Exploring the impact of discovery learning and self-efficacy on students’ mathematical reasoning skills

Authors

  • Sylvia Rabbani IKIP Siliwangi, Cimahi, Indonesia Author
  • Ryan Dwi Puspita IKIP Siliwangi, Cimahi, Indonesia Author

DOI:

https://doi.org/10.33578/jpfkip.v14i5.p722-737

Keywords:

Discovery Learning, Mathematical Reasoning, Self-Efficacy,, Elementary Education

Abstract

The research aims to test the effect of discovery learning on mathematical reasoning and analyse the differences in impact based on elementary school students' self-efficacy level. This study uses a quantitative approach with a quasi-experimental pre-test-post-test control group type design. The research sample consisted of 120 elementary school students randomly divided into experimental and control groups. The experimental group was given treatment for eight meetings using the Discovery Learning model, while the control group followed normal learning. The instruments used included a mathematical reasoning test and a self-efficacy questionnaire. Data analysis was carried out using paired sample t-test and independent sample t-test to determine the effect of the learning model, as well as one-way ANOVA to analyse differences in influence based on the level of self-efficacy. The results showed that the Discovery Learning model significantly improved students' mathematical reasoning skills with a value of <0.001. In addition, there was a significant difference in the acquisition of mathematical reasoning skills based on students' self-efficacy level. These findings indicate the importance of considering academic self-confidence factors in designing effective mathematics learning in elementary schools

References

Alfieri, L., Brooks, P. J., Aldrich, N. J., & Tenenbaum, H. R. (2011). Does discovery-based instruction enhance learning? A meta-analysis. Review of Educational Research, 81(4), 1–36. https://doi.org/10.3102/0034654311404432

Alim, J. A., Asih, S. R., & Putra, Z. H. (2024). The effectiveness of realistic mathematics education to enhance elementary students' learning outcomes and motivation. Primary: Jurnal Pendidikan Guru Sekolah Dasar, 13(6), 242-251. http://dx.doi.org/10.33578/jpfkip-v13i6.p242-251

Almazroui, A. (2023). Fostering twenty-first century skills among primary school students through math project-based learning. Humanities and Social Sciences Communications, 10(1), 1–13. https://doi.org/10.1057/s41599-023-01914-5

Bandura, A. (1997). Self-efficacy: The exercise of control. New York: W. H. Freeman.

Bandura, A. (2023). Self-efficacy: The exercise of control in learning mathematics. Educational Psychologist, 58(1), 1–18. https://doi.org/10.1080/00461520.2023.2134856

Bruner, J. S. (1961). The act of discovery. Harvard Educational Review, 31(1), 21–32.

Capone, R. (2022). Discovery Learning in mathematics education: A path to autonomous thinking and higher-order skills. Education Sciences, 12(8), 529. https://doi.org/10.3390/educsci12080529

Creswell, J. W., & Plano Clark, V. L. (2018). Designing and Conducting Mixed Methods Research (3rd ed.). Sage Publications.

Firmansyah, D., Maulida, U., & Marlina, L. (2023). Electronic Modul Contextual Learning In Mathematics: Analizing Its Impact On Student Self-Efficacy And Problem Solving Abilities. Jurnal Ilmiah Ilmu Terapan, 7(2), 130–139. https://doi.org/10.22437/jiit.v7i2.42554

Fraenkel, J. R., Wallen, N. E., & Hyun, H. H. (2012). How to Design and Evaluate Research in Education (8th ed.). McGraw-Hill.

Glaser, B. G., & Strauss, A. L. (1967). The discovery of grounded theory: Strategies for qualitative research. Chicago: Aldine Publishing.

Goldin, G. A. (2002). Representation in mathematical learning and problem solving. In L. D. English (Ed.), Handbook of international research in mathematics education (pp. 197–218). Lawrence Erlbaum Associates.

Herianto, H., Suryadi, D., & Suryadi, S. (2024). Quantifying the relationship between self-efficacy and mathematical creativity: A meta-analysis. Education Sciences, 14(11), 1251.

https://doi.org/10.3390/educsci14111251

Hiebert, J., & Carpenter, T. P. (1992). Learning and teaching with understanding. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 65–97). New York: Macmillan.

Ismail, M. A., Mohammad, J., & Jusoh, R. (2021). The effectiveness of discovery learning in enhancing mathematical reasoning and representation. Journal of Mathematics Education, 12(3), 45–58. https://doi.org/10.29210/02021106

Ismail, M., Hidayat, W., & Ayu, R. P. (2021). The Effect of Discovery Learning on Mathematical Representation and Reasoning Ability. Journal of Physics: Conference Series, 1833, 012007. https://doi.org/10.1088/1742-6596/1833/1/012007

Joolingen, W. R. van. (1999). Cognitive tools for discovery learning. International Journal of Artificial Intelligence in Education, 10, 385–397.Joolingen, W. R. van. (1999). Cognitive tools for discovery learning. International Journal of Intelligence in Education (IJAIED), 10, 385–397.

Karaoglan Yilmaz, F. G. (2022). The role of self-efficacy in problem-solving and learning participation in adaptive e-learning environments. Education and Information Technologies, 27, 891–907.

https://doi.org/10.1007/s10639-021-10654-w

Klassen, R. M., & Usher, E. L. (2010). Self-efficacy in educational settings: Recent research and emerging directions. In T. C. Urdan & S. A. Karabenick (Eds.), The decade ahead: Theoretical perspectives on motivation and achievement (Vol. 16A, pp. 1–33). Bingley, UK: Emerald Group Publishing Limited.

Lee, J., & Stankov, L. (2022). Non cognitive predictors of mathematics achievement: Self efficacy and anxiety. Learning and Individual Differences, 95, 102098.

https://doi.org/10.1016/j.lindif.2022.102098

Lesh, R., Post, T., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 33–40). Lawrence Erlbaum Associates.

Maritim, E., Ngatmini, & Buchori, A. (2025). Implementation of character education through children's story e-books for elementary school students. Primary: Jurnal Pendidikan Guru Sekolah Dasar, 14(1), 103-121. http://dx.doi.org/10.33578/jpfkip-v13i1.p103-121

Masfingatin, T., & Murtafiah, W. (2020). Exploring the creative mathematical reasoning of mathematics education student through discovery learning. AKSIOMA, 9(2), 296–305.

https://doi.org/10.24127/ajpm.v9i2.2953

Merriam, S. B., & Tisdell, E. J. (2016). Qualitative Research: A Guide to Design and Implementation (4th ed.). Jossey-Bass.

National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. NCTM.

Novikasari, I., & Nuryadi, D. (2021). Development of Discovery Learning-Based Worksheets on Geometry Topics for Junior High School Students. Journal of Mathematics Education Research, 10(2), 120–131.

Nugraha, H. A., & Wulansari, R. (2023). Effectiveness of discovery learning model on student self-efficacy and learning outcomes in mathematics. European Journal of Educational Research, 12(3), 987–994. https://files.eric.ed.gov/fulltext/EJ1441244.pdf

Orosz, G., Péter Szarka, S., & Tóth Király, I. (2022). How discovery learning supports mathematical self efficacy: A classroom based intervention study. Journal of Educational Research, 115(3), 234–247. https://doi.org/10.1080/00220671.2022.2056734

Pajares, F., & Graham, L. (1999). Self-efficacy, motivation constructs, and mathematics performance of entering middle school students. Contemporary Educational Psychology, 24(2), 124–139. https://doi.org/10.1006/ceps.1998.0991

Pangestu, Y., Destiniar., & Sari, E.F.P. (2025). The Effect of Picture and Picture Learning Model on Mathematics Learning Outcomes of Plane Shapes of Grade III Students of SDN 138 Palembang. Jurnal PAJAR (Pendidikan dan Pengajaran), 9(4), 574-581. https://doi.org/10.33578/pjr.v9i4.186

Pantziara, M., & Philippou, G. N. (2023). Students’ motivation and self-efficacy in mathematics: Relations with problem-solving and mathematical reasoning. Mathematics, 11(3), 521.

https://doi.org/10.3390/math11030521

Prasetya, A. (2022). The effect of model discovery learning on students’ self-efficacy in mathematics learning. AlphaMath: Journal of Mathematics Education, 8(1), 45–56.

https://doi.org/10.30595/alphamath.v8i1.12176

Putra, F. G., Anggoro, B. S., Widyawati, S., Maysaroh, S. H., & Imama, K. (2024). Enhancing students’ self-efficacy and mathematical analysis skills: Applying the guided discovery learning model supported by YouTube. Journal of Philology and Educational Sciences, 3(1), 23–33.

Rahartiningsih, Y. A. S., Buchori, A., & Sumarno. (2025). Development of minimum competency assessment (AKM) numeracy test instruments containing ethnomathematics in elementary schools. Primary: Jurnal Pendidikan Guru Sekolah Dasar, 14(2), 149-165.

http://dx.doi.org/10.33578/jpfkip-v14i2.p149-165

Rahmadhani, D. (2020). Pengaruh Discovery Learning terhadap kemampuan penalaran matematis siswa. Jurnal Pendidikan Matematika, 14(1), 34–45.

Raufelder, D., Hoferichter, F., & Bukowski, W. M. (2023). Academic self efficacy development and its role in reasoning ability among early adolescents: A longitudinal study. Journal of Early Adolescence, 43(2), 212–229. https://doi.org/10.1177/02724316221126119

Reeve, J., Deci, E. L., & Ryan, R. M. (2022). Self-determination theory applied to educational settings: Development, performance, and engagement. Frontiers in Psychology, 13, 924812. https://doi.org/10.3389/fpsyg.2022.924812

Siregar, N. C., Rosli, R., & Maat, S. M. (2020). The Effects of a Discovery Learning Module on Geometry for Improving Students’ Mathematical Reasoning Skills, Communication and Self-Confidence. International Journal of Learning, Teaching and Educational Research, 19(3), 214–228. https://doi.org/10.26803/ijlter.19.3.12

Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20–26.

Smith III, J. P., & Confrey, J. (1994). Multiplicative structures and the development of students’ understanding of ratio and proportion. Journal for Research in Mathematics Education, 25(2), 98–114. https://doi.org/10.2307/749516

Sofiyati, A. (2022). Penerapan Discovery Learning untuk meningkatkan berpikir kritis siswa dalam pembelajaran matematika. Jurnal Ilmiah Pendidikan Matematika, 7(2), 88–97.

Stylianides, A. J., & Stylianides, G. J. (2021). Mathematical reasoning: What it is and why it matters in school mathematics. In T. Dreyfus et al. (Eds.), Developing Research in Mathematics Education (pp. 189–204). Routledge.

Surya Rahartiningsih, Y. A. S., Buchori, A., & Sumarno. (2025). Development of minimum competency assessment (AKM) numeracy test instruments containing ethnomathematics in elementary schools. Primary: Jurnal Pendidikan Guru Sekolah Dasar, 14(2), 149-165. http://dx.doi.org/10.33578/jpfkip-v14i2.p149-165

Susilowati, D., Saputro, B. A., & Sutono, A. (2025). The effect of strengthening the literacy movement in natural and social sciences (IPAS) learning on improving students' scientific literacy and critical thinking skills. Primary: Jurnal Pendidikan Guru Sekolah Dasar, 14(1), 11-28. http://dx.doi.org/10.33578/jpfkip-v14i1.p11-28

Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12(2), 151–169. https://doi.org/10.1007/BF00305619

Talsma, K., Schüz, B., Schwarzer, R., & Norris, K. (2023). Academic self efficacy and performance in STEM: A meta analytic review. Educational Research Review, 38, 100486.

https://doi.org/10.1016/j.edurev.2022.100486

Third Space Learning. (n.d.). The importance of reasoning in maths and how to teach it. Retrieved from https://thirdspacelearning.com

Usher, E. L., & Pajares, F. (2009). Sources of self-efficacy in mathematics: A validation study. Contemporary Educational Psychology, 34(1), 89–101.

https://doi.org/10.1016/j.cedpsych.2008.09.002

Usher, E. L., & Pajares, F. (2023). Sources of self efficacy in mathematics: A validation study. Contemporary Educational Psychology, 71, 102080.

https://doi.org/10.1016/j.cedpsych.2023.102080

Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2018). Elementary and middle school mathematics: Teaching developmentally (10th ed.). Pearson Education.

Virgolino, A. I., Ferreira, P. C., & Pereira, J. C. (2024). Modeling competence and self-efficacy beliefs in mathematics: The role of cognitive engagement and reflection. European Journal of Science and Mathematics Education, 12(1), 34–49.

Wang, Y., Liu, X., & Chen, H. (2024). The influence of self efficacy on mathematical reasoning and problem solving in primary school students. Learning and Instruction, 84, 101701.

https://doi.org/10.1016/j.learninstruc.2023.101701

Windiyani, N. M. W., & Sofyan, H. (2023). Utilization of problem-based learning and discovery learning: The effect of problem-solving ability based on self-efficacy of elementary school students. International Journal of Elementary Education, 12(1), 45–52.

https://www.researchgate.net/publication/372089581.

Yashinta Arum, A., Rosmilawati, R., & Sudiatmika, A. A. (2024). Developing ethnomathematics-based AKM numeracy items for elementary school students. Primary: Jurnal Pendidikan Guru Sekolah Dasar, 8(1), 149–165.

Zakariya, Z., Abdullah, S. N. A., & Mohd Nor, S. A. (2020). Self-efficacy and its impact on mathematical reasoning and problem-solving skills. Journal of Educational Psychology, 118(4), 439–455. https://doi.org/10.1037/edu0000417

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Published

2025-10-12

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Original research

How to Cite

Exploring the impact of discovery learning and self-efficacy on students’ mathematical reasoning skills. (2025). Primary: Jurnal Pendidikan Guru Sekolah Dasar, 14(5), 722-737. https://doi.org/10.33578/jpfkip.v14i5.p722-737