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Abstract

An open-ended problem in learning mathematics is a problem with more than one answer or method of solving. In solving open-ended problems in learning mathematics, one of the abilities students must use is decision-making ability. Each student has a variety of capacities, so this study aims to determine students' decision-making abilities in solving open-ended problems in learning mathematics. The type of research used is descriptive qualitative research. The subjects of this study were four students with different numbers of correct answers in working on open-ended problems. Data collection was carried out using tests and interviews. The results showed that (1) the decision-making ability of the subject who answers correctly for both problems is complete because they fulfill all indicators, the subject can identify goals, make decisions, evaluate the results of determination, and present and remember between problems with things known to the problem and related to decisions that have been taken correctly; (2) decision-making ability for subjects with wrong answers on one number or two numbers is incomplete because they only fulfilled two indicators, the subject can identify goals, make decisions, is less able to evaluate decision results and present and remember between problems with things known to the problem, and related to decisions that have been taken with correct. Mathematics teachers should often reinforce students to practice operating integers because it is a prerequisite for learning mathematics at the middle and high school levels.

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Decision Making Mathematical Problem Open-Ended Problem Solving

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References

  1. Afdareza, M. Y., Yuanita, P., & Maimunah, M. (2020). Development of learning device based on 21st century skill with implementation of problem based learning to increase critical thinking skill of students on polyhedron for grade 8th junior high school. Journal of Educational Sciences, 4(2), 273-284. https://doi.org/10.31258/jes.4.2.p.273-284

  2. Anggoro, B. S., Puspita, N., Pratiwi, D. D., Agustina, S., Komala, R., Widyastuti, R., & Widyawati, S. (2021). Mathematical-analytical thinking skills: The impacts and interactions of open-ended learning method & self-awareness (Its application on bilingual Test instruments). Al-Jabar: Jurnal Pendidikan Matematika, 12(1), 89-107. https://doi.org/10.24042/ajpm.v12i1.8516

  3. Baker, D., Bridges, D., Hunter, R., Johnson, G., Krupa, J., Murphy, J., & Sorenson, K. (2001). Guidebook to decision-making methods (Vol. 45). Westinghouse Savannah River Company Aiken, SC, USA.

  4. Bariroh, N. M., Triyanto, T., & Fitriana, L. (2023). Critical thinking ability of students at SMPN 2 Kudus with impulsive cognitive style on two variables linear equation system material. AIP Conference Proceedings, 2540(1), 070012. https://doi.org/10.1063/5.0105903

  5. Bogdao, R. C., & Biklen, S. K. (2003). Qualitative research for education. New York: Pearson.

  6. Bragg, L., & Nicol, C. (2008). Designing open-ended problems to challenge preservice teachers’ views on mathematics and pedagogy. Proceedings of PME 32 and PME-NA 30, 2, 201-208.

  7. Carter, N., Bryant-Lukosius, D., DiCenso, A., Blythe, J., & Neville, A. J. (2014). The use of triangulation in qualitative research. Oncology Nursing Forum, 41(5), 545-547. https://doi.org/10.1188/14.ONF.545-547

  8. Creswell, J. W. (2012). Educational research: Planning, conducting, and evaluating quantitative and qualitative research. USA: Pearson.

  9. Creswell, J. W., & Creswell, J. D. (2017). Research design: Qualitative, quantitative, and mixed methods approaches. Sage publications.

  10. Dauer, J. M., Lute, M. L., & Straka, O. (2017). Indicators of informal and formal decision-making about a socioscientific issue. International Journal of Education in Mathematics, Science and Technology, 5(2), 124-138.

  11. Dede, Y. (2013). Examining the underlying values of Turkish and German mathematics teachers' decision making processes in group studies. Educational Sciences: Theory and Practice, 13(1), 690-706.

  12. Ernawati, E. (2016). Pengembangan perangkat pembelajaran matematika berbasis open-ended approach untuk mengembangkan HOTS siswa SMA [Development of mathematics learning tools based on an open-ended approach to develop HOTS for high school students]. Jurnal Riset Pendidikan Matematika, 3(2), 209-220. https://doi.org/10.21831/jrpm.v3i2.10632

  13. Fatah, A., Suryadi, D., Sabandar, J., & Turmudi, T. (2016). Open-ended approach: An effort in cultivating students' mathematical creative thinking ability and self-esteem in mathematics. Journal on Mathematics Education, 7(1), 11-20. https://doi.org/10.22342/jme.7.1.2813.9-18

  14. Felmer, P. L., Pehkonen, E., & Kilpatrick, J. (2016). Posing and solving mathematical problems. Springer. https://doi.org/10.1007/978-3-319-28023-3

  15. Fuadiah, N. F., Suryadi, D., & Turmudi, T. (2017). Some difficulties in understanding negative numbers faced by students: A qualitative study applied at secondary schools in Indonesia. International Education Studies, 10(1), 24-38. https://doi.org/10.5539/ies.v10n1p24

  16. Guion, L. A., Diehl, D. C., & McDonald, D. (2011). Triangulation: establishing the validity of qualitative studies. Edis, 2011(8), FCS6014.

  17. Hendriana, H., Prahmana, R. C. I., Ristiana, M. G., Rohaeti, E. E., & Hidayat, W. (2022). The theoretical framework on humanist ethno-metaphorical mathematics learning model: An impactful insight in learning mathematics. Frontiers in Education, 7, 773. https://doi.org/10.3389/feduc.2022.1030471

  18. Hernandez-Serrano, J., & Jonassen, D. H. (2003). The effects of case libraries on problem solving. Journal of Computer Assisted Learning, 19(1), 103-114. https://doi.org/10.1046/j.0266-4909.2002.00010.x

  19. Hidayat, W., Rohaeti, E. E., Ginanjar, A., & Putri, R. I. I. (2022). An ePub learning module and students' mathematical reasoning ability: A development study. Journal on Mathematics Education, 13(1), 103-118. https://doi.org/10.22342/jme.v13i1.pp103-118

  20. Hidayat, W., & Sariningsih, R. (2018). Kemampuan pemecahan masalah matematis dan adversity quotient siswa SMP melalui pembelajaran open ended [Mathematical problem-solving abilities and adversity quotient of junior high school students through open-ended learning]. JNPM (Jurnal Nasional Pendidikan Matematika), 2(1), 109-118. https://doi.org/10.33603/jnpm.v2i1.1027

  21. Hutajulu, M., Wijaya, T. T., & Hidayat, W. (2019). The effect of mathematical disposition and learning motivation on problem solving: an analysis. Infinity Journal, 8(2), 229-238. https://doi.org/10.22460/infinity.v8i2.p229-238

  22. Ibrahim, I., & Widodo, S. A. (2020). Advocacy approach with open-ended problems to mathematical creative thinking ability. Infinity Journal, 9(1), 93-102. https://doi.org/10.22460/infinity.v9i1.p93-102

  23. Johnson, R. B., & Christensen, L. (2019). Educational research: Quantitative, qualitative, and mixed approaches. Sage publications.

  24. Khalid, M., & Embong, Z. (2019). Sources and possible causes of errors and misconceptions in operations of integers. International Electronic Journal of Mathematics Education, 15(2), em0568. https://doi.org/10.29333/iejme/6265

  25. Kirk, J., & Miller, M. L. (1986). Reliability and validity in qualitative research. Sage.

  26. Lambert, V. A., & Lambert, C. E. (2012). Qualitative descriptive research: An acceptable design. Pacific Rim International Journal of Nursing Research, 16(4), 255-256.

  27. Lee, C. I. (2016). An appropriate prompts system based on the Polya method for mathematical problem-solving. Eurasia Journal of Mathematics, Science and Technology Education, 13(3), 893-910. https://doi.org/10.12973/eurasia.2017.00649a

  28. Mariam, S., Nurmala, N., Nurdianti, D., Rustyani, N., Desi, A., & Hidayat, W. (2019). Analisis kemampuan pemecahan masalah matematis siswa mtsn dengan menggunakan metode open ended di Bandung Barat [Analysis of the mathematical problem-solving abilities of MTSN students using the open-ended method in West Bandung]. Jurnal Cendekia: Jurnal Pendidikan Matematika, 3(1), 178-186. https://doi.org/10.31004/cendekia.v3i1.94

  29. Miles, M. B., Huberman, A. M., & Saldana, J. (2014). Qualitative Data Analysis. A Methods Sourcebook. SAGE Publications.

  30. Murtafiah, W., Lukitasari, M., & Lestari, N. D. S. (2021). Exploring the decision-making process of pre-service teachers in solving mathematics literacy problems. Jurnal Pendidikan Matematika, 15(2), 145-160. https://doi.org/10.22342/jpm.15.2.13908.145-160

  31. Murtafiah, W., Lukitasari, M., Lestari, N. D. S., Zayyadi, M., & Widodo, S. A. (2022). Decision making students winning microteaching contest in design lesson plan and its implementation in mathematics learning. Cypriot Journal of Educational Sciences, 17(3), 2045-2060. https://doi.org/10.18844/cjes.v17i6.7497

  32. Murtafiah, W., Sa’dijah, C., Chandra, T. D., & Susiswo, S. (2019). Decision making of the winner of the national student creativity program in designing ICT-based learning media. TEM Journal, 8(3), 1039-1045. https://doi.org/10.18421/TEM83-49

  33. Murtafiah, W., Sa’dijah, C., Chandra, T. D., Susiswo, S., & Zayyadi, M. (2020). Novice and experienced mathematics teachers’ decision making process in designing math problem. Journal of Physics: Conference Series, 1464(1), 012030. https://doi.org/10.1088/1742-6596/1464/1/012030

  34. Natow, R. S. (2020). The use of triangulation in qualitative studies employing elite interviews. Qualitative Research, 20(2), 160-173. https://doi.org/10.1177/1468794119830077

  35. Nur, A. S., Kartono, K., Zaenuri, Z., & Rochmad, R. (2022). The learning trajectory construction of elementary school students in solving integer word problems. Participatory Educational Research, 9(1), 404-424. https://doi.org/10.17275/per.22.22.9.1

  36. Özreçberoğlu, N., & Çağanağa, Ç. K. (2018). Making it count: Strategies for improving problem-solving skills in mathematics for students and teachers’ classroom management. Eurasia Journal of Mathematics, Science and Technology Education, 14(4), 1253-1261. https://doi.org/10.29333/ejmste/82536

  37. Pramuditya, S. A., Noto, M. S., & Azzumar, F. (2022). Characteristics of students'mathematical problem solving abilities in open-ended-based virtual reality game learning. Infinity Journal, 11(2), 255-272. https://doi.org/10.22460/infinity.v11i2.p255-272

  38. Puspaningtyas, N. D. (2019). Proses berpikir lateral siswa SD dalam menyelesaikan masalah matematika open-ended ditinjau dari perbedaan gaya belajar [Elementary students' lateral thinking processes in solving open-ended math problems in terms of differences in learning styles]. MAJAMATH: Jurnal Matematika Dan Pendidikan Matematika, 2(2), 80-86. https://doi.org/10.36815/majamath.v2i2.373

  39. Renz, S. M., Carrington, J. M., & Badger, T. A. (2018). Two strategies for qualitative content analysis: An intramethod approach to triangulation. Qualitative Health Research, 28(5), 824-831. https://doi.org/10.1177/1049732317753586

  40. Sa’dijah, C., Rafiah, H., Gipayana, M., Qohar, A., & Anwar, L. (2017). Asesmen pemecahan masalah open-ended untuk mengukur profil berpikir kreatif matematis siswa berdasar gender [An open-ended problem-solving assessment to measure the profile of students' mathematical creative thinking based on gender]. Sekolah Dasar: Kajian Teori dan Praktik Pendidikan, 25(2), 147-159. https://doi.org/10.17977/um009v25i22016p147

  41. Santagata, R., & Yeh, C. (2016). The role of perception, interpretation, and decision making in the development of beginning teachers’ competence. Zdm, 48(1), 153-165. https://doi.org/10.1007/s11858-015-0737-9

  42. Schoenfeld, A. H. (2015). How we think: A theory of human decision-making, with a focus on teaching. In The Proceedings of the 12th International Congress on Mathematical Education: Intellectual and Attitudinal Challenges. https://doi.org/10.1007/978-3-319-12688-3

  43. Septian, A., Widodo, S. A., Afifah, I. N., Nisa, D. Z., Putri, N. P. K., Tyas, M. D., Nisa, R. H., & Andriani, A. (2022). Mathematical problem solving ability in Indonesia. Journal of Instructional Mathematics, 3(1), 16-25. https://doi.org/10.37640/jim.v3i1.1223

  44. Setianingsih, W. L., Ekayanti, A., & Jumadi, J. (2022). Analisis kemampuan numerasi siswa smp dalam menyelesaikan soal tipe asesmen kompetensi minimum (AKM) [Analysis of the numeracy skills of junior high school students in solving minimum competency assessment type questions (AKM)]. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 11(4), 3262-3273. https://doi.org/10.24127/ajpm.v11i4.5915

  45. Sinatra, G. M., Heddy, B. C., & Lombardi, D. (2015). The challenges of defining and measuring student engagement in science. Educational Psychologist, 50(1), 1-13. https://doi.org/10.1080/00461520.2014.1002924

  46. Siswono, T. Y. E. (2008). Promoting creavity in learning mathematics using open-ended problems. In The 3 International Conference on Mathematics and Statistics (ICoMS-3) Institut Pertanian Bogor, Indonesia.

  47. Swartz, R. J., Fischer, S. D., & Parks, S. (1998). Infusing the teaching of critical and creative thinking into secondary science: A lesson design handbook. Critical Thinking Books and Software.

  48. Syawahid, M. (2019). Mathematical literacy in algebra reasoning. International Journal of Insight for Mathematics Teaching, 2(1), 33-46.

  49. Utomo, D. P. (2020). The pattern of a relational understanding of fifth-grade students on integer operations. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 5(2), 119-129. https://doi.org/10.23917/jramathedu.v5i2.9545

  50. Verawati, A., Agustito, D., Pusporini, W., Utami, W. B., & Widodo, S. A. (2022). Designing android learning media to improve problem-solving skills of ratio. Advances in Mobile Learning Educational Research, 2(1), 216-224. https://doi.org/10.25082/AMLER.2022.01.005

  51. Viseu, F., & Oliveira, I. B. (2012). Open-ended tasks in the promotion of classroom communication in mathematics. International Electronic Journal of Elementary Education, 4(2), 287-300.

  52. Wang, Y., & Ruhe, G. (2007). The cognitive process of decision making. International Journal of Cognitive Informatics and Natural Intelligence (IJCINI), 1(2), 73-85. https://doi.org/10.4018/jcini.2007040105

  53. Widodo, S. A. (2017). Development of teaching materials algebraic equation to improve problem solving. Infinity Journal, 6(1), 59-68. https://doi.org/10.22460/infinity.v6i1.p59-68

  54. Widodo, S. A., Darhim, D., & Ikhwanudin, T. (2018). Improving mathematical problem solving skills through visual media. Journal of Physics: Conference Series, 948(1), 012004. https://doi.org/10.1088/1742-6596/948/1/012004

  55. Widodo, S. A., Irfan, M., Trisniawati, T., Hidayat, W., Perbowo, K. S., Noto, M. S., & Prahmana, R. C. I. (2020). Process of algebra problem-solving in formal student. Journal of Physics: Conference Series, 1657(1), 012092. https://doi.org/10.1088/1742-6596/1657/1/012092

  56. Widodo, S. A., Istiqomah, I., Leonard, L., Nayazik, A., & Prahmana, R. C. I. (2019). Formal student thinking in mathematical problem-solving. Journal of Physics: Conference Series, 1188(1), 012087. https://doi.org/10.1088/1742-6596/1188/1/012087

  57. Widodo, S. A., Sari, D. D., Maarif, S., Setiana, D. S., & Perbowo, K. S. (2022). Learning achievement of extroverted students in algebraic operations by tutorial learning: A single subject research. International Journal of Evaluation and Research in Education, 11(1), 99-107. https://doi.org/10.11591/ijere.v11i1.21747

  58. Widodo, S. A., Turmudi, T., & Dahlan, J. A. (2019). An error students in mathematical problems solves based on cognitive development. International Journal Of Scientific & Technology Research, 8(07), 433-439.

  59. Wijaya, A. (2018). How do open-ended problems promote mathematical creativity? A reflection of bare mathematics problem and contextual problem. Journal of Physics: Conference Series, 983(1), 012114. https://doi.org/10.1088/1742-6596/983/1/012114

  60. Wijayanti, A., Widodo, S. A., Pusporini, W., Wijayanti, N., Irfan, M., & Trisniawati, T. (2022). Optimization of Mathematics Learning with Problem Based Learning and 3N (Niteni, Nirokke, Nambahi) to improve mathematical problem solving skills. IndoMath: Indonesia Mathematics Education, 5(2), 123-134.

  61. Winarso, W. (2014). Problem solving, creativity dan decision making dalam pembelajaran matematika [Problem solving, creativity and decision making in learning mathematics]. Eduma: Mathematics Education Learning and Teaching, 3(1), 1-16.