Designing and evaluating SIMaV: A conceptual macro-visualization system to enhance students' mathematical abstraction ability
##plugins.themes.bootstrap3.article.main##
Abstract
This study aims to develop a design SIMaV conceptual macro-visualization system for linear systems with two variables at the junior high school level and to examine its feasibility and effectiveness in improving students’ mathematical abstraction ability. This research is grounded in the limitations of existing instructional media, which tend to present mathematical concepts through partial or fragmented visualizations that hinder students’ holistic understanding and abstraction processes. To address this gap, SIMaV introduces a novel macro-visualization approach that presents mathematical relationships dynamically and comprehensively, making a new contribution to visualization-based learning in mathematics education. The research method employed was Research and Development (R&D) using the ADDIE model, comprising the analysis, design, development, implementation, and evaluation stages. The research subjects included content experts, media experts, and eighth-grade students. The validation results from content and media experts indicated that the developed medium falls into the “feasible” to “highly feasible” category. Students’ responses to the medium were very positive, as indicated by an average questionnaire score of 3.5 out of 4. In addition, the improvement in students’ abstraction ability was shown by an N-Gain score of 0.63, which is categorized as “moderate.” This medium has proven to help students better understand the concept of linear systems with two variables through its interactive features. Therefore, SIMaV media is suitable for use as an innovation in conceptual macro-visualization systems, particularly for improving students' mathematical abstraction skills.
##plugins.themes.bootstrap3.article.details##

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
The author is responsible for acquiring the permission(s) to reproduce any copyrighted figures, tables, data, or text that are being used in the submitted paper. Authors should note that text quotations of more than 250 words from a published or copyrighted work will require grant of permission from the original publisher to reprint. The written permission letter(s) must be submitted together with the manuscript.References
Abdul Latif, N. H., Shahrill, M., & Hidayat, W. (2024). Mastering fractions and innovating with the station rotation model in blended learning. Infinity Journal, 13(2), 501–530. https://doi.org/10.22460/infinity.v13i2.p501-530
Andriatna, R., Nurhasanah, F., & Shahrill, M. (2025). Understanding mathematical abstraction: A systematic literature review of its conceptualizations and research practices. Infinity Journal, 14(4), 1081–1104. https://doi.org/10.22460/infinity.v14i4.p1081-1104
Barbieri, C. A., & Rodrigues, J. (2025). Leveraging cognitive load theory to support students with mathematics difficulty. Educational Psychologist, 60(3), 208–232. https://doi.org/10.1080/00461520.2025.2486138
Dinçer, S. (2025). Coordinating multiple representations in a hybrid real–virtual laboratory: Students’ strategies in learning light reflection and refraction. Journal of Turkish Science Education, 22(4), 703–723. https://doi.org/10.36681/tused.2025.035
Ding, M. (2021). Teaching Early Algebra through Example-Based Problem Solving. Routledge. https://doi.org/10.4324/9781003001713
Ding, M., Wu, Y., Liu, Q., & Cai, J. (2022). Mathematics learning in Chinese contexts. ZDM – Mathematics Education, 54(3), 477–496. https://doi.org/10.1007/s11858-022-01385-z
Hake, R. R. (2002). Relationship of individual student normalized learning gains in mechanics with gender, high-school physics, and pretest scores on mathematics and spatial visualization. In Physics education research conference, (Vol. 8, pp. 1–14).
Hidayat, W., & Aripin, U. (2023). How to develop an E-LKPD with a scientific approach to achieving students' mathematical communication abilities? Infinity Journal, 12(1), 85–100. https://doi.org/10.22460/infinity.v12i1.p85-100
Hidayat, W., Aripin, U., & Widodo, S. A. (2025). Integration of ethno-modelling and 3N: An innovative digital worksheet framework to enhance students' mathematical critical thinking skills. Infinity Journal, 14(4), 1019–1042. https://doi.org/10.22460/infinity.v14i4.p1019-1042
Hidayat, W., Rohaeti, E. E., Ginanjar, A., & Putri, R. I. I. (2022). An ePub learning module and students' mathematical reasoning ability: A development study. Journal on Mathematics Education, 13(1), 103–118. https://doi.org/10.22342/jme.v13i1.pp103-118
Hidayat, W., Rohaeti, E. E., Hamidah, I., & Putri, R. I. I. (2023). How can android-based trigonometry learning improve the math learning process? Frontiers in Education, 7, 1016. https://doi.org/10.3389/feduc.2022.1101161
Li, S., & Fan, L. (2024). Using social network analysis to investigate mathematical connections in U.S. and Chinese textbook problems. Humanities and Social Sciences Communications, 11(1), 495. https://doi.org/10.1057/s41599-024-02991-w
Maifa, T. S., Suryadi, D., & Fatimah, S. (2025). Identifying learning obstacles in proof construction for geometric transformations: Conceptual, procedural, and visualization errors. Infinity Journal, 14(3), 673–694. https://doi.org/10.22460/infinity.v14i3.p673-694
Muhammad, I., Jupri, A., & Herman, T. (2025). Development of web-based learning media with a realistic mathematics education approach to increase student self-determination. Infinity Journal, 14(2), 303–322. https://doi.org/10.22460/infinity.v14i2.p303-322
Nurwita, F., Kusumah, Y. S., & Juandi, D. (2025). Design and evaluation of a mobile application for achieving computational thinking skills through geometric transformation learning in middle school. Infinity Journal, 14(4), 877–898. https://doi.org/10.22460/infinity.v14i4.p877-898
Özdemir, A., Karaşan, S., & Şahal, M. (2021). An examination of the relationship between secondary school students’ abstract thinking skills, self-efficacy perceptions and attitudes towards mathematics. Participatory Educational Research, 8(2), 391–406. https://doi.org/10.17275/per.21.45.8.2
Pertiwi, C. M., Rohaeti, E. E., & Hidayat, W. (2021). The students' mathematical problem-solving abilities, self-regulated learning, and VBA Microsoft word in new normal: A development of teaching materials. Infinity Journal, 10(1), 17–30. https://doi.org/10.22460/infinity.v10i1.p17-30
Pyke, W., Lunau, J., & Javadi, A.-H. (2024). Does difficulty moderate learning? A comparative analysis of the desirable difficulties framework and cognitive load theory. Quarterly Journal of Experimental Psychology, 78(10), 2181–2195. https://doi.org/10.1177/17470218241308143
Robins, A. V. (2022). Dual process theories: Computing cognition in context. ACM Transactions on Computing Education, 22(4), 1–31. https://doi.org/10.1145/3487055
Rodríguez-Nieto, C. A., & Font Moll, V. (2025). Mathematical connections promoted in multivariable calculus’ classes and in problems-solving about vectors, partial and directional derivatives, and applications. Eurasia Journal of Mathematics, Science and Technology Education, 21(4), em2619. https://doi.org/10.29333/ejmste/16187
Rohaeti, E. E., Nurjaman, A., Sari, I. P., Bernard, M., & Hidayat, W. (2019). Developing didactic design in triangle and rectangular toward students mathematical creative thinking through Visual Basic for PowerPoint. Journal of Physics: Conference Series, 1157(4), 042068. https://doi.org/10.1088/1742-6596/1157/4/042068
Santoso, T., Nafis, H. L. H., & Oktama, M. Y. (2019). Analyzing students’ error in problem solving of two-variable linear equation system: A case study of grade eight students of Indonesian junior high school. International Journal of Learning, Teaching and Educational Research, 18(11), 283–296. https://doi.org/10.26803/ijlter.18.11.17
Selowa, R., & Dhlamini, Z. B. (2023). Exploring grade 11 learners’ algebraic thinking in the formulation of quadratic equations from graphs. International Journal of Education, 16(2), 135–144. https://doi.org/10.17509/ije.v16i2.50496
Sihombing, F., Putri, A., Utami, D. Z., Sherlyta, S., & Suwanto, F. R. (2025). Development of KoMaCu learning media for probability: An innovative digital comic to enhance learning effectiveness. JDIME: Journal of Development and Innovation in Mathematics Education, 3(2), 12–22.
Sweller, J. (2020). Cognitive load theory and educational technology. Educational Technology Research and Development, 68(1), 1–16. https://doi.org/10.1007/s11423-019-09701-3
Tang, S., & Pereira, J. (2025). Research on mathematical abstraction literacy in China. Pi Radian: Journal of Mathematics Education, 3(1), 1–16. https://doi.org/10.63214/piradian.v3i1.pp1-16
Taşkın, N., & Kılıç Çakmak, E. (2023). Effects of gamification on behavioral and cognitive engagement of students in the online learning environment. International Journal of Human–Computer Interaction, 39(17), 3334–3345. https://doi.org/10.1080/10447318.2022.2096190
Turan, N., & Karagöz Akar, G. (2024). An examination of Japanese curriculum materials through quantitative and covariational reasoning: the treatment of linear functions. Mathematical thinking and learning, 28(1), 75–100. https://doi.org/10.1080/10986065.2024.2387059
Vermehren, J. A. V., Trikoili, A., & Pittich, D. (2025). Abstract thought in STEM education: An integrative literature review. International journal of STEM education, 12(1), 54. https://doi.org/10.1186/s40594-025-00573-z
Wanabuliandari, S., Wardono, W., Susilo, B. E., Bintoro, H. S., & Mariani, S. (2025). A systematic literature review on slow learners’ problem-solving in mathematics education. International Journal of Learning, Teaching and Educational Research, 24(3), 699–724. https://doi.org/10.26803/ijlter.24.3.33
Wang, G., Kang, Y., Jiao, Z., Chen, X., Zhen, Y., Zhang, D., & Su, M. (2022). Development and application of intelligent assessment system for metacognition in learning mathematics among junior high school students. Sustainability, 14(10), 6278. https://doi.org/10.3390/su14106278
Wang, J., Zhang, L., Li, C., Cai, R., Chen, W., & Rao, Y. (2020). Research on the evaluation of dynamic mathematics software based on user experience. In 15th International Conference on Computer Science & Education (ICCSE), (pp. 445–450). https://doi.org/10.1109/iccse49874.2020.9202400
Zhang, Y., Wang, P., Jia, W., Zhang, A., & Chen, G. (2025). Dynamic visualization by GeoGebra for mathematics learning: A meta-analysis of 20 years of research. Journal of Research on Technology in Education, 57(2), 437–458. https://doi.org/10.1080/15391523.2023.2250886
Zheng, L., Gao, L., Huang, Z., Shi, Z., & Zhou, Y. (2025). A systematic meta-analysis of the impacts of group awareness tools on learning achievements, learning behaviors, and learning perceptions from 2010–2023. Interactive Learning Environments, 33(6), 3871–3888. https://doi.org/10.1080/10494820.2025.2454440
Zulfakri, Z., Ikhsan, M., & Yusrizal, Y. (2019). Improving the ability of representation and problem solving through concrete representational abstract (CRA) approach in mathematical learning. International Journal for Educational and Vocational Studies, 1(3), 244–248. https://doi.org/10.29103/ijevs.v1i3.1585