KEMAMPUAN REPRESENTASI MATEMATIS DALAM MENYELESAIKAN MASALAH TAK TERSTRUKTUR (ILL-STRUCTURED PROBLEM)

Mohamad Salam(1*),

(1) Universitas Halu Oleo
(*) Corresponding Author


Abstract


Abstrak

Masalah tak terstruktur merupakan masalah yang rumit dipecahkan karena informasi yang berkaitan dengan masalah tersebut terbatas, mempunyai solusi yang banyak bahkan tidak mempunyai solusi. Sehingga memecahkan masalah seperti ini mahasiswa mengalami kesulitan dibandingkan dengan masalah terstruktur. Penelitian ini bertujuan untuk menganalisis penerapan representasi matematis dalam menyelesaikan masalah tak terstruktur. Pendekatan kualitatif digunakan untuk mengeksplorasi representasi matematis terhadap dua subjek dari 65 mahasiswa pendidikan matematika Universitas Halu Oleo yang telah mempelajari kalkulus. Hasil penelitian menunjukkan bahwa representasi verbal dan simbolik digunakan kedua subjek untuk memecahkan masalah tak terstruktur, tetapi representasi visual tidak digunakan. Hasil lain yang diperoleh adalah kedua subjek memiliki metode yang berbeda dalam menggunakan representasi matematis untuk memecahkan masalah tak terstruktur. Terakhir, kedua subyek mengungkapkan solusi berbeda terhadap masalah tak terstruktur yang diberikan meskipun kedua solusi tersebut benar.

Abstract

An ill-structured problem is a complex problem to solve because the information associated with the problem is limited, has many solutions, and does not even have a solution. So in solving problems like this, students have difficulty compared to structured problems. This study aims to analyze the application of mathematical representations in solving ill-structured problems. A qualitative approach was used to explore the mathematical representation of two subjects from 65 mathematics education students at Halu Oleo University who had studied calculus. The results showed that verbal and symbolic representations were used by both subjects to solve ill-structured problems, but visual representations were not used. Another result obtained is that the two subjects have different methods of using mathematical representations to solve ill-structured problems. Finally, the two subjects revealed different solutions to the given ill-structured problem even though both solutions were correct.


Keywords


ill-structured problem, mathematical representation, problem-solving

References


al - Ghofiqi, M., Irawati, S., & Rahardi, R. (2019). Analisis Berpikir Kreatif Siswa Berkemampuan Matematika Rendah Dalam Menyelesaikan Ill-Structured Problem. Jurnal Pendidikan: Teori, Penelitian, Dan Pengembangan, 4(10). https://doi.org/10.17977/jptpp.v4i10.12883

Awantagusnik, A., Susiswo, S., & Irawati, S. (2021). Mathematical representation process analysis of students in solving contextual problem based on Polya’s strategy. AIP Conference Proceedings, 2330. https://doi.org/10.1063/5.0043422

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

Byun, J. N., Kwon, D. Y., & Lee, W. G. (2014). Development of Ill-Structured Problems for Elementary Learners to Learn by Computer-Based Modeling Tools. International Journal of Computer Theory and Engineering, 6(4). https://doi.org/10.7763/ijcte.2014.v6.877

Chapman, O. (2010). Teachers’ self-representations in teaching mathematics. In Journal of Mathematics Teacher Education (Vol. 13, Issue 4). https://doi.org/10.1007/s10857-010-9153-9

Cho, M. K., & Kim, M. K. (2020). Investigating elementary students’ problem solving and teacher scaffolding in solving an Ill-structured problem. International Journal of Education in Mathematics, Science and Technology, 8(4). https://doi.org/10.46328/IJEMST.V8I4.1148

Duffy, G., Sorby, S., & Bowe, B. (2020). An investigation of the role of spatial ability in representing and solving word problems among engineering students. Journal of Engineering Education, 109(3). https://doi.org/10.1002/jee.20349

Erdoğan, F. (2020). The relationship between prospective middle school mathematics teachers’ critical thinking skills and reflective thinking skills. Participatory Educational Research, 7(1). https://doi.org/10.17275/per.20.13.7.1

Ge, X., & Land, S. M. (2003). Scaffolding students’ problem-solving processes in an Ill-structured task using question prompts and peer interactions. Educational Technology Research and Development, 51(1). https://doi.org/10.1007/BF02504515

Ge, X., Law, V., & Huang, K. (2016). Detangling the interrelationships between self-regulation and ill-structured problem solving in problem-based learning. Interdisciplinary Journal of Problem-Based Learning, 10(2). https://doi.org/10.7771/1541-5015.1622

Geyer, M.-A., & Kuske-Janßen, W. (2019). Mathematical Representations in Physics Lessons. In Mathematics in Physics Education. https://doi.org/10.1007/978-3-030-04627-9_4

Gina, N. M., Jusniani, N., & Budiman, H. (2021). MATHEMATICAL REPRESENTATION ABILITY OF JUNIOR HIGH SCHOOL STUDENTS ON SURFACE AREA OF CUBE AND CUBOID. Prima: Jurnal Pendidikan Matematika, 5(1). https://doi.org/10.31000/prima.v5i1.2769

Hanifah, Waluya, S. B., Rochmad, & Wardono. (2020). Mathematical Representation Ability and Self -Efficacy. Journal of Physics: Conference Series, 1613(1). https://doi.org/10.1088/1742-6596/1613/1/012062

Hong, J. Y., & Kim, M. K. (2016). Mathematical abstraction in the solving of ill-structured problems by elementary school students in Korea. Eurasia Journal of Mathematics, Science and Technology Education, 12(2). https://doi.org/10.12973/eurasia.2016.1204a

Hutagaol, K. (2013). PEMBELAJARAN KONTEKSTUAL UNTUK MENINGKATKAN KEMAMPUAN REPRESENTASI MATEMATIS SISWA SEKOLAH MENENGAH PERTAMA. Infinity Journal, 2(1). https://doi.org/10.22460/infinity.v2i1.27

Jonassen, D. H. (1997). Instructional design models for well-structured and ill-structured problem-solving learning outcomes. Educational Technology Research and Development, 45(1). https://doi.org/10.1007/bf02299613

Jonassen, D. H. (2013). Ill-Structured Problem-Solving Learning. Educational Technology Research and Development, 45(1).

Kim, J. Y., & Lim, K. Y. (2019). Promoting learning in online, ill-structured problem solving: The effects of scaffolding type and metacognition level. Computers and Education, 138. https://doi.org/10.1016/j.compedu.2019.05.001

Kitchener, K. S. (1983). Cognition, metacognition, and epistemic cognition: A three-level model of cognitive processing. Human Development, 26.

Lai, Y., Zhu, X., Chen, Y., & Li, Y. (2015). Effects of mathematics anxiety and mathematical metacognition on word problem solving in children with and without mathematical learning difficulties. PLoS ONE, 10(6). https://doi.org/10.1371/journal.pone.0130570

Mahmud, M. R., & Pratiwi, I. M. (2019). LITERASI NUMERASI SISWA DALAM PEMECAHAN MASALAH TIDAK TERSTRUKTUR. KALAMATIKA Jurnal Pendidikan Matematika, 4(1). https://doi.org/10.22236/kalamatika.vol4no1.2019pp69-88

Maker, C. J. (2020). Identifying Exceptional Talent in Science, Technology, Engineering, and Mathematics: Increasing Diversity and Assessing Creative Problem-Solving. Journal of Advanced Academics, 31(3). https://doi.org/10.1177/1932202X20918203

Marsigit, M., Retnawati, H., Apino, E., Santoso, R. H., Arlinwibowo, J., Santoso, A., & Rasmuin, R. (2020). Constructing mathematical concepts through external representations utilizing technology: An implementation in IRT course. TEM Journal, 9(1). https://doi.org/10.18421/TEM91-44

Maulyda, M. A., Hidayanto, E., & Rahardjo, S. (2019). Representation of Trigonometry Graph Funcsion Colage Students Using GeoGebra. International Journal of Trends in Mathematics Education Research, 2(4). https://doi.org/10.33122/ijtmer.v2i4.

Murtafiah, W., Sa’Dijah, C., Chandra, T. D., & Susiswo. (2020). Exploring the types of problems task by mathematics teacher to develop students’ HOTS. AIP Conference Proceedings, 2215. https://doi.org/10.1063/5.0000656

Noto, M. S., Hartono, W., & Sundawan, D. (2016). ANALYSIS OF STUDENTS MATHEMATICAL REPRESENTATION AND CONNECTION ON ANALYTICAL GEOMETRY SUBJECT. Infinity Journal, 5(2). https://doi.org/10.22460/infinity.v5i2.216

Nurjanah, S., Hidayanto, E., & Rahardjo, S. (2019). Proses Berpikir Siswa Berkecerdasan Matematis Logis Dalam Menyelesaikan Masalah Matematis “Ill Structured Problems.” Jurnal Pendidikan: Teori, Penelitian, Dan Pengembangan, 4(11). https://doi.org/10.17977/jptpp.v4i11.12977

Prayitno, L. L., Purwanto, P., Subanji, S., Susiswo, S., & As’ari, A. R. (2020). Exploring student’s representation process in solving ill-structured problems geometry. Participatory Educational Research, 7(2). https://doi.org/10.17275/PER.20.28.7.2

Rahmadian, N., Mulyono, & Isnarto. (2019). Kemampuan Representasi Matematis dalam Model Pembelajaran Somatic, Auditory, Visualization, Intellectually (SAVI) | PRISMA, Prosiding Seminar Nasional Matematika. PRISMA, Prosiding Seminar Nasional Matematika, 2.

Rahmawati, D., Purwantoa, P., Subanji, S., Hidayanto, E., & Anwar, R. B. (2021). Process of Mathematical Representation Translation from Verbal into Graphic. International Electronic Journal of Mathematics Education, 12(3). https://doi.org/10.29333/iejme/618

Reed, S. K. (2016). The Structure of Ill-Structured (and Well-Structured) Problems Revisited. In Educational Psychology Review (Vol. 28, Issue 4). https://doi.org/10.1007/s10648-015-9343-1

Sağlam, Y., & Dost, S. (2014). Preservice Science and Mathematics Teachers’ Beliefs about Mathematical Problem Solving. Procedia - Social and Behavioral Sciences, 116. https://doi.org/10.1016/j.sbspro.2014.01.212

Salam, M., Ibrahim, N., & Sukardjo, M. (2019). The Effect of Learning Model and Spatial Intelligence on Learning Outcome. https://doi.org/10.2991/icamr-18.2019.76

Salam, M., & Salim, S. (2020). Analysis of Mathematical Reasoning Ability (MRA) with the Discovery Learning Model in Gender issues. Journal of Educational Science and Technology (EST). https://doi.org/10.26858/est.v6i2.13211

Santia, I., Purwanto, Sutawidjadja, A., Sudirman, & Subanji. (2019). Exploring mathematical representations in solving ill-structured problems: The case of quadratic function. Journal on Mathematics Education, 10(3), 365–378. https://doi.org/10.22342/jme.10.3.7600.365-378

Sari, A. J. (2018). Pengaruh Model Ill-Structured Problem Solving terhadap Kemampuan Berpikir Kreatif Matematis. Pendidikan Matematika.

Sari, D. P., & Darhim. (2020). Implementation of react strategy to develop mathematical representation, reasoning, and disposition ability. In Journal on Mathematics Education (Vol. 11, Issue 1). https://doi.org/10.22342/jme.11.1.7806.145-156

Sarosa, S. (2021). Analisis Data Penelitian Kualitatif. In Rajawali Pers.

Swastika, G. T., Abdurahman, A., Irawan, E. B., Nusantara, T., Subanji, & Irawati, S. (2018). Representation Translation Analysis of Junior High School Students in Solving Mathematics Problems. International Journal of Insights for Mathematics Teaching, 01(2).

Widiyasari, R., & Nurlaelah, E. (2019). Analysis of student’s mathematical reasoning ability materials quadratic equation on selected topics subject of secondary school. Journal of Physics: Conference Series, 1157(2). https://doi.org/10.1088/1742-6596/1157/2/022120




DOI: http://dx.doi.org/10.24127/ajpm.v11i3.5352

Refbacks

  • There are currently no refbacks.