Cognitive barriers in elementary students’ mathematical creative thinking on fraction problems: A hierarchical and multidimensional analysis
DOI:
https://doi.org/10.58524/jasme.v6i2.1372Keywords:
Cognitive Barriers, Differentiated Instruction, Elementary Mathematics Education, Fractions, Mathematical Creative ThinkingAbstract
Background: Mathematical creative thinking is a crucial competency in contemporary mathematics education; however, elementary students often encounter difficulties in developing this ability, particularly in fraction learning. Previous studies have predominantly focused on measuring creative thinking performance, providing limited understanding of the cognitive barriers underlying students’ difficulties across different dimensions of creativity.
Aims: This study aims to identify and describe cognitive barriers in sixth-grade students’ mathematical creative thinking when solving fraction problems across the dimensions of fluency, flexibility, originality, and elaboration.
Method: A descriptive qualitative-dominant mixed-methods design was employed involving 30 sixth-grade students from an elementary school in Bandung, Indonesia. Data were collected through open-ended mathematical creative thinking tasks and semi-structured interviews. Students were categorized into low-, moderate-, and high-ability groups, and the data were analyzed using the Miles, Huberman, and Saldaña qualitative analysis framework.
Results: The findings revealed that cognitive barriers were hierarchical and multidimensional. Low-ability students experienced representational barriers related to fraction concepts, moderate-ability students demonstrated transitional barriers characterized by dependence on visual representations, and high-ability students exhibited metacognitive barriers affecting precision and originality. Among the creative thinking dimensions, elaboration showed the lowest achievement (12.0%), followed by originality (13.1%), while fraction conceptual understanding remained relatively weak (28.0%).
Conclusion: Mathematical creative thinking difficulties develop hierarchically across ability levels and are strongly interconnected across dimensions. The proposed hierarchical-multidimensional framework offers a foundation for diagnosis-based differentiated instruction in elementary mathematics learning.
References
Álvarez-Huerta, P., Muela, A., & Larrea, I. (2022). Disposition toward critical thinking and creative confidence beliefs in higher education students: The mediating role of openness to diversity and challenge. Thinking Skills and Creativity, 43, 101003. https://doi.org/10.1016/j.tsc.2022.101003
Barbieri, C. A., Rodrigues, J., Dyson, N., & Jordan, N. C. (2020). Improving fraction understanding in sixth graders with mathematics difficulties: Effects of a number line approach combined with cognitive learning strategies. Journal of Educational Psychology, 112(3), 628–648. https://doi.org/10.1037/edu0000384
Barnes, A. (2021). Enjoyment in learning mathematics: Its role as a potential barrier to children's perseverance in mathematical reasoning. Educational Studies in Mathematics, 106(1), 45–63. https://doi.org/10.1007/s10649-020-09992-x
Beaty, R. E., & Johnson, D. R. (2021). Automating creativity assessment with SemDis: An open platform for computing semantic distance. Behavior Research Methods, 53(2), 757–780. https://doi.org/10.3758/s13428-020-01453-w
Bicer, A., Chamberlin, S., & Perihan, C. (2021). A meta-analysis of the relationship between mathematics achievement and creativity. The Journal of Creative Behavior, 55(3), 569–590. https://doi.org/10.1002/jocb.474
Bicer, A., Lee, Y., Perihan, C., Capraro, M. M., & Capraro, R. M. (2020). Considering mathematical creative self-efficacy with problem posing as a measure of mathematical creativity. Educational Studies in Mathematics, 105(3), 457–485. https://doi.org/10.1007/s10649-020-09995-8
Dyson, N. I., Jordan, N. C., Rodrigues, J., Barbieri, C., & Rinne, L. (2020). A fraction sense intervention for sixth graders with or at risk for mathematics difficulties. Remedial and Special Education, 41(4), 244–254. https://doi.org/10.1177/0741932518807139
Flores, M. M., Hinton, V. M., & Schweck, K. B. (2024). Using CRA-I to teach fraction and decimal concepts to students with learning disabilities. Learning Disability Quarterly, 47(1), 44–58. https://doi.org/10.1177/07319487231176545
Forthmann, B., Szardenings, C., & Holling, H. (2020). Understanding the confounding effect of fluency in divergent thinking scores: Revisiting average scores to quantify artifactual correlation. Psychology of Aesthetics, Creativity, and the Arts, 14(1), 94–112. https://doi.org/10.1037/aca0000196
Fyfe, E. R., Byers, C., & Nelson, L. J. (2022). The benefits of a metacognitive lesson on children's understanding of mathematical equivalence, arithmetic, and place value. Journal of Educational Psychology, 114(6), 1292–1306. https://doi.org/10.1037/edu0000715
Geary, D. C., & Xu, K. M. (2022). Evolution of self-awareness and the cultural emergence of academic and non-academic self-concepts. Educational Psychology Review, 34(4), 2323–2349. https://doi.org/10.1007/s10648-022-09669-2
Ibrahim, I., Khalil, I. A., & Prahmana, R. C. I. (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
Jarrah, A. M., Wardat, Y., & Gningue, S. (2022). Misconception on addition and subtraction of fractions in seventh-grade middle school students. Eurasia Journal of Mathematics, Science and Technology Education, 18(6), Article em2115. https://doi.org/10.29333/ejmste/12070
Jiang, C., Wang, Y., Wang, S., Zou, Y., Ouyang, J., Jia, D., & Zhou, Y. (2023). Rational design of compact ceramic coating on SiCp/Al composites by tailoring soft sparking discharge of plasma electrolytic oxidation. Surface and Coatings Technology, 466, 129578.
Khalid, M., Saad, S., Hamid, S. R. A., Abdullah, M. R., Ibrahim, H., & Shahrill, M. (2020). Enhancing creativity and problem solving skills through creative problem solving in teaching mathematics. Creativity Studies, 13(2), 270–291. https://doi.org/10.3846/cs.2020.11027
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
Lassig, C. (2020). A typology of student creativity: Creative personal expression, boundary pushing and task achievement. Thinking Skills and Creativity, 36, 100654. https://doi.org/10.1016/j.tsc.2020.100654
Lenz, K., Dreher, A., Holzäpfel, L., & Wittmann, G. (2020). Are conceptual knowledge and procedural knowledge empirically separable? The case of fractions. British Journal of Educational Psychology, 90(3), 809–829. https://doi.org/10.1111/bjep.12333
Murniasih, T. R., Sa'dijah, C., Muksar, M., & Susiswo. (2020). Fraction sense: An analysis of preservice mathematics teachers' cognitive obstacles. Center for Educational Policy Studies Journal, 10(2), 27–47. https://doi.org/10.26529/cepsj.742
Pedersen, P. L., & Bjerre, M. (2021). Two conceptions of fraction equivalence. Educational Studies in Mathematics, 107(1), 135–157. https://doi.org/10.1007/s10649-021-10030-7
Polydoros, G., Artikis, C., & Voudouri, A. (2025). Optimizing fraction learning for elementary students with learning difficulties in mathematics: EdTech-based educational settings. International Journal of Educational Reform. Advance online publication. https://doi.org/10.1177/10567879251355557
Rajadurai, R., & Ganapathy, H. (2023). Effect of use of metacognitive instructional strategies in promoting mathematical problem solving competence amongst undergraduate students in facing competitive examination. Cogent Social Sciences, 9(1), 2173103. https://doi.org/10.1080/23311886.2023.2173103
Rawlings, B. S., Chetwynd-Talbot, D., Husband, E., Nuttall, A., Quinn, E., Taggart, R., & Roome, H. E. (2025). Divergent thinking is linked with convergent thinking: Implications for models of creativity. Thinking & Reasoning, 31(4), 586–608. https://doi.org/10.1080/13546783.2025.2485059
Sadak, M., Incikabi, L., Ulusoy, F., & Pektas, M. (2022). Investigating mathematical creativity through the connection between creative abilities in problem posing and problem solving. Thinking Skills and Creativity, 45, 101108. https://doi.org/10.1016/j.tsc.2022.101108
Sari, A. D., Suryadi, D., & Dasari, D. (2024). Learning obstacle of probability learning based on the probabilistic thinking level. Journal on Mathematics Education, 15(1), 207–226. https://doi.org/10.22342/jme.v15i1.pp207-226
Schadl, C., & Ufer, S. (2023). Beyond linearity: Using IRT-scaled level models to describe the relation between prior proportional reasoning skills and fraction learning outcomes. Child Development, 94(6), 1642–1658. https://doi.org/10.1111/cdev.13954
Schoevers, E. M., Kroesbergen, E. H., & Kattou, M. (2020). Mathematical creativity: A combination of domain-general creative and domain-specific mathematical skills. The Journal of Creative Behavior, 54(2), 242–252. https://doi.org/10.1002/jocb.361
Shaw, S. T., Luna, M. L., Rodriguez, B., Yeh, J., Villalta, N., & Ramirez, G. (2022). Mathematical creativity in elementary school children: General patterns and effects of an incubation break. Frontiers in Education, 7. https://doi.org/10.3389/feduc.2022.835911
Star, J. R., Tuomela, D., Joglar-Prieto, N., Hästö, P., Palkki, R., Abánades, M. Á., Pejlare, J., Jiang, R. H., Li, L., & Liu, R.-D. (2022). Exploring students' procedural flexibility in three countries. International Journal of STEM Education, 9(1), 4. https://doi.org/10.1186/s40594-021-00322-y
Suherman, S., & Vidákovich, T. (2022). Assessment of mathematical creative thinking: A systematic review. Thinking Skills and Creativity, 44, 101019. https://doi.org/10.1016/j.tsc.2022.101019
Sweller, J., van Merriënboer, J. J. G., & Paas, F. (2019). Cognitive architecture and instructional design: 20 years later. Educational Psychology Review, 31(2), 261–292. https://doi.org/10.1007/s10648-019-09465-5
Thompson, P. W., & Harel, G. (2021). Ideas foundational to calculus learning and their links to students' difficulties. ZDM–Mathematics Education, 53(3), 507–519. https://doi.org/10.1007/s11858-021-01270-1
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
Wang, T., Zhang, L., Xie, Z., & Liu, J. (2023). How does mathematical modeling competency affect the creativity of middle school students? The roles of curiosity and guided inquiry teaching. Frontiers in Psychology, 13. https://doi.org/10.3389/fpsyg.2022.1044580
Weiss, S., & Wilhelm, O. (2022). Is flexibility more than fluency and originality? Journal of Intelligence, 10(4). https://doi.org/10.3390/jintelligence10040096
Winata, W., Widiyasari, R., Pramuditya, S. A., Anwar, H., & Ramadhanty, K. P. (2025). Difficulties in learning mathematics: Qualitative studies using NVivo 15. Educational Process: International Journal. https://doi.org/10.22521/edupij.2025.17.397
Yayuk, E., Purwanto, P., As'ari, A. R., & Subanji, S. (2020). Primary school students' creative thinking skills in mathematics problem solving. European Journal of Educational Research, 9(3), 1281–1295. https://doi.org/10.12973/eu-jer.9.3.1281
Zabelina, D. L., Zaonegina, E., Revelle, W., & Condon, D. M. (2022). Creative achievement and individual differences: Associations across and within the domains of creativity. Psychology of Aesthetics, Creativity, and the Arts, 16(4), 618–636. https://doi.org/10.1037/aca0000439
Zhang, Z. S., Hoxha, L., Aljughaiman, A., Arënliu, A., Gomez-Arizaga, M. P., Gucyeter, S., Ponomareva, I., Shi, J., Irueste, P., Rogl, S., Nunez, M., & Ziegler, A. (2021). Social environmental factors and personal motivational factors associated with creative achievement: A cross-cultural perspective. The Journal of Creative Behavior, 55(2), 410–432. https://doi.org/10.1002/jocb.463
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