Measuring Creative Thinking Skills Using the Feasibility of Mathematics Problems with an Open-Ended Approach in Two-Dimensional Plane Geometry Topic
), Fajar Arianto(2), Husni Mubarok(3)
| 
Country:
(1) Department of Educational Technology, Universitas Negeri Surabaya, Indonesia, Indonesia
(2) Department of Educational Technology, Universitas Negeri Surabaya, Indonesia, Indonesia
(3) Department of Educational Technology, Universitas Negeri Surabaya, Indonesia, Indonesia
Corresponding Author
10.23960/jpmipa.v26i2.pp1173-1195
| Metrics→ |
| Indexing Site→ |  |
 |
 |
 |
Copyright (c) 2025 Hari Sugiharto Setyaedhi, Fajar Arianto, Husni Mubarok
The study aims to develop and validate open-ended mathematics questions, where measuring students' abilities at the field test stage is part of the final validation process to show that the instrument is functional. The development model with Tessmer's formative evaluation approach includes self-evaluation, expert review, one-to-one, small group, and field tests. The participants included one lecturer, two mathematics teachers, and students from grade IX. Individual trials involved three students, small group trials 12 students, and field trials 40 students. The data obtained came from quantitative and qualitative data. The instruments used included observation sheets, interviews, questionnaires, and tests. Analysis for quantitative data was carried out using the SPSS application. The findings of the study indicate that (1) this study produces a mathematics question product with an open-ended approach of 5 descriptive questions. Content validity (90.33%), construct validity (94.25%), and language validity (92.25%). High validity is caused by the formulation of questions that explicitly ask students to provide various ways, which directly target indicators of fluency and flexibility in creative thinking. In addition, the validity of each question item in the small group, namely r count > r table (0.576), with a reliability value of 0.931. (2) Open-ended math questions that are valid and reliable, so that they are used to measure students' creative skills in problem solving. Based on the results of the field test (20% of students are very creative, 30% creative, 10% quite creative, 5% not creative, and 5% very not creative), this proves that the instrument developed is able to differentiate the level of student ability. This study concludes that the development of math questions with an open-ended approach is feasible to be applied to measure creative thinking skills in solving math problems related to the two-dimensional plane geometry topic.
Keywords: creative skills, feasibility of mathematical problems, open-ended approach, two-dimensional plane geometry topic.
Adelabu, F. M., & Alex, J. K. (2023). Analysis of difficult concepts in Senior Phase Mathematics baseline assessments: First-year student teachers’ reflections. Research in Social Sciences and Technology, 8(4), 56–75. https://doi.org/10.46303/ressat.2023.20
Aini, N. R., Syafril, S., Netriwati, N., Pahrudin, A., Rahayu, T., & Puspasari, V. (2019). Problem-Based learning for critical thinking skills in mathematics. Journal of Physics: Conference Series, 1155(1). https://doi.org/10.1088/1742-6596/1155/1/012026
Aldiono, Purnomo, T., & Prastowo, T. (2023). Profile of problem-solving ability in junior high school students on global warming lesson material. IJORER : International Journal of Recent Educational Research, 4(3), 355–364. https://doi.org/10.46245/ijorer.v4i3.301
Alman, A. (2017). The influence of open-ended and STAD method on the mathematical problem-solving skills in terms of learning achievement. Jurnal Prima Edukasia, 5(2), 112–124. https://doi.org/10.21831/jpe.v5i2.14280
Amelia, S., Widiati, I., & Yadrika, G. (2023). Pengembangan soal numerasi untuk peserta didik fase d. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 12(3), 3048. https://doi.org/10.24127/ajpm.v12i3.7236
Anwar, M. N., Aness, M., Khizar, A., Naseer, M., & Muhammad, G. (2012). Relationship of academic, creative thinking with the school, achievements of secondary interdisciplinary students. International. Journal of Education, 1(1(3)), 1–4. Retrieved from https://www.researchgate.net/publication/338549060_Relationship_of_Creative_Thinking_with_the_Academic_Achievements_of_Secondary_School_Students
Aziza, M. (2021). A teacher questioning activity: The use of oral open-ended questions in mathematics classroom. Qualitative Research in Education, 10(1), 31–61. https://doi.org/10.17583/qre.2021.6475
Bahar, A., & Maker, 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
Balan, L., Yuen, T., & Mehrtash, M. (2019). Problem-Based learning strategy for cad software using free-choice and open-ended group projects. Procedia Manufacturing, 32, 339–347. https://doi.org/10.1016/j.promfg.2019.02.223
Bora, A. (2020). Critical thinking and creative thinking as the focus on mathematics education. International Journal of Scientific Development and Research (IJSDR) , 5(3), 235–241. Retrieved from www.ijsdr.org235
Çelik, H., & Özdemir, F. (2020). Mathematical thinking as a predictor of critical thinking dispositions of pre-service mathematics teachers. International Journal of Progressive Education, 16(4), 81–98. https://doi.org/10.29329/ijpe.2020.268.6
Chang, M.-M., & Lan, S.-W. (2021). Exploring undergraduate efl students’ perceptions and experiences of a moodle-based reciprocal teaching application. Open Learning: The Journal of Open, Distance and e Learning, 36(1), 29–44. Retrieved from https://eric.ed.gov/?id=EJ1288659
Christopher, I. O., Julie, O. I., Charity, U. C., & Janehilda, A. O. (2020). Assessment of students’ creative thinking ability in mathematical tasks at senior secondary school level. International Journal of Curriculum and Instruction, 12(2), 494–506.
Cotič, M., Doz, D., Jenko, M., & Žakelj, A. (2024). Mathematics education: What was it, what is it, and what will it be? International Electronic Journal of Mathematics Education, 19(3), 1–14. https://doi.org/10.29333/iejme/14663
Dermawan, D. D., & Andartiani, K. (2022). Worksheets Electronic Development of STEAM-Based to Improve Students’ Creative Thinking Ability. Hipotenusa : Journal of Mathematical Society, 4(1), 48–55. https://doi.org/10.18326/hipotenusa.v4i1.7213
Emara, M., Hutchins, N. M., Grover, S., Snyder, C., & Biswas, G. (2021). Examining student regulation of collaborative, computational, problem-solving processes in openended learning environments. Journal of Learning Analytics, 8(1), 49–74. https://doi.org/10.18608/JLA.2021.7230
Era Setiyawati, Endang Fauziati, Darsinah, Minsih, & Yenny Prastiwi. (2022). Problem solving errors in mathematics story questions. JPI (Jurnal Pendidikan Indonesia), 11(3), 466–479. https://doi.org/10.23887/jpiundiksha.v11i3.46980
Fatah, A., Suryadi, D., Sabandar, J., & Turmudi. (2016). Open-ended approach: An effort in cultivating students’ mathematical creative thinking ability and self-esteem in mathematics. Journal on Mathematics Education, 7(1), 9–18. https://doi.org/10.22342/jme.7.1.2813.9-18
Fauzi, M. N., Usodo, B., & Subanti, S. (2017). The effect of make a match (mam) type model and bamboo dance type model through cooperative learning on students' motivation. Suska Journal of Mathematics Education, 3(1), 26. https://doi.org/10.24014/sjme.v3i1.3511
Febriani, R., & Hendra Syarifuddin, M. (2021). Pengaruh pendekatan open - ended terhadap keterampilan berfikir kreatif dan kemampuan pemecahan masalah matematis di sekolah dasar. Jurnal Basicedu, 5(5), 3829–3840. Retrieved from https://jbasic.org/index.php/basicedu/article/view/582
Gafour O.W., & Gafour, W.A. (2020). Creative thinking skills – a review article. Journal of Education and E-Learning, (May 2020), 1–21. Retrieved from https://e-iji.net/ats/index.php/pub/article/view/474
Hadar, L. L., & Tirosh, M. (2019). Creative thinking in mathematics curriculum: An analytic framework. Thinking Skills and Creativity, 33(1). Retrieved from https://www.sciencedirect.com/science/article/abs/pii/S1871187118302943?via%3Dihub
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. IJEMS:Indonesian Journal of Education and Mathematical Science, 2(1), 44. https://doi.org/10.30596/ijems.v2i1.6176
Hamid, R., Baharom, S., Taha, M. R., & Kadaruddin, L. K. (2013). Competition as an innovative student-centered learning method for open-ended laboratory work. Procedia - Social and Behavioral Sciences, 102(Ifee 2012), 148–152. https://doi.org/10.1016/j.sbspro.2013.10.726
Hasret, N., & Savaş, A. (2019). Analysis of the relation between creativity level and problem solving skills of gifted and talented students. Educational Research and Reviews, 14(15), 518–532. https://doi.org/10.5897/err2019.3790
Hassan, S. R., Rosli, R., & Zakaria, E. (2016). The use of i-think map and questioning to promote higher-order thinking skills in mathematics. Creative Education, 07(07), 1069–1078. https://doi.org/10.4236/ce.2016.77111
Heliawati, L., Afakillah, I. I., & Pursitasari, I. D. (2021). Creative problem-solving learning through open-ended experiment for students’ understanding and scientific work using online learning. International Journal of Instruction, 14(4), 321–336. https://doi.org/10.29333/iji.2021.14419a
Heong, Y. M., Othman, W. B., Yunos, J. B. M., Kiong, T. T., Hassan, R. Bin, & Mohamad, M. M. B. (2011). The Level of Marzano's higher-order thinking skills among technical education students. International Journal of Social Science and Humanity, 1(2), 121–125. https://doi.org/10.7763/ijssh.2011.v1.20
Ibrahim, K., I. A., & Indra Prahmana, R. C. (2024). Mathematics learning orientation: Mathematical creative thinking ability or creative disposition? Journal on Mathematics Education, 15(1), 253–276. https://doi.org/10.22342/jme.v15i1.pp253-276
Kartikasari, I. A., Usodo, B., & Riyadi. (2022). The effectiveness open-ended learning and creative problem solving models to teach creative thinking skills. Pegem Egitim ve Ogretim Dergisi, 12(4), 29–38. https://doi.org/10.47750/pegegog.12.04.04
Khoerunnisa, P. (2021). Ability of students in completing mathematical story problems. ETUDE: Journal of Educational Research, 1(3), 91–102. https://doi.org/10.56724/etude.v1i3.39
Kowiyah, & Mulyawati, I. (2018). An analysis of primary school students’ representational ability in mathematics based on gender perspective. Journal of Physics: Conference Series, 948(1). https://doi.org/10.1088/1742-6596/948/1/012016
Kurniawan, D. V., Susiswo, S., & Hafiizh, M. (2024). Fluency and flexibility of students in solving arithmetic sequence problems based on self efficacy. Prisma, 13(1), 113. https://doi.org/10.35194/jp.v13i1.3961
Langoban, M. A. (2020). What makes mathematics difficult as a subject for most students in higher education? International Journal of English and Education, 9(3), 214–220.
Lince, R. (2016). Creative thinking ability to increase student mathematical of junior high school by applying models numbered heads together. Journal of Education and Practice, 7(6), 206–212. Retrieved from https://eric.ed.gov/?id=EJ1092494
Mahmoud, A., Hashim, S. S., & Sunarso, J. (2020). Learning permeability and fluidisation concepts via open-ended laboratory experiments. Education for Chemical Engineers, 32, 72–81. Retrieved from https://www.sciencedirect.com/science/article/abs/pii/S1749772820300361
Maričić1, S., Špijunović1, K., & Lazić2, B. (2015). The influence of content on the thinking in the initial teaching of mathematics. Croatian Journal of Education, 18(1), 11–40. Retrieved from https://typeset.io/papers/the-influence-of-content-on-the-development-of-students-16z5vaco8u
Moate, J., Kuntze, S., & Chan, M. C. E. (2021). Student participation in peer interaction - Use of material resources as a key consideration in an open-ended problem-solving mathematics task. Lumat, 9(1), 29–55. https://doi.org/10.31129/LUMAT.9.1.1470
Munahefi, D. N., Mulyono, Zahid, M. Z., Syaharani, E. A., & Fariz, R. (2021). Analysis of mathematical creative thinking test instruments on open-ended problems with ethnomathematic nuances. Journal of Physics: Conference Series, 1918(4). https://doi.org/10.1088/1742-6596/1918/4/042060
Munroe, L. (2015). The open-ended approach framework. European Journal of Educational Research, volume-5-2(volume4-issuse3.html), 97–104. https://doi.org/10.12973/eu-jer.4.3.97
Nathan, K. R. K. & M. J. (2004). The real story behind story problems: effects of representations on quantitative reasoning. The Journal of the Learning Sciences, 13(2), 129–164. Retrieved from https://www.jstor.org/stable/1466903
OECD. (2022). PISA 2022 Results. In Journal Pendidikan. Retrieved from https://www.oecd.org/en/publications/pisa-2022-results-volume-i-and-ii-country-notes_ed6fbcc5-en/indonesia_c2e1ae0e-en.html
OECD. (2024). New PISA results on Creative Thinking: can students think outside the box? (125), 1–54. Retrieved from https://www.oecd-ilibrary.org/docserver/b3a46696-en.pdf?expires=1719223615&id=id&accname=guest&checksum=6903016C113653E6A8F3D68306123565
Oliveira, A. W., Brown, A. O., Zhang, W. S., LeBrun, P., Eaton, L., & Yemen, S. (2021). Fostering creativity in science learning: The potential of open-ended student drawing. Teaching and Teacher Education, 105, 103416. https://doi.org/10.1016/j.tate.2021.103416
Palennari, M., Lasmi, L., & Rachmawaty, R. (2021). Keterampilan pemecahan masalah peserta didik: studi kasus di SMA Negeri 1 Wonomulyo. Diklabio: Jurnal Pendidikan Dan Pembelajaran Biologi, 5(2), 208–216. https://doi.org/10.33369/diklabio.5.2.208-216
Rahayuningsih, S., Sirajuddin, S., & Ikram, M. (2021). Using open-ended problem-solving tests to identify students’ mathematical creative thinking ability. Participatory Educational Research, 8(3), 285–299. https://doi.org/10.17275/per.21.66.8.3
Randles, C., Overton, T., Galloway, R., & Wallace, M. (2018). How do approaches to solving open-ended problems vary within the science disciplines? International Journal of Science Education, 40(11), 1367–1390. Retrieved from https://eric.ed.gov/?id=EJ1188376
Raupu, S., Nurdin, K., Hasriana, & Said, A. (2023). The analysis of students ’ learning difficulties in mathematics algebraic arithmetic operation. Sujana (Journal of Education and Learning Review), 2(2), 11–26. Retrieved from https://journal.jfpublisher.com/index.php/sujana/article/view/314
Rizos, I., & Gkrekas, N. (2023). Incorporating history of mathematics in open-ended problem solving: An empirical study. Eurasia Journal of Mathematics, Science and Technology Education, 19(3). https://doi.org/10.29333/ejmste/13025
Sadak, M., & Pektas, M. (2022). Investigating mathematical creativity through the connection between creative abilities in problem posing and problem solving. Thinking Skills and Creativity, 45. Retrieved from https://www.sciencedirect.com/science/article/abs/pii/S1871187122001110#preview-section-introduction
Setyaedhi, H. S., & Pramana, A. (2024). Feasibility of e-learning textbooks of item analysis material to improve student competence. 12(1), 39–51. Retrieved from https://ejournal.undiksha.ac.id/index.php/JEU/article/view/62084
Shafie, N., Shahdan, T. N. T., & Liew, M. S. (2010). Mastery Learning Assessment Model (MLAM) in teaching and learning mathematics. Procedia - Social and Behavioral Sciences, 8(5), 294–298. https://doi.org/10.1016/j.sbspro.2010.12.040
Silva, H., Lopes, J., Dominguez, C., & Morais, E. (2022). Lecture, cooperative learning and concept mapping: any differences on critical and creative thinking development. International Journal of Instruction, 15(1), 765–780. https://doi.org/10.29333/iji.2022.15144a
Stacey, K., & Turner, R. (2015). The evolution and key concepts of the pisa mathematics frameworks. In Assessing Mathematical Literacy, 5–33. Retrieved from https://link.springer.com/chapter/10.1007/978-3-319-10121-7_1
Stojanović, J., Petkovic, D., Alarifi, I. M., Cao, Y., Denic, N., Ilic, J., … Milickovic, M. (2021). Application of distance learning in mathematics through adaptive neuro-fuzzy learning method. Computers and Electrical Engineering, 93(July 2020). https://doi.org/10.1016/j.compeleceng.2021.107270
Suherman, S., & Vidákovich, T. (2022). Assessment of mathematical creative thinking: A systematic review. Thinking Skills and Creativity, 44(January). https://doi.org/10.1016/j.tsc.2022.101019
Tanjung, D. F., Syahputra, E., & Irvan, I. (2020). Problem based learning, discovery learning, and open ended models: an experiment on mathematical problem solving ability. JTAM | Jurnal Teori Dan Aplikasi Matematika, 4(1), 9. https://doi.org/10.31764/jtam.v4i1.1736
Warmansyah, J., Azizah, F., Yuningsih, R., Sari, M., Nurhasanah, N., Amalina, A., & Utami, W. T. (2023). The use of an open-ended learning approach on the ability to recognize the concept of numbers: its effectiveness for children 4-5 years old. Child Education Journal, 5(2), 110–119. https://doi.org/10.33086/cej.v5i2.4225
Wati, S., Fitriana, L., & Mardiyana. (2018). Students’ difficulties in solving linear equation problems. Journal of Physics: Conference Series, 983(1). https://doi.org/10.1088/1742-6596/983/1/012137
Yunus, J., Zaura, B., & Yuhasriati, Y. (2019). Analysis of students error according to newman in solving mathematics problems of algebra in the form of story in second grade of Smpn 1 Banda Aceh. Jurnal Geuthèë: Penelitian Multidisiplin, 2(2), 308. https://doi.org/10.52626/jg.v2i2.63
Zulkardi, Z., & Kohar, A. W. (2018). Designing PISA-Like mathematics tasks in indonesia: experiences and challenges. Journal of Physics: Conference Series, 947(1). https://doi.org/10.1088/1742-6596/947/1/012015
Refbacks
- There are currently no refbacks.
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.