Article Development and Evaluation of BrunerFrame: An EIS-Based Ten-Frame for Improving First-Grade Students' Conceptual Understanding of Subtraction
DOI:
https://doi.org/10.61255/jupiter.v4i3.1526Keywords:
Brunerframe, Bruner's EIS Theory, Conceptual Understanding, Elementary Mathematics, Subtraction, Ten-Frame Learning MediaAbstract
Objective: Many first-grade students struggle to develop conceptual understanding of subtraction because mathematics instruction predominantly emphasizes symbolic procedures while providing limited opportunities to connect concrete, visual, and symbolic representations. Although Ten-Frame media are widely used in early mathematics education, few instructional media systematically integrate Bruner's Enactive–Iconic–Symbolic (EIS) representations to facilitate meaningful conceptual learning. Purpose: This study aimed to develop and evaluate the effectiveness of BrunerFrame, an EIS-based Ten-Frame learning media, in enhancing first-grade students' conceptual understanding of subtraction. Methods: This study employed a Research and Development (R&D) approach using the ADDIE model, followed by a quasi-experimental pretest-posttest control group design involving 34 first-grade students from two elementary schools. Data were collected through expert validation, teacher and student response questionnaires, classroom observations, and conceptual understanding tests, then analyzed using descriptive and inferential statistics to examine the validity, practicality, and effectiveness of the developed media. Results: BrunerFrame demonstrated high validity, with material and media validation scores of 88.75% and 90.40%, respectively. Teacher and student practicality scores reached 87.00% and 86.00%, indicating that the media was highly practical for classroom implementation. Students who learned using BrunerFrame achieved significantly higher conceptual understanding than those receiving conventional instruction (p < .001), with a high normalized gain (N-Gain = 0.71) and a very large effect size (Cohen's d = 2.64), demonstrating substantial educational effectiveness. Conclusion: BrunerFrame is a valid, practical, and effective instructional medium that facilitates students' progression from concrete manipulation to visual representation and symbolic reasoning, thereby strengthening conceptual understanding of subtraction. Research Implications: These findings provide empirical evidence supporting the integration of Bruner's EIS theory into elementary mathematics media and offer a practical instructional model for promoting meaningful conceptual learning in primary classrooms. Originality: This study introduces BrunerFrame, a validated instructional medium that systematically integrates Bruner's Enactive, Iconic, and Symbolic representations within a Ten-Frame framework, extending the practical application of EIS theory to early subtraction learning.
Abstract views: 0
, 
PDF downloads: 0
Downloads
References
Abraham, M., & Prediger, S. (2025). Scaffolding fifth graders’ learning with a digital multi-representation applet: Design research on focusing multiplicative structures with dynamic dot arrays. Digital Experiences in Mathematics Education, 11(2), 219–246. https://doi.org/10.1007/s40751-024-00156-7
Anam, R. S., Gumilar, S., & Widodo, A. (2024). The use of the constructivist teaching sequence (CTS) to facilitate changes in the visual representations of fifth-grade elementary school students: A case study on teaching heat convection concepts. International Journal of Science and Mathematics Education, 22(1). https://doi.org/10.1007/s10763-023-10358-x
Anwar, R. B., Rahmawati, D., & Wulandari, A. A. (2025). Trends in research on mathematical representation in mathematics learning: A systematic literature review. Journal of Education in Mathematics, Science and Technology, 13(3), 58–71. https://doi.org/10.1017/S0958344023000162
Björkhammer, C., Samuelsson, J., Träff, U., & Östergren, R. (2024). The effects of a whole-class mathematics intervention on students’ fraction knowledge in primary school. Scandinavian Journal of Educational Research, 68(6), 1275–1289. https://doi.org/10.1080/00313831.2023.2228818
Bruner, J. S. (1966). Toward a theory of instruction. Harvard University Press.
Dreher, A., Wang, T.-Y., Feltes, P., Hsieh, F.-J., & Lindmeier, A. (2024). High-quality use of representations in the mathematics classroom – A matter of the cultural perspective? ZDM–Mathematics Education, 56(5), 965–980. https://doi.org/10.1007/s11858-024-01597-5
Drijvers, P., & Sinclair, N. (2024). The role of digital technologies in mathematics education: Purposes and perspectives. ZDM–Mathematics Education, 56(2), 239–248. https://doi.org/10.1007/s11858-023-01535-x
Erbilgin, E., & Gningue, S. M. (2023). Using the onto-semiotic approach to analyze novice algebra learners’ meaning-making processes with different representations. Educational Studies in Mathematics, 114(2), 337–357. https://doi.org/10.1007/s10649-023-10247-8
Fujita, T., Komatsu, K., Obayashi, S., Miyawaki, S., Peters, A., & Yamamoto, S. (2025). Primary school students’ explanatory activities in geometry. International Journal of Science and Mathematics Education, 23(8), 3789–3814. https://doi.org/10.1007/s10763-025-10588-1
Gilmore, C. (2023). Understanding the complexities of mathematical cognition: A multi-level framework. Quarterly Journal of Experimental Psychology, 76(9), 1953–1972. https://doi.org/10.1177/17470218231175325
Hankeln, C., & Prediger, S. (2025). Language is essential for avoiding surface translations: Associations of students’ spontaneous use of meaning-related phrases for explicating structures with conceptual understanding of multiplication. Educational Studies in Mathematics, 120(1), 57–79. https://doi.org/10.1007/s10649-025-10414-z
Hedges, L. V., Tipton, E., Zejnullahi, R., & Diaz, K. G. (2023). Effect sizes in ANCOVA and difference-in-differences designs. British Journal of Mathematical and Statistical Psychology, 76(2), 259–282. https://doi.org/10.1111/bmsp.12296
Herheim, R. (2023). On the origin, characteristics, and usefulness of instrumental and relational understanding. Educational Studies in Mathematics, 113(3), 389–404. https://doi.org/10.1007/s10649-023-10225-0
Hsu, S.-K., & Hsu, Y. (2025). Supporting young learners in learning geometric area concepts through static versus dynamic representation and imagination strategies. International Journal of Science and Mathematics Education, 23(2), 441–459. https://doi.org/10.1007/s10763-024-10481-3
Hui, H. B., Mahmud, & S, M. (2023). Influence of game-based learning in mathematics education on the students’ cognitive and affective domain: A systematic review. Frontiers in Psychology, 14, Article 1105806. https://doi.org/10.3389/fpsyg.2023.1105806
Jäder, J., & Johansson, H. (2025). Exploring students’ conceptual understanding through mathematical problem solving: Students’ use of and shift between different representations of rational numbers. Research in Mathematics Education, 27(1), 1–22. https://doi.org/10.1080/14794802.2025.2456840
Kim, J. (2025). How representations support young students’ conceptual understanding of multiplication? A study on exploring third-grade students’ representational reasoning. Asian Journal for Mathematics Education, 4(3), 311–331. https://doi.org/10.1177/27527263251335686
Lee, J. (2022). Misunderstandings and right understandings regarding bruner’s modes of representation. Journal of Narrative and Educational Research, 10(3), 243–262. https://doi.org/10.25051/JNER.2022.10.3.010
Post, M., & Prediger, S. (2024). Teaching practices for unfolding information and connecting multiple representations: The case of conditional probability information. Mathematics Education Research Journal, 36(1), 97–129. https://doi.org/10.1007/s13394-022-00431-z
Quane, K., & Ní Ríordáin, M. (2025). The confluence of attitudes towards mathematics and pedagogical practice: Evaluating the use of mathematical manipulatives. Mathematics Education Research Journal, 37(2), 369–398. https://doi.org/10.1007/s13394-024-00494-0
Shakeel, S. I., Al Mamun, M. A., & Haolader, M. F. A. (2023). Instructional design with ADDIE and rapid prototyping for blended learning. Education and Information Technologies, 28(6), 7601–7630. https://doi.org/10.1007/s10639-022-11471-0
Sigus, H., & Mädamürk, K. (2025). Students’ motivation as a mediator between extra-mathematical knowledge and word problem-solving. Discover Education, 4, 172. https://doi.org/10.1007/s44217-025-00595-3
Siller, H.-S., & Ahmad, S. (2024). The effect of concrete and virtual manipulative blended instruction on mathematical achievement for elementary school students. Canadian Journal of Science, Mathematics and Technology Education, 24(2), 229–266. https://doi.org/10.1007/s42330-024-00336-y
Wynne, S., Robinson, C., & O’Connor, D. (2026). A Brunerian theoretical framework for ECE: A review of Jerome Bruner’s theoretical contributions to early childhood education. International Journal of Early Childhood, 58(2), 1003–1020. https://doi.org/10.1007/s13158-026-00502-3
Zentgraf, A. K., & Prediger, S. (2024). Demands and scaffolds for explaining the connection of multiple representations: Revisiting the bottle-filling task. The Journal of Mathematical Behavior, 73, Article 101118. https://doi.org/10.1016/j.jmathb.2023.101118
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Sri Utoyo, Bagus Ardi Saputro, Achmad Buchori
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
