving Mathematics Problem Based Polya’s Stages. International Education Studies, 10(10), 20. https://doi.org/10.5539/ies.v10n10p20

Arsaythamby, V., & Zubainur, C. M. (2014). How a Realistic Mathematics Educational Approach Affect Students’ Activities in Primary Schools? Procedia - Social and Behavioral Sciences, 159, 309–313. https://doi.org/10.1016/j.sbspro.2014.12.378

Boaler, J., Chen, L., Williams, C., & Cordero, M. (2016). Seeing as Understanding: The Importance of Visual Mathematics for our Brain and Learning. Journal of Applied & Computational Mathematics, 05(05). https://doi.org/10.4172/2168-9679.1000325

Bossé, M., Adu-Gyamfi, K., & Chandler, K. (2014). Students’ Differentiated Translation Processes. International Journal for Mathematics Teaching and Learning, (828).

Bossé, M., Gyamfi, K. A., & Chandler, K. (2014). Students’ Differentiated Translation Processes. International Journal for Mathematics Teaching and Learning, (828).

Bossé, M. J., Bayaga, A., Fountain, C., & Young, E. S. (2019). Mathematical Representational Code Switching. International Journal for Mathematics Teaching and Learning, 20, 33–61.

Creswell, J. W., & Creswell, J. D. (2017). Research Design: Qualitative, Quantitative, and Mixed Methods Approaches. Retrieved from https://books.google.co.id/books?id=335ZDwAAQBAJ

Dewolf, T., Van Dooren, W., Ev Cimen, E., & Verschaffel, L. (2014). The Impact of Illustrations and Warnings on Solving Mathematical Word Problems Realistically. The Journal of Experimental Education, 82(1), 103–120. https://doi.org/10.1080/00220973.2012.745468

Dündar, S. (2015). Mathematics Teacher Candidates’ Performance in Solving Problems with Different Representation Styles: The Trigonometry Example. Eurasia Journal of Mathematics, Science and Technology Education, 11(6), 1379–1397. https://doi.org/10.12973/eurasia.2015.1396a

Ersoy, E. (2016). Problem Solving and Its Teaching in Mathematics. The Online Journal of New Horizons in Education, 6(2), 79–87.

Fitzpatrick, C. L., Hallett, D., Morrissey, K. R., Yıldız, N. R., Wynes, R., & Ayesu, F. (2020). The relation between academic abilities and performance in realistic word problems. Learning and Individual Differences, 83–84(October), 101942. https://doi.org/10.1016/j.lindif.2020.101942

Gokalp, N. D., & Bulut, S. (2018). A New Form of Understanding Maps: Multiple Representations with Pirie and Kieren Model of Understanding. International Journal of Innovation in Science and Mathematics Education, 26(6), 1–21.

Goos, M., Geiger, V., & Dole, S. (2014). Transforming Professional Practice in Numeracy Teaching BT - Transforming Mathematics Instruction: Multiple Approaches and Practices (Y. Li, E. A. Silver, & S. Li, eds.). https://doi.org/10.1007/978-3-319-04993-9_6

Helingo, D. D. Z., Amin, S. M., & Masriyah, M. (2019). Translation process of mathematics representation: From graphics to symbols and vice versa. Journal of Physics: Conference Series, 1188(1). https://doi.org/10.1088/1742-6596/1188/1/012055

Hoogland, K., Koning, J. de, Bakker, A., Pepin, B. E. U., & Gravemeijer, K. (2018). Changing representation in contextual mathematical problems from descriptive to depictive: The effect on students’ performance. Studies in Educational Evaluation, 58(November 2017), 122–131. https://doi.org/10.1016/j.stueduc.2018.06.004

Incikabi, S. (2017). Multiple Representations and Teaching Mathematics: An Analysis of the Mathematics Textbooks. Cumhuriyet International Journal of Education, 6(1), 66–81. https://doi.org/10.30703/cije.321438

Iskak, K. B., Kusmayati, T. A., & Fitriana, L. (2020). Students’ mathematics representation ability from picture form to equation. Journal of Physics: Conference Series, 1469(1). https://doi.org/10.1088/1742-6596/1469/1/012164

Jha, S. K. (2012). Mathematics performance of primary school students in Assam (India): An analysis using Newman Procedure. International Journal of Computer Applications in in Engineering Sciences, 2(I), 17–21.

Lobato, J. (2012). The Actor-Oriented Transfer Perspective and Its Contributions to Educational Research and Practice. Educational Psychologist, 47(3), 232–247. https://doi.org/10.1080/00461520.2012.693353

Mainali, B. (2021). Representation in teaching and learning mathematics. International Journal of Education in Mathematics, Science and Technology, 9(1), 1–21. https://doi.org/10.46328/ijemst.1111

Moreno-Arotzena, O., Pombar-Hospitaler, I., & Barragués, J. I. (2021). University student understanding of the gradient of a function of two variables: an approach from the perspective of the theory of semiotic representation registers. Educational Studies in Mathematics, 106(1), 65–89. https://doi.org/10.1007/s10649-020-09994-9

Mosese, N., & Ogbonnaya, U. I. (2021). GeoGebra and students’ learning achievement in trigonometric functions graphs representations and interpretations. Cypriot Journal of Educational Sciences, 16(2), 827–846. https://doi.org/https://doi.org/10.18844/cjes.v16i2.5685

Nizaruddin, S., Waluyo, B., Rochmad, & Isnarto. (2020). Mathematical Translation of Verbal Representation to Symbol Representation: A Case Study in Prospective Teachers Having High Mathematical Ability. 443, 87–91. https://doi.org/10.2991/assehr.k.200620.017

Njagi, M. W. (2015). Language Issues on Mathematics Achievement. International Journal of Education and Research, 3(6), 167–178.

Nurrahmawati, N., Sa’dijah, C., Sudirman, S., & Muksa, M. (2019). Multiple representations’ ability in solving word problem. International Journal of Recent Technology and Engineering, 8(1C2), 737–745.

Rahmawati, D. (2019). Translation Between Mathematical Representation: How Students Unpack Source Representation? Matematika Dan Pembelajaran, 7(1), 50. https://doi.org/10.33477/mp.v7i1.1045

Rahmawati, D., & Anwar, R. B. (2020). Translation of mathematical representation: characteristics of verbal representation unpacking. Journal of Education and Learning (EduLearn), 14(2), 162. https://doi.org/10.11591/edulearn.v14i2.9538

Rahmawati, D., Purwanto, P., Subanji, S., Hidayanto, E., & Anwar, R. B. (2017). Process of mathematical representation translation from verbal into graphic. International Electronic Journal of Mathematics Education, 12(4), 367–381.

Reddy, M. V. B., & Panacharoensawad, B. (2017). Students Problem-Solving Difficulties and Implications in Physics : An Empirical Study on Influencing Factors. Journal of Education and Practice, 8(14), 59–62.

Samsuddin, A. F., & Retnawati, H. (2018). Mathematical representation: The roles, challenges and implication on instruction. Journal of Physics: Conference Series, 1097(1). https://doi.org/10.1088/1742-6596/1097/1/012152

Sandie, Purwanto, Subanji, & Hidayanto, E. (2020). Student difficulties when constructing a hidden bridge to solve dynamic event problems. AIP Conference Proceedings, 2215(April). https://doi.org/10.1063/5.0000792

Selling, S. K. (2016). Learning to represent, representing to learn. Journal of Mathematical Behavior, 41, 191–209. https://doi.org/10.1016/j.jmathb.2015.10.003

Sitorus, J., & Masrayati. (2016). Students’ creative thinking process stages: Implementation of realistic mathematics education. Thinking Skills and Creativity, 22, 111–120. https://doi.org/10.1016/j.tsc.2016.09.007

Sumirattana, S., Makanong, A., & Thipkong, S. (2017). Using realistic mathematics education and the DAPIC problem-solving process to enhance secondary school students’ mathematical literacy. Kasetsart Journal of Social Sciences, 38(3), 307–315. https://doi.org/10.1016/j.kjss.2016.06.001

Turgut, M. (2017). Students’ reasoning on linear transformations in a DGS: a semiotic perspective. Proceedings of the 10th Congress of European Society for Research in Mathematics Education, 2652–2659.

Uptegrove, E. B. (2015). Shared communication in building mathematical ideas: A longitudinal study. Journal of Mathematical Behavior, 40, 106–130. https://doi.org/10.1016/j.jmathb.2015.02.001

Yee, S. P., & Bostic, J. D. (2014). Developing a contextualization of students’ mathematical problem solving. Journal of Mathematical Behavior, 36, 1–19. https://doi.org/10.1016/j.jmathb.2014.08.002

Zhang, L., Li, W., Yu, L., Sun, L., Dong, X., & Ning, X. (2021). GmFace: An explicit function for face image representation. Displays, 68(March), 102022. https://doi.org/10.1016/j.displa.2021.102022

Zhe, L. (2012). Survey of Primary Students’ Mathematical Representation Status and Study on the Teaching Model of Mathematical Representation. Journal of Mathematics Education, 5(1), 63–76.

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.




DOI: http://dx.doi.org/10.24127/ajpm.v11i2.4856

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