Comparative Effectiveness of AIR (Auditory, Intellectually, Repetition) and Realistic Mathematics Education Approaches on Students’ Mathematical Reasoning Ability
Abstract
Purpose of the study: This study aims to compare the effectiveness of the AIR (Auditory, Intellectually, Repetition) and Realistic Mathematics Education (RME) approaches in improving students’ mathematical reasoning ability at the senior high school level.
Methodology: This study employed a quantitative quasi-experimental method with a posttest-only design, using essay-based test instruments, interviews, observations, and documentation; data were analyzed using descriptive statistics, Liliefors normality test, F-test homogeneity, and independent sample t-test with statistical calculation procedures.
Main Findings: The results showed a significant difference between the two approaches, where the AIR approach produced higher mean scores than the RME approach in students’ mathematical reasoning ability. Statistical testing indicated tvalue > ttable, confirming that AIR is more effective in enhancing students’ reasoning skills compared to RME.
Novelty/Originality of this study: This study provides a direct comparative analysis between AIR and RME approaches within a single quasi-experimental framework, focusing specifically on mathematical reasoning ability and offering empirical evidence to support instructional decision-making in mathematics education.
References
M. R. Breixo, M. Isabel, and D. Ruíz, “Urban landscapes through the eyes of people with intellectual disability and down syndrome. The case of the city of Pontevedra (Spain),” Urban, Plan. Transp. Res., vol. 13, no. 1, pp. 1–18, 2025, doi: 10.1080/21650020.2025.2486191.
A. Alam and A. Mohanty, “Unveiling the complexities of ‘Abstract Algebra’ in University Mathematics Education (UME): Fostering ‘Conceptualization and Understanding’ through advanced pedagogical approaches,” Cogent Educ., vol. 11, no. 1, pp. 1–25, 2024, doi: 10.1080/2331186X.2024.2355400.
E. Saparbayeva, M. Abdualiyeva, Y. Torebek, A. Tursynbayev, and G. Takibayeva, “Transforming mathematics education in Kazakhstan: Evaluating the impact of innovative teaching methods on student outcomes in technical universities,” Cogent Educ., vol. 12, no. 1, pp. 1–21, 2025, doi: 10.1080/2331186X.2025.2461978.
E. Kristine, S. Hansen, M. Naalsund, E. Kristine, and S. Hansen, “Toward an analytical model for noticing interaction patterns in creative collaborative mathematical reasoning,” Math. Think. Learn., vol. 00, no. 00, pp. 1–19, 2025, doi: 10.1080/10986065.2025.2452222.
U. Wathne and M. Carlsen, “Third grade students’ multimodal mathematical reasoning when collaboratively solving combinatorial problems in small groups,” Math. Think. Learn., vol. 26, no. 3, pp. 258–277, 2024, doi: 10.1080/10986065.2022.2099611.
S. K. Boadu and E. Bonyah, “The role of philosophy of mathematics education in mathematics teacher education,” Cogent Educ., vol. 11, no. 1, pp. 1–20, 2024, doi: 10.1080/2331186X.2024.2433832.
I. Anugraheni, A. Gufron, and Y. W. Purnomo, “The impact of realistic problem-based learning on mathematical connection abilities: Evidence from elementary schools in Indonesia,” Cogent Educ., vol. 12, no. 1, pp. 1–17, 2025, doi: 10.1080/2331186X.2025.2523078.
M. Nhiry, S. Abouhanifa, E. Mostapha, and E. Khouzai, The characterization of mathematical reasoning through an analysis of high school curricula and textbooks in Morocco, vol. 10, no. 1. Cogent, 2023. doi: 10.1080/2331186X.2023.2188797.
J. Olsson and C. Granberg, “Teacher-student interaction supporting students’ creative mathematical reasoning during problem solving using Scratch,” Math. Think. Learn., vol. 26, no. 3, pp. 278–305, 2024, doi: 10.1080/10986065.2022.2105567.
A. Canogullari and F. Radmehr, “Task design principles in mathematics education: A literature review,” Int. J. Math. Educ. Sci. Technol., vol. 57, no. 4, pp. 615–647, 2026, doi: 10.1080/0020739X.2025.2457365.
R. Smit et al., “Supporting primary students’ mathematical reasoning practice: The effects of formative feedback and the mediating role of self-efficacy,” Res. Math. Educ., vol. 25, no. 3, pp. 277–300, 2023, doi: 10.1080/14794802.2022.2062780.
M. Graven and H. Venkat, “SAARMSTE’s role in building and connecting early grade mathematics research: A review of SAARMSTE proceedings 2003-2022,” African J. Res. Math. Sci. Technol. Educ., vol. 27, no. 3, pp. 255–272, 2023, doi: 10.1080/18117295.2023.2223376.
T. Trinh, T. Phuong, N. N. Danh, T. Tuyet, T. Le, and T. Nguyen, “Research on the application of ICT in mathematics education: Bibliometric analysis of scientific bibliography from the Scopus database,” Cogent Educ., vol. 9, no. 1, pp. 1–15, 2022, doi: 10.1080/2331186X.2022.2084956.
S. Sekimoto, “Reading the air: Toward multisensory literacy for the Anthropocene,” Senses Soc., vol. 20, no. 3, pp. 281–297, 2025, doi: 10.1080/17458927.2025.2586439.
C. Olteanu and C. Olteanu, “Programming, mathematical reasoning and sense-making,” Int. J. Math. Educ. Sci. Technol., vol. 53, no. 8, pp. 2046–2064, 2022, doi: 10.1080/0020739X.2020.1858199.
M. Hickendorff, M. Van Zanten, and M. Hickendorff, “Opportunity to learn flexible and adaptive strategy use in current and past dutch mathematics textbooks,” Math. Think. Learn., vol. 00, no. 00, pp. 1–18, 2024, doi: 10.1080/10986065.2024.2435827.
I. M. Christiansen and E. Erixon, “Opportunities to learn mathematics pedagogy and learning to teach mathematics in Swedish mathematics teacher education: A survey of student experiences,” Eur. J. Teach. Educ., vol. 47, no. 1, pp. 159–177, 2024, doi: 10.1080/02619768.2021.2019216.
M. Ballesteros-mejía and M. A. Madero, “Mapping visual-based methods: An interdisciplinary approach,” J. Vis. Lit., vol. 43, no. 4, pp. 285–307, 2024, doi: 10.1080/1051144X.2024.2420304.
D. Wijayanti, A. Lutfi, T. T. Wijaya, and O. Bah, “Mapping research on Indonesia’s government mathematics textbooks: Current insights and potential directions,” Cogent Educ., vol. 12, no. 1, pp. 1–18, 2025, doi: 10.1080/2331186X.2025.2560052.
T. B. Takane and H. Venkat, “Intervening to improve additive relations mathematising in home language classrooms,” African J. Res. Math. Sci. Technol. Educ., vol. 29, no. 1, pp. 1–12, 2025, doi: 10.1080/18117295.2025.2469468.
E. De Waal, “Idealistic mathematics education: The institute for the development of mathematics education (IOWO) and dutch education reform, 1970 –1980,” J. Hist. Educ. Soc., vol. 55, no. 1, pp. 89–112, 2026, doi: 10.1080/0046760X.2025.2553159.
L. Anaya, F. Stafford, and G. Zamarro, “Gender gaps in math performance, perceived mathematical ability and college STEM education: The role of parental occupation,” Educ. Econ., vol. 30, no. 2, pp. 113–128, 2022, doi: 10.1080/09645292.2021.1974344.
P. Partanen, B. Jansson, and Ö. Sundin, “Fluid reasoning, working memory and planning ability in assessment of risk for mathematical difficulties,” Educ. Psychol. Pract., vol. 36, no. 3, pp. 229–240, 2020, doi: 10.1080/02667363.2020.1736518.
R. Di Fuccio, M. Ponticorvo, and M. A. Nadim, “Exploring the effect of digital and multisensory educational materials on retention in primary school using Tangible User Interfaces,” Interact. Learn. Environ., vol. 33, no. 4, pp. 2928–2938, 2025, doi: 10.1080/10494820.2024.2427277.
L. I. Putri, H. Retnawati, A. Jaedun, and A. Murfi, “Enhancing mathematical skills through multicontextual approaches: A meta-analysis of realistic mathematics, ethnomathematics, and technology integration,” Cogent Educ., vol. 12, no. 1, pp. 1–20, 2025, doi: 10.1080/2331186X.2025.2548648.
J. Zhu, Q. Liu, and W. Zhang, “Effect of approximate system training on mathematical ability,” Cogent Psychol., vol. 12, no. 1, pp. 1–8, 2025, doi: 10.1080/23311908.2025.2496026.
J. Visnovska et al., “Decolonising content narratives in mathematics and science education: The case of reinventing length measurement,” African J. Res. Math. Sci. Technol. Educ., vol. 29, no. 1, pp. 28–41, 2025, doi: 10.1080/18117295.2024.2420469.
J. Molho, P. Levitt, N. Dines, and A. Triandafyllidou, “Cultural policies in cities of the ‘global South’: A multi-scalar approach,” Int. J. Cult. Policy, vol. 26, no. 6, pp. 711–721, 2020, doi: 10.1080/10286632.2020.1811256.
M. Braun et al., “Current digital consumer technology: Barriers, facilitators, and impact on participation for persons with intellectual disabilities – a scoping review,” Disabil. Rehabil., vol. 47, no. 21, pp. 5413–5434, 2025, doi: 10.1080/09638288.2025.2471567.
F. J. A. Cívico et al., “Comparing open and closed number-based algorithms for enhancing mathematical competence and reasoning in primary education,” Res. Math., vol. 12, no. 01, pp. 1–18, 2025, doi: 10.1080/27684830.2025.2529621.
M. Yang et al., “Augmented reality as a novel approach for addiction treatment: Development of a smoking cessation app,” Ann. Med., vol. 54, no. 1, pp. 3096–3106, 2022, doi: 10.1080/07853890.2022.2140451.
M. P. Schroeder-strong, B. Schreiber, W. Bennett, B. Schreiber, and W. Bennett, “A methodology for projecting the return on investment of training technologies,” Mil. Psychol., vol. 36, no. 1, pp. 125–136, 2024, doi: 10.1080/08995605.2022.2050164.
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