Analysis of elementary school students mathematical problem-solving abilities based on the IDEAL model stages

Asep Ahyar, Yunus Abidin, Yeni Yuniarti, Ai Sutini, Burieva Kibrio Ergashevna

Abstract

The mathematical problem solving abilities of elementary school students still show variations in achievement at each stage of problem solving. This study aims to map the mathematical problem solving abilities of fourth-grade elementary school students based on the five stages of the IDEAL model (Identify, Define, Explore, Act, Look Back). The study used a quantitative descriptive approach with total sampling of 24 students. The instrument was a contextual problem solving test assessed using an analytical rubric on a scale of 0–4 at each stage. The scores were analyzed through average calculations and conversion of ability categories. The results showed that the Act (2.79) and Explore (2.54) stages were in the capable category, while the Identify (2.46) and Define (2.33) stages were in the sufficient category, and the Look Back (1.92) stage was the weakest aspect. Overall, most students were classified as capable, but weaknesses were still found in the stages of formulating information and verifying solutions. These findings emphasize the importance of strengthening reflective strategies in mathematics learning. This IDEAL stage-based competency mapping can serve as the basis for more systematic problem solving learning planning in elementary schools.

Keywords

elementary school; problem solving; mathematics learning; IDEAL model

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References

Abduh, M. F., Waluya, S. B., & Mariani, S. (2020). Analysis of problem-solving on IDEAL problem-solving learning based on Van Hiele theory assisted by GeoGebra on geometry. Unnes Journal of Mathematics Education Research, 9(2), 170-178. https://journal.unnes.ac.id/sju/ujmer/article/view/33198

Agusfianuddin, A., Herman, T., & Turmudi, T. (2024). Investigation of students' difficulties in mathematical language: problem-solving in mathematical word problems at elementary schools. Jurnal Kependidikan: Jurnal Hasil Penelitian dan Kajian Kepustakaan di Bidang Pendidikan, Pengajaran, dan Pembelajaran, 10(2), 578-590. https://doi.org/10.33394/jk.v10i2.11257

Amalina, I. K., & Vidákovich, T. (2023). Cognitive and socioeconomic factors that influence the mathematical problem-solving skills of students. Heliyon, 9(9). https://doi.org/10.1016/j.heliyon.2023.e19539

Amelia, R. N., Listiaji, P., Dewi, N. R., Heriyanti, A. P., Atmaja, B. D., Shoba, T. M., & Sajidi, I. (2024). Developing and validating a rubric for measuring skills in designing science experiments for prospective science teachers. Jurnal Inovasi Pendidikan IPA, 10(1), 32-46. https://doi.org/10.21831/jipi.v10i1.65853

Apino, E., Retnawati, H., Purbani, W., & Hidayati, K. (2024). The statistical literacy of mathematics education students: An investigation on understanding the margin of error. TEM Journal, 13(1), 293. https://doi.org/10.18421/tem131-31

Arianto, F., & Hanif, M. (2024). Evaluating metacognitive strategies and self-regulated learning to predict primary school students' self-efficacy and problem-solving skills in science learning. Journal of Pedagogical Research, 8(3), 301-319. https://doi.org/10.33902/jpr.202428575

Azizah, I., Suryanti, S., & Mariana, N. (2025). Profiling students’ problem-solving skills through the ethno-STEAM approach in elementary school contexts. Journal of Innovation and Research in Primary Education, 4(3), 1297–1306. https://doi.org/10.56916/jirpe.v4i3.1534

Bransford, J. D., & Stein, B. S. (1984). The IDEAL problem solver: A guide for improving thinking, learning, and creativity. New York, NY: W. H. Freeman.

Ceballos, H., van den Bogaart, T., van Ginkel, S., Spandaw, J., & Drijvers, P. (2025). How collaborative problem-solving promotes higher-order thinking skills: A systematic review of design features and processes. Thinking Skills and Creativity, 102001. https://doi.org/10.1016/j.tsc.2025.102001

Dignath, C., & Veenman, M. V. (2021). The role of direct strategy instruction and indirect activation of self-regulated learning—Evidence from classroom observation studies. Educational Psychology Review, 33(2), 489-533. https://doi.org/10.1007/s10648-020-09534-0

Fauziana, F., & Fazilla, S. (2022). The impact of metacognition on elementary school students’ problem-solving skills in science learning. Jurnal Ilmiah Sekolah Dasar, 6(2), 278-286. https://doi.org/10.23887/jisd.v6i2.44889

Hermalindawati, H., & Marlina, M. (2021). Peningkatan minat dan hasil belajar siswa dengan model problem-solving pada pembelajaran matematika di sekolah dasar. Jurnal Basicedu, 5(5), 4361-4368. https://doi.org/10.31004/basicedu.v5i5.1429

Iswara, H. S., Ahmadi, F., & Ary, D. D. (2022). Numeracy literacy skills of elementary school students through ethnomathematics-based problem-solving. Interdisciplinary Social Studies, 2(2), 1604–1616. https://doi.org/10.55324/iss.v2i2.316

Kaitera, S., & Harmoinen, S. (2022). Developing mathematical problem-solving skills in primary school by using visual representations on heuristics. LUMAT: International Journal on Math, Science and Technology Education, 10(2), 111-146. https://doi.org/10.31129/lumat.10.2.1696

Kholid, M. N., & Ahadiyati, A. (2022). Students' metacognition in solving non-routine problems. Al-Jabar: Jurnal Pendidikan Matematika, 13(1), 125-138. https://doi.org/10.24042/ajpm.v13i1.11776

Klotz, E., Ehmke, T., & Leiss, D. (2025). Text comprehension as a mediator in solving mathematical reality-based tasks: the impact of linguistic complexity, cognitive factors, and social background. European Journal of Educational Research, 14(1), 23-39. https://doi.org/10.12973/eu-jer.14.1.23

Kurniasih, E. (2021). Implementasi model IDEAL problem-solving berbantuan media “beko” untuk meningkatkan prestasi belajar materi keliling dan luas lingkaran siswa kelas vi sekolah dasar. Jurnal Riset Pendidikan Dasar (JRPD), 2(1), 53-65. https://doi.org/10.30595/jrpd.v2i1.9540

Lestari, I. D., & Juandi, D. (2023). Students’ mathematical problem-solving ability reviewed from adversity quotient: systematic literature review. Journal of Mathematics and Mathematics Education, 13(1), 56-75. https://doi.org/10.20961/jmme.v13i1.73997

Lu, D., & Xie, Y. N. (2024). The application of educational technology to develop problem-solving skills: A systematic review. Thinking Skills and Creativity, 51, 101454. https://doi.org/10.1016/j.tsc.2023.101454

Mufliva, R., Turmudi, T., Herman, T., Iriawan, S. B., & Fitriani, A. D. (2024). Problem-solving skills and productive struggle of students in solving mathematical problems in elementary school. Southeast Asian Mathematics Education Journal, 14(1), 69-82. https://doi.org/10.46517/seamej.v14i1.376

Munawaroh, Q., Wulandari, M. D., & Astuti, H. T. M. (2024). Improving elementary school students' mathematics problem-solving skills through problem-based learning (PBL) based on Higher Order Thinking Skills (HOTS). JENIUS (Journal of Education Policy and Elementary Education Issues), 5(1), 1-11. https://doi.org/10.22515/jenius.v5i1.8912

Nabihah, M., Arrahim, & Budianti, Y. (2025). Analysis of mathematics problem-solving skills through problem-solving model in elementary school students. Attadib:Journal Of Elementary Education, 9(1), 1–16. https://doi.org/10.32832/at-tadib.v9i1.19884

Noor, N. L., Waluya, S. B., & Widodo, S. A. (2025). Self-regulated learning for solving mathematical problems: a systematic literature review . Jurnal Riset Pendidikan Matematika, 12(2), 235–245. https://doi.org/10.21831/jrpm.v12i2.89026

Nugraheni, L. P., & Marsigit, M. (2021). Realistic mathematics education: An approach to improve problem-solving ability in primary school. Journal of Education and Learning (EduLearn), 15(4), 511-518. https://doi.org/10.11591/edulearn.v15i4.19354

Panadero, E., Jonsson, A., Pinedo, L., & Fernández-Castilla, B. (2023). Effects of rubrics on academic performance, self-regulated learning, and self-efficacy: A meta-analytic review. Educational Psychology Review, 35(4), 113. https://doi.org/10.1007/s10648-023-09823-4

Paz-Baruch, N., Grovas, G., & Mevarech, Z. R. (2025). The effects of meta-creative pedagogy on elementary school students’ creative thinking. Metacognition and Learning, 20(1), 9. https://doi.org/10.1007/s11409-025-09412-6

Pertiwi, C. M., & Rohaendi, N. (2022). Kemampuan pemecahan masalah matematik dan productive disposition siswa SD (upaya peningkatan menggunakan pendekatan problem-solving berbantuan microsoft mathematics). COLLASE (Creative of Learning Students Elementary Education), 5(1), 199-206. https://doi.org/10.22460/collase.v5i1.10100

Raganit, A. A. (2021). A comparative analysis of Mean Percentage Scores (MPS) of senior high school classes. International Journal of Multidisciplinary: Applied Business and Education Research, 2(7), 587-590. https://doi.org/10.11594/ijmaber.02.07.06

Říčan, J., Chytrý, V., & Medová, J. (2022). Aspects of self-regulated learning and their influence on the mathematics achievement of fifth graders in the context of four different proclaimed curricula. Frontiers in Psychology, 13, 963151. https://doi.org/10.3389/fpsyg.2022.963151

Riyadi, R., Syarifah, T. J., & Nikmaturrohmah, P. (2021). Profile of students’ problem-solving skills viewed from Polya's four-steps approach and elementary school students. European Journal of Educational Research, 10(4), 1625-1638. https://doi.org/10.12973/eu-jer.10.4.1625

Rosyada, M. I., & Wibowo, S. E. (2023). Analysis of mathematics problem-solving ability based on ideal problem-solving steps given student learning styles. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 12(1), 1332. https://doi.org/10.24127/ajpm.v12i1.6880

Setiyani, S., Fitriyani, N., & Sagita, L. (2020). Improving student's mathematical problem-solving skills through Quizizz. Journal of Research and Advances in Mathematics Education, 5(3), 276-288.

Siedlecki, S. L. (2020). Understanding descriptive research designs and methods. Clinical Nurse Specialist, 34(1), 8-12. https://doi.org/10.1097/nur.0000000000000493

Slater, P., & Hasson, F. (2025). Quantitative research designs, hierarchy of evidence and validity. Journal of Psychiatric and Mental Health Nursing, 32(3), 656-660. https://doi.org/10.1111/jpm.13135

Susanna, T., Lasse, E., Henrik, N. J., & Sari, H. N. (2026). From problem-solving to reflection: activating diverse metacognitive skills in mathematics: T. Susanna et al. International Journal of Science and Mathematics Education, 24(2), 10. https://doi.org/10.1007/s10763-025-10643-x

Toikka, S., Eronen, L., Atjonen, P., & Havu-Nuutinen, S. (2024). Combined conceptualisations of metacognitive knowledge to understand students’ mathematical problem-solving. Cogent Education, 11(1), 2357901. https://doi.org/10.1080/2331186x.2024.2357901

Torregrosa, A., & Albarracín, L. (2025). Characterizing metacognitive processes and mathematical skills during problem-solving by using a non-linear orientation base as a self-regulation tool. Educational Studies in Mathematics, 1-32. https://doi.org/10.1007/s10649-025-10451-8

Utami, D. S. P., & Setiyawati, E. (2022). Students' mathematical problem-solving ability in elementary school. Academia Open, 7, 10-21070. https://doi.org/10.21070/acopen.7.2022.4064

van Loon, M. H., Bayard, N. S., Steiner, M., & Roebers, C. M. (2021). Connecting teachers’ classroom instructions with children’s metacognition and learning in elementary school. Metacognition and Learning, 16(3), 623-650. https://doi.org/10.1007/s11409-020-09248-2

van Loon, M., & Roebers, C. M. (2024). Development of metacognitive monitoring and control skills in elementary school: a latent profile approach. Metacognition and Learning, 19(3), 1065-1089. https://doi.org/10.1007/s11409-024-09400-2

Vo, K., Sarkar, M., White, P. J., & Yuriev, E. (2024). Development of problem-solving skills supported by metacognitive scaffolding: insights from students’ written work. Chemistry Education Research and Practice, 25(4), 1197-1209. https://doi.org/10.1039/d3rp00284e

Wahyuni, R., Armanto, D., & Surya, E. (2025). Students’ mathematical problem-solving skills in solving math problems at the elementary school level. European Alliance for Innovation, https://doi.org/10.4108/eai.28-11-2024.2355419

Xie, Y., Zeng, F., & Yang, Y. (2024). A meta-analysis of the relationship between metacognition and academic achievement in mathematics: From preschool to university. Acta Psychologica, 249, 104486. https://doi.org/10.1016/j.actpsy.2024.104486

Yanti, S., Tjalla, A., Sutisna, A., & Ramdhan, T. W. (2026). Constructing an instrument to measure and evaluate problem-solving skills in elementary school students: A focus on mathematical word problem-solving. Kasetsart Journal of Social Sciences, 47(1), 470113-470113. https://doi.org/10.34044/j.kjss.2026.47.1.13

DOI: https://doi.org/10.20961/jdc.v10i1.116187

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