Junior high school students’ abilities in solving the open-ended mathematical problems with the context of Songket motif

Jeri Araiku, Elika Kurniadi, Weni Dwi Pratiwi


Many researchers stated that most students struggle to solve higher mathematical problems, including open-ended problems. One of many solutions is to apply a realistic context close to students. Hence, this research aimed to analyze students’ abilities in solving an open-ended mathematical problem using the Songket context, particularly the Kembang Tengah motif. The subjects were 24 seventh graders. The instruments for this descriptive research were an open-ended problem and an interview sheet. The results show that in solving the open-ended problem, 88.33% of students understood the problem, 59.72% were able to construct, and 72.22% applied the plan, while 52.78% wrote the conclusion. No students evaluated their solution to the problem. In implementing open-ended problems in the traditional context, students have different solutions based on their various experiences with the context, problem-solving schema, and mean-putting on the problem. They also applied multiple problem-solving strategies in working the problem. The similarity was the use of assumptions in solving the problem. However, some assumptions were inconsistent, neither their prior work nor other mathematical concepts. Therefore, teachers and researchers need to emphasize students’ written self-evaluation to check and improve their solutions. Another suggestion is to see the metacognitive process in solving the open-ended mathematical problem using a specific tradition. Furthermore, teachers should engage more in using open-ended problems and scaffold students when facing obstacles in solving them.


open-ended; mathematical problem; problem solving; Songket motif

Full Text:



Abiam, P., Abonyi, O. S., Ugama, J. O., & Okafor, G. (2015). Effects of ethnomathematics-based instructional approach on primary school pupils’ achievement in geometry. Journal of Scientific Research and Reports, 9(2), 1–15. https://doi.org/10.9734/JSRR/2016/19079

Amir, Faizal, M., Hasanah, Nur, F., & Musthofa, H. (2018). Interactive multimedia based mathematics problem solving to develop students’ reasoning. International Journal of Engineering & Technology, 7, 272–276. https://doi.org/10.31219/osf.io/qx63e

Andrade, H., & Du, Y. (2007). Student responses to criteria-referenced self-assessment. Assessment & Evaluation in Higher Education, 32(2), 159–181. https://doi.org/10.1080/02602930600801928

Andrade, H., & Valtcheva, A. (2009). Promoting learning and achievement through self-assessment. Theory Into Practice, 48(1), 12–19. https://doi.org/10.1080/00405840802577544

Annizar, Ma’ruf, A., Maulyda, Archi, M., Khairunnisa, G. F., & Hijriani, L. (2020). Kemampuan pemecahan masalah matematis siswa dalam menyelesaikan soal pisa pada topik geometri [Students’ mathematical problem solving ability in solving pisa problems on geometry topics]. Jurnal Elemen, 6(1), 39–55. https://doi.org/10.29408/jel.v6i1.1688

Araiku, J., Parta, I. N., & Rahardjo, S. (2015). Pengembangan perangkat pembelajaran materi dimensi tiga bercirikan problem-based learning untuk meningkatkan kemampuan berpikir kritis siswa [Development of learning tools for three-dimensional material characterized by problem-based learning to improve students' critical thinking ability]. Magister thesis. Universitas Negeri Malang.

Araiku, J., Somakim, & Pratiwi, W. D. (2020). Ethnomathematics: Utilizing South Sumatra’s cultures to emphasize prospective teachers’ creativity in creating mathematical problem. Journal of Physics: Conference Series, 1581, 012032. https://doi.org/10.1088/1742-6596/1581/1/012032

Bahar, A., & Maker, C. J. (2015). Cognitive backgrounds of problem solving: A comparison of open-ended vs. closed mathematics problems. Eurasia Journal of Mathematics, Science and Technology Education, 11(6), 1531–1546. https://doi.org/10.12973/eurasia.2015.1410a

Basri, H., Purwanto, As’ari, A. R., & Sisworo. (2019). Investigating critical thinking skill of junior high school in solving mathematical problem. International Journal of Instruction, 12(3), 745–758. https://doi.org/10.29333/iji.2019.12345a

Becker, J. P., & Shimada, S. (1997). The open ended approach: A new proposal for teaching mathematics. The National Council of Teachers of Mathematics, Inc.

Biber, Ç., Tuna, A., & Korkmaz, S. (2013). The mistakes and the misconceptions of the eighth grade students on the subject of angles. European Journal of Science and Mathematics Education, 1(2), 50–59. https://doi.org/10.30935/scimath/9387

Boesen, J., Helenius, O., Bergqvist, E., Bergqvist, T., Lithner, J., Palm, T., & Palmberg, B. (2014). Developing mathematical competence: From the intended to the enacted curriculum. The Journal of Mathematical Behavior, 33(1), 72–78. https://doi.org/10.1016/j.jmathb.2013.10.001

Charmila, N., Zulkardi, & Darmawijoyo. (2016). Pengembangan soal matematika model PISA menggunakan konteks Jambi [Development of PISA model math problems using the Jambi context]. Jurnal Penelitian Dan Evaluasi, 20(2), 198–207. https://doi.org/10.21831/pep.v20i2.7444

Chong, M. S. F., Shahrill, M., Putri, R. I. I., & Zulkardi. (2018). Teaching problem solving using non-routine tasks. AIP Conference Proceedings, 1952. https://doi.org/10.1063/1.5031982

Damayanti, H. T., & Sumardi, S. (2018). Mathematical creative thinking ability of junior high school students in solving open-ended problem. Journal of Research and Advances in Mathematics Education, 3(1), 36–45. https://doi.org/10.23917/jramathedu.v3i1.5869

Diefes-Dux, H. A., Zawojewski, J. S., & Hjalmarson, M. A. (2010). Using educational research in the design of evaluation tools for open-ended problems. Int. J. Engng Ed, 26(4), 807–819.

Douglas, E. P., Koro-Ljungberg, M., McNeill, N. J., Malcolm, Z. T., & Therriault, D. J. (2012). Moving beyond formulas and fixations: solving open-ended engineering problems. European Journal of Engineering Education, 37(6), 627–651. https://doi.org/10.1080/03043797.2012.738358

Dym, C. L., Agogino, A. M., Eris, O., & Frey, D. D. (2005). Engineering design thinking teaching and learning. Journal of Engineering Education, 94(1), 103–120. https://doi.org/10.1002/j.2168-9830.2005.tb00832.x

Earl, L. (2006). Assessment – A powerful lever for learning. Brock Education, 16(1), 1–15. https://doi.org/10.26522/brocked.v16i1.29

Edson, A. J. (2017). Learner-controlled scaffolding linked to open-ended problems in a digital learning environment. ZDM, 49(5), 735–753. https://doi.org/10.1007/s11858-017-0873-5

Francois, K. (2012). Ethnomathematics in a european context: towards an enrichment meaning of ethnomathematics. Journal of Mathematics and Culture, 6(1), 191–208.

Hadi, S., Retnawati, H., Munadi, S., Apino, E., & Wulandari, N. F. (2018). The difficulties of high school students in solving higher-order thinking skills problems. Problems of Education in the 21st Century, 76(4), 520–532. https://doi.org/10.33225/pec/18.76.520

Hafidzah, N. A., Azis, Z., & Irvan, I. (2021). The effect of open ended approach on problem solving ability and learning independence in students’ mathematics lessons. Indonesian Journal of Education and Mathematics Science [IJEMS], 2(1), 11–18. https://doi.org/10.30596/ijems.v2i1.6176

Hamimah, Kenedi, A. K., & Zuryanty. (2020). Efforts to increase high-level thinking ability using open-ended approaches. Jurnal Pajar, 4(2), 296–302. https://doi.org/10.33578/pjr.v4i2.7935

Harding, J. L. (2021). Ethnomathematics affirmed through cognitive mathematics and academic achievement: quality mathematics teaching and learning benefits. In M. Danesi (Ed.), Handbook of Cognitive Mathematics (pp. 1–30). Springer. https://doi.org/10.1007/978-3-030-44982-7_5-1

Haryanto, C., & Pujiastuti, E. (2020). Analysis of students mistakes in solving open ended question based on Newman’s procedures on Treffinger learning model. Unnes Journal of Mathematics Education, 9(3), 211–217.

Hasbi, M., Lukito, A., & Sulaiman, R. (2019). Mathematical connection middle-school students 8th in realistic mathematics education. Journal of Physics: Conference Series, 1417, 012047. https://doi.org/10.1088/1742-6596/1417/1/012047

Hasyim, Maylita; Andreina, F. K. (2019). Analisis high order thinking skill (HOTS) siswa dalam menyelesaikan soal open ended matematika [Analysis of students’ high order thinking skills (HOTS) in solving open ended math problems]. Fibonacci, 5(1), 55–64. https://doi.org/10.24853/fbc.5.1.55-64

Hendriana, H., Johanto, T., & Sumarmo, U. (2018). The role of problem-based learning to improve students’ mathematical problem-solving ability and self confidence. Journal on Mathematics Education, 9(2), 291–300. https://doi.org/10.22342/jme.9.2.5394.291-300

Hewi, La; Shaleh, M. (2020). Refleksi hasil PISA (the programme for international student assesment): Upaya perbaikan bertumpu pada pendidikan anak usia dini) [Reflection on PISA (the program for international student assessment) results: Improvement efforts rely on early childhood education]. Jurnal Golden Age, 4(1), 30–41. https://doi.org/10.29408/jga.v4i01.2018

Hiebert, J. (2003). What research says about the NCTM standards. In J. Kilpatrick, G. Martin, & D. Schifter (Eds.), A research companion to the principles and standards for school mathematics (pp. 5–23). National Council of Teachers of Mathematics.

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), 267–281. https://doi.org/10.1002/j.1556-6678.2010.tb00013.x

Imai, T. (2000). The influence of overcoming fixation in mathematics towards divergent thinking in open-ended mathematics problems on Japanese junior high school students. International Journal of Mathematical Education in Science and Technology, 31(2), 187–193. https://doi.org/10.1080/002073900287246

Intaros, P., Inprasitha, M., & Srisawadi, N. (2014). Students’ problem solving strategies in problem solving-mathematics classroom. Procedia - Social and Behavioral Sciences, 116, 4119 – 4123. https://doi.org/10.1016/j.sbspro.2014.01.901

Jäder, J., Lithner, J., & Sidenvall, J. (2020). Mathematical problem solving in textbooks from twelve countries. International Journal of Mathematical Education in Science and Technology, 51(7), 1120–1136. https://doi.org/10.1080/0020739X.2019.1656826

Jupri, A., Nurlaelah, E., & Dahlan, J. A. (2022). Strategi pemecahan masalah geometri mahasiswa calon guru matematika: Antara prediksi dan kenyataan [Geometry problem solving strategies for prospective mathematics teacher students: Between prediction and reality]. Jurnal Gantang, 6(2), 141–149. https://doi.org/10.31629/jg.v6i2.3539

Kumar, R., Edaltpanah, S. A., Jha, S., Broumi, S., & Dey, A. (2018). Neutrosophic shortest path problem. Neutrosophic Sets Systems, 23, 5–15.

Kurniawan, H., Putri, R. I. I., & Hartono, Y. (2018). Developing open-ended questions for surface area and volume of beam. Journal on Mathematics Education, 9(1), 157–168. https://doi.org/10.22342/jme.9.1.4640.157-168

Lehman, J., & Stanley, K. O. (2008). Exploiting open-endedness to solve problems through the search for novelty. ALIFE, 329–336.

Lester, F. K., & Cai, J. (2016). Can mathematical problem solving be taught? preliminary answers from 30 years of research. In J. Felmer, P.; Pehkonen, E.; Kilpatrick (Ed.), Posing and Solving Mathematical Problems. Research in Mathematics Education (pp. 117–135). Springer. https://doi.org/10.1007/978-3-319-28023-3_8

Lithner, J. (2004). Mathematical reasoning in calculus textbook exercises. The Journal of Mathematical Behavior2004, 23(4), 405–427. https://doi.org/10.1016/j.jmathb.2004.09.003

Lock, R. (1990). Open-ended, problem-solving investigations: What do we mean and how can we use them? School Science Review, 71(256), 63–72.

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

Maskur, R., Sumarno, Rahmawati, Y., Pradana, K., Syazali, M., Septian, A., & inarya Palupi, E. (2020). The effectiveness of problem based learning and aptitude treatment interaction in improving mathematical creative thinking skills on curriculum 2013. European Journal of Educational Research, 9(1), 375–383. https://doi.org/10.12973/eu-jer.9.1.375

McCormick, M. (2022). Teacher perceptions of the opportunities and constraints when integrating problem solving in student-centred mathematics teaching and learning.

Mourtos, N. J., DeJong-Okamoto, N., & Rhee., J. (2004). Open-ended problem-solving skills in thermal-fluids engineering. Global Journal of Engineering Education, 189–199.

Mowling, C. M., & Sims, S. K. (2021). The metacognition journey: strategies for teacher candidate exploration of self and student metacognition. A Journal for Physical and Sport Educators, 34(2), 13–23. https://doi.org/10.1080/08924562.2020.1867268

Mustapha, S., Rosli, M. S., & Saleh, N. S. (2019). Online learning environment to enhance HOTS in mathematics using Polya’s problem solving model. Journal of Physics: Conference Series, 1366, 012081. https://doi.org/10.1088/1742-6596/1366/1/012081

Nasution, D. S., & Pasaribu, L. H. (2021). The influence of interest, independence and learning resources on student learning achievement in mathematics lessons. Budapest International Research and Critics Institute-Journal (BIRCI-Journal), 4(2), 2743–2747. https://doi.org/10.33258/birci.v4i2.1983

Nursyahidah, F., Saputro, B. A., & Rubowo, M. R. (2018). Students problem solving ability based on realistic mathematics with ethnomathematics. Journal of Research and Advances in Mathematics Education, 3(1), 13–24. https://doi.org/10.23917/jramathedu.v3i1.5607

OECD. (2019). Programme for international student assessment (PISA) results from PISA 2018. OECD Publishing. https://www.oecd.org/pisa/publications/PISA2018_CN_IDN.pdf

Olewnik, A., Yerrick, R., Simmons, A., Lee, Y., & Stuhlmiller, B. (2020). Defining open-ended problem solving through problem typology framework. International Journal of Engineering Pedagogy (IJEP), 10(1), 7–30. https://doi.org/10.3991/ijep.v10i1.11033

Peranginangin, S. A., Saragih, S., & Siagian, P. (2019). Development of learning materials through PBL with Karo culture context to improve students’ problem solving ability and self-efficacy. International Electronic Journal of Mathematics Educatio, 14(2), 265–274. https://doi.org/10.29333/iejme/5713

Polya, G. (1973). How to solve it (2nd ed.). Princeton University.

Porgow, S. (2005). HOTS revisited: A thinking development approach to reducing the learning gap after grade 3. Phi Delta Kappan, 87(1), 64–75. https://doi.org/10.1177/003172170508700111

Pratama, L., Lestari, W., & Jailani. (2018). Metacognitive skills in mathematics problem solving. Daya Matematis: Jurnal Inovasi Pendidikan Matematika, 6(3), 286–297. https://doi.org/10.26858/jds.v6i3.8537

Putri, O. R. U. (2017). Pengembangan buku siswa bercirikan open ended mathematics problem untuk membangun berpikir kreatif [Development of student books characterized by open ended mathematics problems to build creative thinking]. Jurnal Silogisme: Kajian Ilmu Matematika Dan Pembelajarannya, 2(1), 7–14. https://doi.org/10.24269/js.v2i1.502

Rudi, Suryadi, D., & Rosjanuardi, R. (2020). Identifying students’ difficulties in understanding and applying pythagorean theorem with an onto-semiotic approach. MaPan: Jurnal Matematika Dan Pembelajaran, 8(1), 1–18. https://doi.org/10.24252/mapan.2020v8n1a1

Russo, J., Bobis, J., Downton, A., Hughes, S., Livy, S., McCormick, M., & Sullivan, P. (28 C.E.). Students who surprise teachers when learning mathematics through problem solving in the early primary years. International Journal of Innovation in Science and Mathematics Education, 3, 14–23. https://doi.org/10.30722/IJISME.28.03.002

Sapta, A., Pakpahan, S. P., & Sirait, S. (2019). Using the problem posing learning model based on open ended to improve mathematical critical thinking ability. Journal of Research in Mathematics Trends and Technology, 1(1), 12–15. https://doi.org/10.32734/jormtt.v1i1.752

Saputri, J. R., & Mampouw, H. L. (2018). Kemampuan pemecahan masalah dalam menyelesaikan soal materi pecahan oleh siswa SMP ditinjau dari tahapan Polya [Problem solving ability in solving fractional material problems by junior high school students in terms of the Polya stage]. Math Didactic: Jurnal Pendidikan Matematika, 4(2), 146–154. https://doi.org/10.33654/math.v4i2.104

Saragih, S., & Napitupulu, E. (2015). Developing student-centered learning model to improve high order mathematical thinking ability. International Education Studies, 8(6), 104–112. https://doi.org/10.5539/ies.v8n6p104

Shinariko, L. J., Saputri, N. W., Hartono, Y., & Araiku, J. (2020). Analysis of students’ mistakes in solving mathematics olympiad problems. Journal of Physics: Conference Series, 1480, 012039. https://doi.org/10.1088/1742-6596/1480/1/012039

Siagian, M. V., Saragih, S., & Sinaga, B. (2019). Development of learning materials oriented on problem-based learning model to improve students’ mathematical problem solving ability and metacognition ability. International Electronic Journal of Mathematics Education, 14(2), 331–340. https://doi.org/10.29333/iejme/5717

Simamora, R. E., Saragih, S., & Hasratuddin, H. (2018). Improving students’ mathematical problem solving ability and self-efficacy through guided discovery learning in local culture context. International Electronic Journal of Mathematics Education, 14(1), 61–72. https://doi.org/10.12973/iejme/3966

Stohlmann, M. S., & Albarracín, L. (2016). What is known about elementary grades mathematical modelling. Education Research International, 2016, 1–9. https://doi.org/10.1155/2016/5240683

Surya, Y. F., Zulfah, Astuti, Marta, R., & Wijaya, T. T. (2020). The development of open-ended math questions on grade v students of elementary school. Journal of Physics: Conference Serie, 1613, 012081. https://doi.org/10.1088/1742-6596/1613/1/012081

Swenson, J., Beranger, K., & Johnson, A. W. (2021). How students take up open-ended, real world problems. 2021 IEEE Frontiers in Education Conference (FIE), 1–5. https://doi.org/10.1109/FIE49875.2021.9637362

Swenson, J., Rola, M., Johnson, A., Treadway, E., Nitingale, A., Koushyar, H., & Wingate, K. (2021). Consideration for scaffolding open-ended engineering problems: instructor reflections after three years. 2021 IEEE Frontiers in Education Conference (FIE), 1–8. https://doi.org/10.1109/FIE49875.2021.9637392

Tambychik, T., & Meerah, T. T. S. M. (2010). Students’ difficulties in mathematics problem-solving: what do they say? Procedia Social and Behavioral Science, 8, 142–151. https://doi.org/10.1016/j.sbspro.2010.12.020

Tanudjaya, C. P., & Doorman, M. (2020). Examining higher order thinking in Indonesian lower secondary mathematics classrooms. Journal on Mathematics Education, 11(2), 277–300. https://doi.org/10.22342/jme.11.2.11000.277-300

Tanujaya, B., Mumu, J., & Margono, G. (2017). The relationship between higher order thinking skills and academic performance of student in mathematics instruction. International Education Studies, 10(11), 78–85. https://doi.org/10.5539/ies.v10n11p78

Ulinnuha, R., BudiWaluya, S., & Rochmad. (2021). Creative thinking ability with open-ended problems based on self-efficacy in Gnomio blended learning. Unnes Journal of Mathematics Education Research, 10(1), 20–25.

Walle, J., Karp, K., & Williams, J. (2010). Elementary and middle school mathematics: teaching developmentally seventh edition. Pearson Education, Inc.

Widana, I. W., Parwata, I. M. Y., Parmithi, N. N., Jayantika, I. G. A. T., Sukendra, K., & Sumandya, I. W. (2018). Higher order thinking skills assessment towards critical thinking on mathematics lesson. International Journal of Social Sciences and Humanities, 2(1), 24–32. https://doi.org/10.29332/ijssh.v2n1.74

Wulandari, P., Mujib, M., & Putra, F. G. (2016). Pengaruh model pembelajaran investigasi kelompok berbantuan perangkat lunak Maple terhadap kemampuan pemecahan masalah matematis [The Effect of Maple Software Assisted Group Investigation Learning Model on Mathematical Problem Solving Ability]. Al-Jabar : Jurnal Pendidikan Matematika, 7(1), 101–106. https://doi.org/10.24042/ajpm.v7i1.134

Yee, F. P. (2000). Open-ended problems for higher-order thinking in mathematics. Teaching and Learning, 20(2), 48–57.

Yunita, D. R., Maharani, A., & Sulaiman, H. (2019). Identifying of rigorous mathematical thinking on olympic students in solving non-routine problems on geometry topics. Advances in Social Science, Education and Humanities Research, 495–499. https://doi.org/10.2991/aes-18.2019.111

Yuwono, T., Supanggih, M., & Ferdiani, R. D. (2018). Analisis kemampuan pemecahan masalah matematika dalam menyelesaikan soal cerita berdasarkan prosedur Polya [Analysis of mathematical problem solving ability in solving story problems based on Polya’s procedures]. Jurnal Tadris Matematika, 1(2), 137–144. https://doi.org/10.21274/jtm.2018.1.2.137-144

Zulfah, Astuti, Insani, S. U., Zulhendri, & Akbar, P. (2019). Development of open-ended based mathematics problem to measure high-level thinking ability. Journal of Physics: Conference Series, 1315(1). https://doi.org/10.1088/1742-6596/1315/1/012047

DOI: https://doi.org/10.29408/jel.v8i2.5659


  • There are currently no refbacks.

Copyright (c) 2022 Jeri Araiku, Elika Kurniadi, Weni Dwi Pratiwi

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

 Creative Commons License
Jurnal Elemen is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

View My Stats