Implementation of Deep Scaffolding Based on Realistic Mathematics Education to Improve Thinking Errors of Students with Mild Intellectual Disabilities in Solving Numeracy Problems
Keywords:
deep scaffolding; realistic mathematics education; numeracy; inclusion; mild intellectual disabilitiesAbstract
Students with mild intellectual disabilities (MID) often struggle with numeracy concepts, particularly in representing geometric forms, performing arithmetic operations and applying mathematics to real-life contexts. This study aimed to examine how deep scaffolding grounded in Realistic Mathematics Education (RME) could remediate thinking errors of MID students in solving contextual numeracy problems. Using an interpretative qualitative approach with an exploratory single-case study design, one student (S1) with MID was selected from 61 participants identified through the Culture Fair Intelligence Test (CFIT). Data were collected through contextual numeracy worksheets, semi-structured interviews and observation, then analysed thematically using the mindful–meaningful–joyful scaffolding framework. The results revealed a significant transformation in S1’s cognitive and emotional engagement. Initially, S1 was unable to represent or solve contextual problems. Through mindful scaffolding, S1 identified and corrected reasoning errors; meaningful scaffolding helped link prior experiences to mathematical contexts; and joyful scaffolding fostered confidence and reflective awareness. By the final session, S1 successfully solved multi-step numeracy tasks and demonstrated improved metacognitive and spatial reasoning abilities. This study highlights that deep scaffolding, when integrated with RME, not only enhances conceptual understanding but also promotes emotional resilience and reflective learning in students with MID. Theoretically, it expands Freudenthal’s progressive mathematisation by incorporating affective and metacognitive dimensions. Practically, it offers an inclusive pedagogical model that can guide teachers in designing empathetic, contextual and transformative numeracy instruction for diverse learners.
https://doi.org/10.26803/ijlter.24.12.28
References
American Psychiatric Association. (2013). Diagnostic and statistical manual of mental disorders (5th ed.). Washington, DC.
Bouck, E., Park, J., Shurr, J., Bassette, L., & Whorley, A. (2018). Using the virtual–representational–abstract approach to support students with intellectual disability in mathematics. Focus on Autism and Other Developmental Disabilities, 33(4), 237–248. https://doi.org/10.1177/1088357618755696
Brankaer, C., Ghesquière, P., & de Smedt, B. (2013). The development of numerical magnitude processing and its association with working memory in children with mild intellectual disabilities. Research in Developmental Disabilities, 34(10), 3361–3371. https://doi.org/10.1016/j.ridd.2013.06.034
Braun, V., & Clarke, V. (2019). Reflecting on reflexive thematic analysis. Qualitative Research in Sport, Exercise and Health, 11(4), 589–597. https://doi.org/10.1080/2159676X.2019.1628806
Cheong, J. M., Walker, Z. M., & Rosenblatt, K. (2017). Numeracy abilities of children in grades 4 to 6 with mild intellectual disability in Singapore. International Journal of Disability, Development and Education, 64(2), 150–168. https://doi.org/10.1080/1034912X.2016.1188919
Chua, V. (2021). Improving learners’ productive disposition through realistic mathematics education, a teacher’s critical reflection of personal pedagogy. Reflective Practice, 22(6), 809–823. https://doi.org/10.1080/14623943.2021.1974373
Clements, D. H., & Sarama, J. (2018). Learning trajectories in early mathematics. Mathematical Thinking and Learning, 20(1), 1–28. https://doi.org/10.1080/10986065.2018.1403628
Das, K. (2020). Realistic mathematics & Vygotsky’s theories in mathematics education. Education 3–13, 9(1), 104–108. https://doi.org/10.34293/education.v9i1.3346
Esparcia, R., Piñero, B., & Futalan, M. C. (2024). Learners’ scaffolding techniques: Their advantages in learning mathematics. Journal of Interdisciplinary Perspectives, 2(7), 76–86. https://doi.org/10.5281/zenodo.11185028
Geiger, V., & Schmid, M. (2024). A critical turn in numeracy education and practice. Frontiers in Education. https://doi.org/10.3389/feduc.2024.1363566
Hord, C. (2022). Middle and high school math teaching for students with mild intellectual disability. Support for Learning, 37(3), 401–415. https://doi.org/10.1111/1467-9604.12425
Huu, D., Nguyen, T., Phuong, B., Kim, L., Truong, L., & Thi, P. (2022). Realistic Mathematics Education’s effect on students’ performance and attitudes: A case of ellipse topics learning. European Journal of Educational Research, 11(1), 403–416. https://doi.org/10.12973/eu-jer.11.1.403
Listiawati, N., Sabon, S. S. S., Wibowo, S. Z., & Riyanto, B. (2023). Analysis of implementing Realistic Mathematics Education principles to enhance mathematics competence of slow learner students. Journal on Mathematics Education. https://doi.org/10.22342/jme.v14i4.pp683-700
Long, H., Bouck, E., & Domka, A. (2020). Manipulating algebra: Comparing concrete and virtual algebra tiles for students with intellectual and developmental disabilities. Exceptionality, 29, 197–214. https://doi.org/10.1080/09362835.2020.1850454
Malik, R., Abdi, D., Wang, R., & Demszky, D. (2025). Scaffolding middle school mathematics curricula with large language models. British Journal of Educational Technology, 56(4), 999–1027. https://doi.org/10.1111/bjet.13571
Nurmasari, L. B., Nurkamto, J., & Ramli, M. (2023). Realistic mathematics engineering for improving elementary school students’ mathematical literacy. Journal on Mathematics Education, 15(1), 1–26. https://doi.org/10.22342/jme.v15i1.pp1-26
Organisation for Economic Co-operation and Development. (2022). PISA 2022 assessment and analytical framework: Mathematics, reading, science, and creative thinking. OECD Publishing. https://doi.org/10.1787/69096873-en
Reinhold, F., Hoch, S., Werner, B., Richter-Gebert, J., & Reiss, K. (2020). Learning fractions with and without educational technology: What matters for high-achieving and low-achieving students? Learning and Instruction, 65, 101264. https://doi.org/10.1016/j.learninstruc.2019.101264
Root, J., Cox, S., Hammons, N., Saunders, A., & Gilley, D. (2018). Contextualizing mathematics: Teaching problem solving to secondary students with intellectual and developmental disabilities. Intellectual and Developmental Disabilities, 56(6), 442–457. https://doi.org/10.1352/1934-9556-56.6.442
Sellars, M. (2017). Numeracy in authentic contexts: Making meaning across the curriculum. Springer.
Sobkow, A., Olszewska, A., & Traczyk, J. (2020). Multiple numeric competencies predict decision outcomes beyond fluid intelligence and cognitive reflection. Intelligence, 80, 101452. https://doi.org/10.1016/j.intell.2020.101452
Sobkow, A., Jurewicz, K., Zaleskiewicz, T., Pronczuk, A., Mondal, S., Badecka, J., ... & Traczyk, J. (2025). The role of numeracy in judgment and decision making: the replication of eleven effects across various numeracy scales. Collabra: Psychology, 11(1), 128514. . https://doi.org/10.1525/collabra.128514
Van den Heuvel-Panhuizen, M., & Drijvers, P. (2020). Realistic Mathematics Education. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 713–717). Springer International Publishing. https://doi.org/10.1007/978-3-030-15789-0_170
Xiao, F., Barnard-Brak, L., Lan, W., & Burley, H. (2019). Examining problem-solving skills in technology-rich environments as related to numeracy and literacy. International Journal of Lifelong Education, 38(3), 327–338. https://doi.org/10.1080/02601370.2019.1598507
Yilmaz, R. (2019). Prospective mathematics teachers’ cognitive competencies on realistic mathematics education. Journal on Mathematics Education, 11(1), 17–44. https://doi.org/10.22342/jme.11.1.8690.17-44
Yustitia, V., Kusmaharti, D., & Wardani, I. (2025). Students’ critical thinking in numeracy problem-solving through moderate self-efficacy: A mixed-methods study. Multidisciplinary Science Journal, 5(4), 410–421. https://doi.org/10.31893/multiscience.2025410
Zehner, T., Paes, T., Devlin, B., Geer, E., Posada, G., Duncan, R., Purpura, D., & Schmitt, S. (2024). Social–emotional competence as a predictor of early numeracy skills. Early Education and Development, 35(10), 1695–1711. https://doi.org/10.1080/10409289.2024.2360878
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Kadek Adi Wibawa, I Made Dharma Atmaja, I Gde Dhika Widarnandana
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
All articles published by IJLTER are licensed under a Creative Commons Attribution Non-Commercial No-Derivatives 4.0 International License (CCBY-NC-ND4.0).
