Mathematical Reasoning and Mathematical Problem-Solving Skills of Elementary School Students: A Correlational Study

Hesty Tri Wardani Putri; Octarina Hidayatus Sholikhah; Upik Wahyuni Nawang Putri; Nico Irawan

doi:10.37630/bijee.v4i2.5046

Authors

Hesty Tri Wardani Putri Universitas PGRI Madiun
Octarina Hidayatus Sholikhah Universitas PGRI Madiun
Upik Wahyuni Nawang Putri SDN 02 Kanigoro
Nico Irawan Stamford International University, Thailand

DOI:

https://doi.org/10.37630/bijee.v4i2.5046

Keywords:

mathematical reasoning, problem-solving, Elementary School

Abstract

This study aims to analyze the relationship between mathematical reasoning and mathematical problem-solving skills among elementary school students. Mathematical reasoning is an essential competency in mathematics education, playing a key role in helping students understand concepts, construct logical arguments, and determine systematic problem-solving strategies. The study employed a quantitative approach with a correlational design. The participants consisted of 59 fifth-grade students from SDN Kanigoro in Kartoharjo District, Madiun City, East Java, Indonesia, selected through purposive sampling. Data were collected using mathematical reasoning and mathematical problem-solving tests with established validity and reliability (content validity index = 0.92; Cronbach's alpha = 0.88 and 0.91). Data were analyzed using Pearson correlation and simple linear regression. The results revealed a very strong positive relationship between mathematical reasoning and mathematical problem-solving skills, with r = 0.874 and p < 0.001. Furthermore, the coefficient of determination (R² = 0.763) indicates that mathematical reasoning accounts for 76.3% of the variance in students' mathematical problem-solving scores. These findings suggest that higher mathematical reasoning skills correspond to better performance in solving mathematical problems. The novelty of this study lies in providing empirical evidence from the elementary school context that quantifies the substantial proportion of problem-solving performance explained by mathematical reasoning through a correlational approach. Therefore, fostering mathematical reasoning should be a primary focus in elementary mathematics instruction to enhance students' mathematical problem-solving capabilities.

References

Aguirre, J. M., Turner, E. E., McVicar, E., McDuffie, A. R., Foote, M. Q., & Carll, E. (2024). Mathematizing the world: A routine to advance mathematizing in the elementary classroom. The Journal of Mathematical Behavior, 76, 101196. https://doi.org/10.1016/j.jmathb.2024.101196

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

Amalina, I. K., Vidákovich, T., Akhmetova, A., & Brečka, P. (2026). Integrated STEM-based mathematical problem-solving skills of students: The role of prior mathematical knowledge and text comprehension skills. Thinking Skills and Creativity, 61, 102149. https://doi.org/10.1016/j.tsc.2026.102149

Bahar, A. K., Can, I., & Maker, C. J. (2024). What does it take to be original? An exploration of mathematical problem solving. Thinking Skills and Creativity, 53, 101592. https://doi.org/10.1016/j.tsc.2024.101592

Bicer, A., Aldemir, T., Krall, G., Quiroz, F., Chamberlin, S., Nelson, J. L., Lee, Y., & Kwon, H. (2024). Exploring creativity in mathematics assessment: An analysis of standardized tests. Thinking Skills and Creativity, 54, 101652. https://doi.org/10.1016/j.tsc.2024.101652

Breit, M., Schneider, M., & Preckel, F. (2025). Mathematics achievement and learner characteristics: A systematic review of meta-analyses. Learning and Individual Differences, 118, 102621. https://doi.org/10.1016/j.lindif.2024.102621

Chaiarwut, S., Srikoon, S., Siritaratiwat, A., & Kwangmuang, P. (2025). Enhancing executive mathematics problem-solving through a constructivist digital learning platform: Design, development and evaluation. Social Sciences & Humanities Open, 11, 101338. https://doi.org/10.1016/j.ssaho.2025.101338

Chan, J. Y.-C., Ottmar, E. R., & Lee, J.-E. (2022). Slow down to speed up: Longer pause time before solving problems relates to higher strategy efficiency. Learning and Individual Differences, 93, 102109. https://doi.org/10.1016/j.lindif.2021.102109

Clerjuste, S. N., Guang, C., Miller-Cotto, D., & McNeil, N. M. (2024). Unpacking the challenges and predictors of elementary–middle school students’ use of the distributive property. Journal of Experimental Child Psychology, 244, 105922. https://doi.org/10.1016/j.jecp.2024.105922

De Keersmaeker, K., Onghena, P., Van den Branden, K., & Van Dooren, W. (2025). The pathway to advanced mathematical understanding: The contribution of general and mathematical language and the home environment. Early Childhood Research Quarterly, 73, 191–204. https://doi.org/10.1016/j.ecresq.2025.07.009

Dewey, J. (1933). How we think: A restatement of the relation of reflective thinking to the educative process.

Ding, M., & Cai, J. (2023). Mathematics in STEM education (R. J. Tierney, F. Rizvi, & K. B. T.-I. E. of E. (Fourth E. Ercikan, Eds.; pp. 19–27). Elsevier. https://doi.org/10.1016/B978-0-12-818630-5.13035-0

Doz, E., Taruscia, M., Agnoli, S., Cuder, A., Pellizzoni, S., & Passolunghi, M. C. (2026). Creative potential as a bridge between mathematics and the real-life: The case of word problem-solving in primary school students. Thinking Skills and Creativity, 61, 102161. https://doi.org/10.1016/j.tsc.2026.102161

Facione, P. A. (1992). Critical thinking: What it is and why it counts. Insight Assesment. Measured Reasons, CA: Estados Unidos.

Gun, O., & Bossé, M. J. (2025). Synthesizing cognitive mathematics learning taxonomies. Thinking Skills and Creativity, 57, 101796. https://doi.org/10.1016/j.tsc.2025.101796

Harris, D., Logan, T., & Lowrie, T. (2023). Spatial visualization and measurement of area: A case study in spatialized mathematics instruction. The Journal of Mathematical Behavior, 70, 101038. https://doi.org/10.1016/j.jmathb.2023.101038

Hawthorne, C., Philipp, R. A., Lamb, L. L., Bishop, J. P., Whitacre, I., & Schappelle, B. P. (2022). Reconceptualizing a mathematical domain on the basis of student reasoning: Considering teachers’ perspectives about integers. The Journal of Mathematical Behavior, 65, 100931. https://doi.org/10.1016/j.jmathb.2021.100931

He, S., & Xin, Y. P. (2025). Design knowledge scaffolds to facilitate students’ probabilistic thinking skills for solving classical probability problems: An exploratory study. Thinking Skills and Creativity, 58, 101928. https://doi.org/10.1016/j.tsc.2025.101928

Hu, L., & Wang, H. (2024). Unplugged activities in the elementary school mathematics classroom: The effects on students’ computational thinking and mathematical creativity. Thinking Skills and Creativity, 54, 101653. https://doi.org/10.1016/j.tsc.2024.101653

Ibrahim, M., Herwin, H., Retnawati, H., Firdaus, F. M., & Umar, U. (2024). STEM Learning for Students’ Mathematical Numeracy Ability. European Journal of STEM Education, 9(1), 20.

Im, S., & Jitendra, A. K. (2020). Analysis of proportional reasoning and misconceptions among students with mathematical learning disabilities. The Journal of Mathematical Behavior, 57, 100753. https://doi.org/10.1016/j.jmathb.2019.100753

Johar, R., Harnita, F., Sasaki, D., & Oktari, R. S. (2025). Incorporating disaster context into mathematical problem-solving abilities: The role of cognitive and affective needs. International Journal of Disaster Risk Reduction, 116, 105083. https://doi.org/10.1016/j.ijdrr.2024.105083

Joswick, C., McMillan, B. G., & Conner, K. A. (2025). Opportunities to collectively reason about numbers while building connections to key conceptual ideas in mathematics: Examining the questions used by teachers studying and implementing Number Talks. Teaching and Teacher Education, 155, 104908. https://doi.org/10.1016/j.tate.2024.104908

Kain, C., Koschmieder, C., Matischek-Jauk, M., & Bergner, S. (2024). Mapping the landscape: A scoping review of 21st century skills literature in secondary education. Teaching and Teacher Education, 151, 104739. https://doi.org/10.1016/j.tate.2024.104739

Kalinec-Craig, C., & Rios, A. (2024). An exploratory mixed methods study about teacher candidates’ descriptions of children’s confusion, productive struggle, and mistakes in an elementary mathematics methods course. The Journal of Mathematical Behavior, 73, 101103. https://doi.org/10.1016/j.jmathb.2023.101103

Kavanagh, S. S., Prough, S., Guillotte, A., Wilhelm, A. G., Gibbons, L. K., & Manz, E. (2025). Elementary teachers’ conceptualizations of classroom discussions across content areas: An epistemic network analysis. Teaching and Teacher Education, 165, 105173. https://doi.org/10.1016/j.tate.2025.105173

Knox, J., & Kontorovich, I. (2023). Leveraging interdiscursivity to support elementary students in bridging the empirical-deductive gap: the case of parity. The Journal of Mathematical Behavior, 70, 101052. https://doi.org/10.1016/j.jmathb.2023.101052

Liu, J., & Jacobson, E. (2022). Examining US elementary students’ strategies for comparing fractions after the adoption of the common core state standards for mathematics. The Journal of Mathematical Behavior, 67, 100985. https://doi.org/10.1016/j.jmathb.2022.100985

Liu, J., Sun, D., Sun, J., Wang, J., & Yu, P. L. H. (2025). Designing a generative AI enabled learning environment for mathematics word problem solving in primary schools: Learning performance, attitudes and interaction. Computers and Education: Artificial Intelligence, 9, 100438. https://doi.org/10.1016/j.caeai.2025.100438

Marasabessy, R. (2021). Study of mathematical reasoning ability for mathematics learning in schools: A literature review. Indonesian Journal of Teaching in Science, 1(2), 79–90.

Mata-Pereira, J., & da Ponte, J.-P. (2017). Enhancing students’ mathematical reasoning in the classroom: teacher actions facilitating generalization and justification. Educational Studies in Mathematics, 96(2), 169–186.

Moreno-León, J., Román-González, M., Martín-Barroso, E., Zapata-Cáceres, M., Jiménez, M., & Robles, G. (2025). Enhancing computational thinking skills in early education: exploring the efficacy and feasibility of unplugged methodologies. Thinking Skills and Creativity, 58, 101879. https://doi.org/10.1016/j.tsc.2025.101879

Morgan, P. L., Farkas, G., Oh, Y., & Hillemeier, M. M. (2024). Executive functions, oral vocabularies, and early literacy skills mediate sociodemographic gaps in mathematics and science achievement during elementary school. Learning and Individual Differences, 112, 102447. https://doi.org/10.1016/j.lindif.2024.102447

NCTM, À. (n.d.). National Council of Teachers of Mathematics (2000) Principles and standards for school mathematics. Council of Teachers of Mathematics.

Nufus, H., Muhandaz, R., Hasanuddin, Nurdin, E., Ariawan, R., Fineldi, R. J., Hayati, I. R., & Situmorang, D. D. B. (2024). Analyzing the students’ mathematical creative thinking ability in terms of self-regulated learning: How do we find what we are looking for? Heliyon, 10(3), e24871. https://doi.org/10.1016/j.heliyon.2024.e24871

Organisation for Economic Co-operation and Development. (2023). PISA 2022 results (Volume I): The state of learning and equity in education. OECD Publishing. https://doi.org/10.1787/53f23881-en

Piaget, J. (1972). Development and learning. Reading in Child Behavior and Development, 38–46.

Polya, G. (1945). How to solve it: A new aspect of mathematical method. Princeton university press.

Possamai, J. P., & Allevato, N. S. G. (2024). Teaching mathematics through problem posing: Elements of the task. The Journal of Mathematical Behavior, 73, 101133. https://doi.org/10.1016/j.jmathb.2024.101133

Powell, S. R., Berry, K. A., & Benz, S. A. (2020). Analyzing the word-problem performance and strategies of students experiencing mathematics difficulty. The Journal of Mathematical Behavior, 58, 100759. https://doi.org/10.1016/j.jmathb.2020.100759

Purpura, D. J., Hume, L. E., Sims, D. M., & Lonigan, C. J. (2011). Early literacy and early numeracy: The value of including early literacy skills in the prediction of numeracy development. Journal of Experimental Child Psychology, 110(4), 647–658.

Rittle-Johnson, B., & Siegler, R. S. (2022). The relation between conceptual and procedural knowledge in learning mathematics: A review. The Development of Mathematical Skills, 75–110.

Russo, J., Bobis, J., Downton, A., Hughes, S., Livy, S., McCormick, M., & Sullivan, P. (2020). Elementary teachers’ beliefs on the role of struggle in the mathematics classroom. The Journal of Mathematical Behavior, 58, 100774. https://doi.org/10.1016/j.jmathb.2020.100774

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

Sanders, M., Kwok, M., & Gooden, M. (2025). What makes a math word problem solvable and clear? An analysis of pre-service teachers’ two-step problem posing. The Journal of Mathematical Behavior, 80, 101267. https://doi.org/10.1016/j.jmathb.2025.101267

Sholikhah, O. H., Hadi, S., & Muksar, M. (2026). The effect of numeracy on reflective thinking moderated by leadership and digital information literacy among prospective elementary school teachers. Multidisciplinary Reviews, 9(2).

Stenberg Hartviksen, E., & Haavold, P. Ø. (2025). Differences between experts in mathematical problem solving. Thinking Skills and Creativity, 58, 101875. https://doi.org/10.1016/j.tsc.2025.101875

Sukirwan, Darhim, & Herman, T. (2018). Analysis of students’ mathematical reasoning. Journal of Physics: Conference Series, 948(1), 12036.

Vanhees, C., Nijlunsing, J., Muijs, D., Crato, N., Wils, M., Wiliam, D., Surma, T., & Kirschner, P. A. (2025). The role of knowledge-rich curricula in promoting deep thinking and complex skill acquisition. Learning and Individual Differences, 121, 102729. https://doi.org/10.1016/j.lindif.2025.102729

Vessonen, T., Hellstrand, H., Kurkela, M., Aunio, P., & Laine, A. (2025). The effectiveness of mathematical word problem-solving interventions among elementary schoolers: A systematic review and meta-analysis. International Journal of Educational Research, 132, 102642. https://doi.org/10.1016/j.ijer.2025.102642

Xin, Y. P., Park, J. Y., Tzur, R., & Si, L. (2020). The impact of a conceptual model-based mathematics computer tutor on multiplicative reasoning and problem-solving of students with learning disabilities. The Journal of Mathematical Behavior, 58, 100762. https://doi.org/10.1016/j.jmathb.2020.100762

Zachariades, T., Sakonidis, C., & Zoitsakos, S. (2025). The impact of advanced mathematics in teaching school mathematics through secondary teachers’ reflections on students’ reasoning. The Journal of Mathematical Behavior, 80, 101277. https://doi.org/10.1016/j.jmathb.2025.101277

Zheng, L., & Xiao, Y. (2026). Supervised or autonomous? Exploring the effect of instructional strategies on elementary school students’ mathematics and science achievement. Teaching and Teacher Education, 170, 105315. https://doi.org/10.1016/j.tate.2025.105315

Zhu, X., Tang, Y., Pang, Z., & Zhao, X. (2025). Executive functions and mathematical ability in early elementary school children: The moderating role of family socioeconomic status. Journal of Experimental Child Psychology, 256, 106252. https://doi.org/10.1016/j.jecp.2025.106252