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Abstract
Mathematics learning is widely recognized as a fundamental component of school curricula, as it equips students with essential competencies, particularly mathematical reasoning, which underpins logical analysis, problem solving, and decision making. The importance of cultivating reasoning skills is especially pronounced in the current era of disruption, characterized by rapid advances in information and communication technology and the automation of human labor by machines and autonomous systems. As physical tasks are increasingly performed by technology, human capacities such as reasoning and emotional intelligence become critical. Mathematical reasoning provides the foundation for understanding concepts, formulating logical arguments, and generating solutions across domains such as the natural sciences, society, and engineering, while also enabling students to approach problems critically and systematically. However, despite its significance, research in primary education has often emphasized procedural knowledge rather than examining how students construct and apply reasoning when confronted with mathematical challenges, leaving a gap in understanding how reasoning develops in authentic classroom contexts. To address this issue, the present study investigates how Grade 4 and Grade 5 students in a primary school in Banjarmasin, Indonesia, employ mathematical reasoning strategies to solve non-routine problems. Through a classroom-based experimental approach, we analyzed students’ solution pathways and the reasoning patterns they demonstrated in navigating mathematical tasks. The findings offer insights into the developmental characteristics of mathematical reasoning in upper primary school and contribute to broader discussions on fostering reasoning skills effectively, with implications for designing mathematics instruction that prepares students to meet the cognitive demands of an era increasingly shaped by automation and technological disruption.
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References
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- Baroody, A. J., & Coslick, R. T. (1998). Fostering children's mathematical power: An investigative approach to K-8 mathematics instruction. Routledge. https://doi.org/10.4324/9781410602084
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- Callingham, R., & Siemon, D. (2021). Connecting multiplicative thinking and mathematical reasoning in the middle years. The Journal of Mathematical Behavior, 61, 100837. https://doi.org/10.1016/j.jmathb.2020.100837
- Carayannis, E. G., Christodoulou, K., Christodoulou, P., Chatzichristofis, S. A., & Zinonos, Z. (2022). Known unknowns in an era of technological and viral disruptions—Implications for theory, policy, and practice. Journal of the knowledge economy, 13(1), 587-610. https://doi.org/10.1007/s13132-020-00719-0
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- Clements, D. H., Sarama, J., & DiBiase, A. M. (2003). Engaging young children in mathematics: Findings of the 2000 National Conference on Standards for Preschool and Kindergarten Mathematics Education. Lawrence Erlbaum Associates.
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- Herbert, S., & Williams, G. (2023). Eliciting mathematical reasoning during early primary problem solving. Mathematics Education Research Journal, 35(1), 77-103. https://doi.org/10.1007/s13394-021-00376-9
- Hsu, F. H. (2022). Behind Deep Blue: Building the computer that defeated the world chess champion. Princeton University Press.
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- Papandreou, M., & Tsiouli, M. (2022). Noticing and understanding children’s everyday mathematics during play in early childhood classrooms. International Journal of Early Years Education, 30(4), 730-747. https://doi.org/10.1080/09669760.2020.1742673
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- Pramudiani, P. (2023). Professional development for supporting primary school teachers in promoting students’ mathematical reasoning using realistic mathematics education. Dissertation. Indonesia University of Education.
- Ramlan, A. M., Budayasa, I. K., & Rahaju, E. B. (2025). Proportional reasoning in the artisan personality type: A case study of high school students in trigonometry ratios. Journal on Mathematics Education, 16(1), 73–90. https://doi.org/10.22342/jme.v16i1.pp73-90
- Raza, M. (2024). AI in Education: Balancing Benefits and Challenges Through Professional Development of Teachers. Qlantic Journal of Social Sciences, 5(4), 168-174. https://doi.org/10.55737/qjss.v-iv.24071
- Resnick, L. B. (1989). Developing mathematical knowledge. American Psychologist, 44(2), 162–169. https://doi.org/10.1037/0003-066X.44.2.162
- Rianasari, V. F., & Guzon, A. F. H. (2024). Designing learning trajectory to support preservice mathematics teachers’ skills in creating and implementing realistic mathematics tasks. Journal on Mathematics Education, 15(3), 701–716. https://doi.org/10.22342/jme.v15i3.pp701-716
- Russell, S. J. (1999). Mathematical reasoning in the early grades. In L. V. Stiff & F. R. Curcio (Eds.), Developing mathematical reasoning, K–12 (pp. 22 – 36). National Council of Teachers of Mathematics.
- Sari, R. N., Rosjanuardi, R., Isharyadi, R., & Nurhayati, A. (2024). Level of students’ proportional reasoning in solving mathematical problems. Journal on Mathematics Education, 15(4), 1095–1114. https://doi.org/10.22342/jme.v15i4.pp1095-1114
- Siswantari, Sabon, S. S., Listiawati, N., Wirda, Y., Zulkardi, & Riyanto, B. (2025). Bridging mathematics and communication: Implementing realistic mathematics education principles for skill development. Journal on Mathematics Education, 16(2), 729–752. https://doi.org/10.22342/jme.v16i2.pp729-752
- Sousa, D. A. (2015). How the brain learns mathematics (Second Edition). A Sage Publishing Company.
- Sun, J., Zheng, C., Xie, E., Liu, Z., Chu, R., Qiu, J., ... & Li, Z. (2025). A survey of reasoning with foundation models: Concepts, methodologies, and outlook. ACM Computing Surveys, 57(11), 1-43. https://doi.org/10.1145/3729218
- Torres-Peña, R. C., Peña-González, D., Lara-Orozco, J. L., Ariza, E. A., & Vergara, D. (2025). Enhancing numerical thinking through problem solving: A teaching experience for third-grade mathematics. Education Sciences, 15(6), 667. https://doi.org/10.3390/educsci15060667
- Widjaja, W., Vale, C., Herbert, S., Loong, E. Y., & Bragg, L. A. (2021). Linking comparing and contrasting, generalising and justifying: A case study of primary students’ levels of justifying. Mathematics Education Research Journal, 33(2), 321-343. https://doi.org/10.1007/s13394-019-00306-w
- Xu, J., & Cai, D. (2024). The cognitive foundations of different hierarchical levels of mathematical skills in primary school children: extending the mathematics pathways model. European Journal of Psychology of Education, 39(4), 3919-3941. https://doi.org/10.1007/s10212-024-00823-8
References
Alexander, P. A., White, C. S., & Daugherty, M. (1997). Children’s use of analogical reasoning in early mathematics learning. In L. English (Ed.), Mathematical reasoning: Analogies, metaphors, and images (pp. 117 – 147). Mahwah, NJ: Lawrence Erlbaum Associates.
Aljura, A. N., Retnawati, H., Dewanti, S. R., Kassymova, G. K., Sotlikova, R., & Septiana, A. R. (2025). Mathematical reasoning and communication word problems with mathematical problem-solving orientation: A relation between the skills. Journal on Mathematics Education, 16(2), 529–558. https://doi.org/10.22342/jme.v16i2.pp529-558
Baroody, A. J., & Coslick, R. T. (1998). Fostering children's mathematical power: An investigative approach to K-8 mathematics instruction. Routledge. https://doi.org/10.4324/9781410602084
Bragg, L. A., Loong, E. Y. K., Widjaja, W., Vale, C., & Herbert, S. (2015). Promoting reasoning through the magic V task. Australian Primary Mathematics Classroom, 20(2), 10-14. https://search.informit.org/doi/abs/10.3316/INFORMIT.330329444881101
Callingham, R., & Siemon, D. (2021). Connecting multiplicative thinking and mathematical reasoning in the middle years. The Journal of Mathematical Behavior, 61, 100837. https://doi.org/10.1016/j.jmathb.2020.100837
Carayannis, E. G., Christodoulou, K., Christodoulou, P., Chatzichristofis, S. A., & Zinonos, Z. (2022). Known unknowns in an era of technological and viral disruptions—Implications for theory, policy, and practice. Journal of the knowledge economy, 13(1), 587-610. https://doi.org/10.1007/s13132-020-00719-0
Chiu, S., & Tron, M. O. (2004). Classroom discourse and the development of mathematical and analogical reasoning. In L. English (Ed.), Mathematical and analogical reasoning of young learners. Lawrence Erlbaum Associates.
Clements, D. H., Sarama, J., & DiBiase, A. M. (2003). Engaging young children in mathematics: Findings of the 2000 National Conference on Standards for Preschool and Kindergarten Mathematics Education. Lawrence Erlbaum Associates.
Ernie, K., LeDocq, R., Serros, S., & Tong, S. (2023). Mathematical reasoning: Challenging students' beliefs about mathematics. In R. A. R. Gurung, N. L. Chick, and A. Haynie (eds.), Exploring Signature Pedagogies (pp. 260-279). Routledge. https://doi.org/10.4324/9781003444732
Fonseca, L. (2018). Mathematical reasoning and proof schemes in the early years. Journal of the European Teacher Education Network, 13, 34-44. https://drive.google.com/file/d/1zc18YZ7V1mNSzEbrEMN036fCSd5lyJys/view
García-García, J., & Dolores-Flores, C. (2021). Exploring pre-university students’ mathematical connections when solving Calculus application problems. International Journal of Mathematical Education in Science and Technology, 52(6), 912-936.
Ginsburg, H. P., Pappas, S., & Seo, K.-H. (2001). Everyday mathematical knowledge: Asking young children what is developmentally appropriate. In S. L. Golbeck (Ed.), Psychological perspectives on early childhood education: Reframing dilemmas in research and practice (pp. 181–219). Lawrence Erlbaum Associates Publishers.
Hacıeminoğlu, E., Yıldız, N. G., & Şeker, R. (2022). Factors related to cognitive reasoning of pre-service teachers’ science process skills: Role of experiments at home on meaningful learning. Sustainability, 14(13), 7703. https://doi.org/10.3390/su14137703
Herbert, S., & Williams, G. (2023). Eliciting mathematical reasoning during early primary problem solving. Mathematics Education Research Journal, 35(1), 77-103. https://doi.org/10.1007/s13394-021-00376-9
Hsu, F. H. (2022). Behind Deep Blue: Building the computer that defeated the world chess champion. Princeton University Press.
Hwang, J., & Ham, Y. (2021). Relationship between mathematical literacy and opportunity to learn with different types of mathematical tasks. Journal on Mathematics Education, 12(2), 199-222. http://doi.org/10.22342/jme.12.2.13625.199-222
Junaid, M. (2022). Mathematical intelligence: A story of human superiority over machines. Simon and Schuster.
Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. National Academy Press.
Lee, S., Lee, M., & Lee, S. (2023). What if artificial intelligence become completely ambient in our daily lives? Exploring future human-AI interaction through high fidelity illustrations. International Journal of Human–Computer Interaction, 39(7), 1371-1389. https://doi.org/10.1080/10447318.2022.2080155
Mukuka, A., Balimuttajjo, S., & Mutarutinya, V. (2023). Teacher efforts towards the development of students’ mathematical reasoning skills. Heliyon, 9(4), e14789. http://dx.doi.org/10.1016/j.heliyon.2023.e14789
NCTM (2000). Principles and standards for school mathematics. NCTM.
Panaoura, R., & Nitsiou, C. (2023). Children’s informal learning in mathematics through parental involvement with play-based activities: A nonformal training program. Education Sciences, 13(9), 870. https://doi.org/10.3390/educsci13090870
Papandreou, M., & Tsiouli, M. (2022). Noticing and understanding children’s everyday mathematics during play in early childhood classrooms. International Journal of Early Years Education, 30(4), 730-747. https://doi.org/10.1080/09669760.2020.1742673
Prabhu, M., & Premraj, J. A. (2025). Artificial consciousness in AI: A posthuman fallacy. AI & Society, 40(4), 2995-3008. https://doi.org/10.1007/s00146-024-02061-4
Pramudiani, P. (2023). Professional development for supporting primary school teachers in promoting students’ mathematical reasoning using realistic mathematics education. Dissertation. Indonesia University of Education.
Ramlan, A. M., Budayasa, I. K., & Rahaju, E. B. (2025). Proportional reasoning in the artisan personality type: A case study of high school students in trigonometry ratios. Journal on Mathematics Education, 16(1), 73–90. https://doi.org/10.22342/jme.v16i1.pp73-90
Raza, M. (2024). AI in Education: Balancing Benefits and Challenges Through Professional Development of Teachers. Qlantic Journal of Social Sciences, 5(4), 168-174. https://doi.org/10.55737/qjss.v-iv.24071
Resnick, L. B. (1989). Developing mathematical knowledge. American Psychologist, 44(2), 162–169. https://doi.org/10.1037/0003-066X.44.2.162
Rianasari, V. F., & Guzon, A. F. H. (2024). Designing learning trajectory to support preservice mathematics teachers’ skills in creating and implementing realistic mathematics tasks. Journal on Mathematics Education, 15(3), 701–716. https://doi.org/10.22342/jme.v15i3.pp701-716
Russell, S. J. (1999). Mathematical reasoning in the early grades. In L. V. Stiff & F. R. Curcio (Eds.), Developing mathematical reasoning, K–12 (pp. 22 – 36). National Council of Teachers of Mathematics.
Sari, R. N., Rosjanuardi, R., Isharyadi, R., & Nurhayati, A. (2024). Level of students’ proportional reasoning in solving mathematical problems. Journal on Mathematics Education, 15(4), 1095–1114. https://doi.org/10.22342/jme.v15i4.pp1095-1114
Siswantari, Sabon, S. S., Listiawati, N., Wirda, Y., Zulkardi, & Riyanto, B. (2025). Bridging mathematics and communication: Implementing realistic mathematics education principles for skill development. Journal on Mathematics Education, 16(2), 729–752. https://doi.org/10.22342/jme.v16i2.pp729-752
Sousa, D. A. (2015). How the brain learns mathematics (Second Edition). A Sage Publishing Company.
Sun, J., Zheng, C., Xie, E., Liu, Z., Chu, R., Qiu, J., ... & Li, Z. (2025). A survey of reasoning with foundation models: Concepts, methodologies, and outlook. ACM Computing Surveys, 57(11), 1-43. https://doi.org/10.1145/3729218
Torres-Peña, R. C., Peña-González, D., Lara-Orozco, J. L., Ariza, E. A., & Vergara, D. (2025). Enhancing numerical thinking through problem solving: A teaching experience for third-grade mathematics. Education Sciences, 15(6), 667. https://doi.org/10.3390/educsci15060667
Widjaja, W., Vale, C., Herbert, S., Loong, E. Y., & Bragg, L. A. (2021). Linking comparing and contrasting, generalising and justifying: A case study of primary students’ levels of justifying. Mathematics Education Research Journal, 33(2), 321-343. https://doi.org/10.1007/s13394-019-00306-w
Xu, J., & Cai, D. (2024). The cognitive foundations of different hierarchical levels of mathematical skills in primary school children: extending the mathematics pathways model. European Journal of Psychology of Education, 39(4), 3919-3941. https://doi.org/10.1007/s10212-024-00823-8
