Kegagalan RZ Memecahkan Ill-Structured Problem Persegi Panjang
Keywords:
persegi panjang, konsep, trial and error
Abstract
Siswa dituntut harus menjadi pemecah masalah yang handal dalam berbagai situasi, salah satunya ill-structured problems. Penelitian ini merupakan study kasus bertujuan untuk mendeskripsikan penyebab kegagalan RZ dalam memecahkan ill-structured problems tentang persegi panjang untuk menginvestigasi secara mendalam, proses, aktivitas subjek RZ. RZ diminta untuk memecahkan masalah kemudian dilakukan wawancara secara mendalam. Hasil penelitian menunjukkan bahwa subjek mampu merepresentasikan masalah dengan bahasanya sendiri. Subjek gagal membangun solusi yang sesuai dengan masalah dikarenakan penguasaan konsep segiempat yang parsial. Subjek menggunakan trial and error karena gagal mengaitkan masalah dengan konsep persegi yang merupakan kunci keberhasilan pemecahan masalah. Dalam memberikan justifikasi, subjek tidak mengalami kendala karena proses yang dilakukan adalah penghitungan saja tanpa memaknainya. Sedangkan, proses monitoring dan evaluasi yang dilakukan subjek mengalami kegagalan. Subjek kebingungan menentukan solusi akhir dikarenakan solusi yang dibangunnya tidak memenuhi syarat dari masalah. Untuk itu, guru mempunyai peranan untuk mengajarkan siswanya dalam membangun relasi antar konsep yang dapat dimanfaatkan dalam pemecahan masalah.
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References
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Prayitno, L. L., Purwanto, P., Subanji, S., & Susiswo, S. (2018). Identification Errors of Problem Posed by Prospective Teachers About Fraction Based Meaning Structure. International Journal of Insights for Mathematics Teaching, 01(1), 76–84.
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), 183–202. https://doi.org/10.17275/PER.20.28.7.2
Rachmawati, Y. I., Sugandi, E., & Prayitno, L. L. (2019). Senior High School Students’ Ability in Posing System of Linear Equations in Two Variables Problems. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 4(1), 57–65. https://doi.org/10.23917/jramathedu.v4i1.6954
Shin, N., Jonassen, D. H., & McGee, S. (2003). Predictors of well-structured and ill-structured problem solving in an astronomy simulation. Journal of Research in Science Teaching, 40(1), 6–33. https://doi.org/https://doi.org/10.1002/tea.10058
Stylianou, D. A. (2013). An Examination of Connections in Mathematical Processes in Students ’ Problem Solving : Connections between Representing and Justifying. Journal of Education and Learning, 2(2), 23–35. https://doi.org/10.5539/jel.v2n2p23
Stylianou, D. A., & Silver, E. A. (2004). The Role of Visual Representations in Advanced Mathematical Problem Solving : An Examination of Expert- Novice Similarities and Differences. Mathematical Thinking and Learning, 6(4), 353–387.
Voss, J., & Post, T. (1988). On the solving of ill-structured problems. In The Nature of Expertise (pp. 261–285). Erlbaum.
Xin, Y. P., Jitendra, A. K., & Buchman, A. D. (2005). Effects of Mathematical Word Problem – Solving Instruction on Middle School Students with Learning Problems. The Journal of Special Education, 39(3), 181–192.
Anwar, R. B., Yuwono, I., As’ari, A. R., Sisworo, & Rahmawati, D. (2016). Mathematical Representation by Students in Building Relational Understanding on Concepts of Area and Primeter of Rectangle. Educational Research and Reviewsv, 11(21), 2002–2008. https://doi.org/10.5897/ERR2016.2813
Arends, R. (2009). Learning to Teach. McGraw-Hill.
Arifin, S., Zulkardi, P., Hartono, Y., & Susanti, E. (2017). Developing ill-defined problem-solving for the context of “South Sumatera.” IOP Conf. Series: Journal of Physics: Conf. Series.
Bal, A. P. (2014). The Examination of Representations used by Classroom Teacher Candidates in Solving Mathematical Problems. Educational Sciences: Theory & Practice, 14(6), 2349–2365. https://doi.org/10.12738/estp.2014.6.2189
Boonen, A. J. H., Reed, H. C., Schoonenboom, J., & Jolles, J. (2016). It’s Not a Math Lesson - We’re Learning to Draw ! Teachers’ Use of Visual Representations in Instructing Word Problem Solving in Sixth Grade of Elementary School. Frontline
Learning Research, 4(5), 55–82. https://doi.org/http://dx.doi.org/10.14786/flr.v4i5.245
Chi, M. T. H. H., & Glaser, R. (1985). Problem Solving Abilities. In Human Abilities: An Information Processing Approach.
Douglas, E., Ljungberg, M., McNeill, N., Malcolm, Z., & Therriault, D. (2012). Moving beyond formulas and fixations: Solving open-ended engineering problems. European Journal of Engineering Education, 37(6), 627–651.
Goldin, G. A. (1998). Representational systems, learning, and problem solving in mathematics. The Journal of Mathematical Behavior, 17(2), 137–165. https://doi.org/10.1016/S0364-0213(99)80056-1
Hegarty, M., Mayer, R. E., & Monk, C. A. (1995). Comprehension of Arithmetic Word Problems : A Comparison of Successful and Unsuccessful Problem Solvers inconsistent problems with those of problem solvers who do. Journal of Educational Psychology, 87(1), 18–32.
Hong, J., & Kim, M. (2016). Mathematical abstraction in the solving of ill-structured problems by elementary school students in Korea. Eurasia Journal of Mathematics, Science & Technology Education, 12(2), 267–281.
Hong, N. (1998). The Relationship Between Well-Structured and Ill-Structured Problem Solving in Multimedia Simulation (Issue August). The Pennsylvania State University.
Hoogland, K., de Koning, J., 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
Hoogland, K., & Pepin, B. (2016). The Intricacies of Assessing Numeracy : Investigating Alternatives to Word Problems Kees Hoogland. Adults Learning Mathematics: An International Journal, 11(2), 14–26.
Jonassen, D. (1997). Instructional design models for well-structured and ill-structured problem-solving learning outcomes. Educational Technology Research and Development, 45(1), 65–94.
Jonassen, D. (2003). Using cognitive tools to represent problems. Journal of Research on Technology in Education, 35(3), 362–381. https://doi.org/10.1080/15391523.2003.10782391
Mairing, J. P. (2017). Thinking Process of Naive Problem Solvers to Solve Mathematical Problems. International Education Studies, 10(1), 1–11. https://doi.org/10.5539/ies.v10n1p1
Merriam, S. (2009). Qualitative Research and Case Study Aplication in Education. Jossey-Bass.
Miles, M. B., & Huberman, M. A. (1994). Qualitative Data Analysis: A Sourcebook of New Methods. SAGE Publications, Inc.
NCTM. (2000). Principles and Standards for School Mathematics. In The National Council of Teachers of Mathematics Inc. The National Council of Teachers of
Mathematics Inc. https://doi.org/10.12816/0019740
Pape, S. J. (2004). Middle School Children’s Problem-Solving Behavior: A Cognitive Analysis from a Reading Comprehension Perspective. Journal for Research in Mathematics Education, 35(3), 187–219.
Pravesti, C. A., Wiyono, B. B., Handarini, D. M., Triyono, & Atmoko, A. (2020). Examining the effects of guidance and counseling services to the self-regulated learning for college students. Journal for the Education of Gifted Young Scientists, 8(1), 33–45. https://doi.org/10.17478/jegys.664548
Prayitno, L. L., & Budiyono, S. C. (2018). Error Analysis of Problem Posed by Pre-service Primary Teachers based on Semantic Structures. In Advances in Social Science, Education and Humanities Research (Issue 174). https://doi.org/10.2991/ice-17.2018.84
Prayitno, L. L., & Mutianingsih, N. (2021). Penggunaan SPADA Selama Masa Covid-19: Studi Kasus di Universitas PGRI Adi Buana Surabaya. Wahana: Tridarma Perguruan Tinggi, 73(1), 19–30.
Prayitno, L. L., Purwanto, P., Subanji, S., & Susiswo, S. (2018). Identification Errors of Problem Posed by Prospective Teachers About Fraction Based Meaning Structure. International Journal of Insights for Mathematics Teaching, 01(1), 76–84.
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), 183–202. https://doi.org/10.17275/PER.20.28.7.2
Rachmawati, Y. I., Sugandi, E., & Prayitno, L. L. (2019). Senior High School Students’ Ability in Posing System of Linear Equations in Two Variables Problems. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 4(1), 57–65. https://doi.org/10.23917/jramathedu.v4i1.6954
Shin, N., Jonassen, D. H., & McGee, S. (2003). Predictors of well-structured and ill-structured problem solving in an astronomy simulation. Journal of Research in Science Teaching, 40(1), 6–33. https://doi.org/https://doi.org/10.1002/tea.10058
Stylianou, D. A. (2013). An Examination of Connections in Mathematical Processes in Students ’ Problem Solving : Connections between Representing and Justifying. Journal of Education and Learning, 2(2), 23–35. https://doi.org/10.5539/jel.v2n2p23
Stylianou, D. A., & Silver, E. A. (2004). The Role of Visual Representations in Advanced Mathematical Problem Solving : An Examination of Expert- Novice Similarities and Differences. Mathematical Thinking and Learning, 6(4), 353–387.
Voss, J., & Post, T. (1988). On the solving of ill-structured problems. In The Nature of Expertise (pp. 261–285). Erlbaum.
Xin, Y. P., Jitendra, A. K., & Buchman, A. D. (2005). Effects of Mathematical Word Problem – Solving Instruction on Middle School Students with Learning Problems. The Journal of Special Education, 39(3), 181–192.
Published
2022-10-20
How to Cite
Mutianingsih, N., & Prayitno, L. (2022). Kegagalan RZ Memecahkan Ill-Structured Problem Persegi Panjang. Jurnal Cendekia : Jurnal Pendidikan Matematika, 6(3), 3167-3179. https://doi.org/10.31004/cendekia.v6i3.1091
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Articles
Copyright (c) 2022 Ninik Mutianingsih, Lydia Lia Prayitno
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