Developing RME-Based Learning Trajectory for Teaching Addition to A Dyscalculia Student in Elementary School

Ahmad Fauzan, Cahyo Dwi Andita, Gusti Rada, Afifah Zafirah, Abdul Halim bin Abdullah


This research aimed to design an RME-based learning trajectory for a dyscalculia student to learn the addition of whole numbers. The research used design research approach that consists of three phases: preparing for the experiment, conducting the experiment, and retrospective analysis. This research's data collection techniques were observations, interviews, videotaping, and analyzing the student’ works. The main result of this research is the learning trajectory for teaching addition of whole numbers to a dyscalculia student using RME approach. The series of activities in the learning trajectory are addition of whole numbers between 1 and 10 by combining the objects, addition of whole numbers between 1 and 10 using number relations, addition of whole numbers between 1 and 20 using number relations, and finding the concept of place value of tens and ones in addition of numbers. This research also shows the cognitive improvement of dyscalculia student in learning the addition of  whole numbers. Learning activities carried out by the dyscalculia student help him to shif from informal knowledge to formal mathematical knowledge in order to understand the concept of addition of whole numbers. It makes dyscalculia student has number sense, number construction, and number relation abilities which increase significantly in the learning process.


design research, hypothetical learning trajectory (HLT), realistic mathematics education (RME), local instructional theory (LIT), dyscalculia

Full Text:



Ahmad, S. S, Shaari, M. F., Hashim, R., & Kariminia, S. (2015). Conducive attributes of the physical learning environment at the preschool level for slow learners. Procedia-Social and Behavioral Sciences, 201, 110-120.

American Psychological Association. (1994). DSM-IV – A diagnostic and statistical manual of mental disorders (4th ed.). Washington, DC: Author.

American Psychological Association. (2013). DSM-V – A diagnostic and statistical manual of mental disorders (5th ed.). Washington, DC: Author.

Ananda, R. (2018). Penerapan pendekatan realistic mathematis education (RME) untuk meningkatkan hasil belajar matematika siswa sekolah dasar. Jurnal Cendikia: Jurnal Pendidikan Matematika, 2(1), 125-133.

Arini, A. (2018). Development of local instruction theory of multiplication based on realistic mathematics education in primary schools. International Journal of Educational Dynamics, 1(1), 188-204. doi: 10.24036/ijeds.v1i1.54

Attout, L., & Majerus, S. (2015). Working memory deficits in developmental dyscalculia: The importance of serial order. Child Neuropsychology, 21(4), 432–450. doi:10.1080/09297049.2014.922170.

Attout, L., Salmon, E., & Majerus, S. (2015). Working memory for serial order is dysfunctional in adults with a history of developmental dyscalculia: Evidence from behavioral and neuroimaging data. Developmental neuropsychology, 40(4), 230-247.

Ayunika, E. (2011). Pengembangan hipotesis trayektori pembelajaran untuk konsep. Yogyakarta: Pendidikan Matematika Universitas Sanata Dharma.

Bishara, S., & Kaplan, S. (2018). The relationship of locus of control and metacognitive knowledge of math with math achievements. International Journal of Disability, Development and Education, 65(6), 631-648. DOI: 10.1080/1034912X.2018.1432033

Bustang. (2013). Looking at angels: developing a local instruction theory for learning the concept of angel by exploring the nation of vision lines. Palembang: FKIP Sriwijaya University

Butterworth, B. (2011). Foundational numerical capacities and the origins of dyscalculia. In S. Dehaene & E. Brannon (Eds.), Space, time and number in the brain: Searching for the foundations of mathematical thought. London: Academic Press. doi:10.1016/B978-0-12-385948-8.00016-5

Campbell, JID (2005). Handbook of mathematical cognition. New York: Psychology Press.

Chodura, S., Kuhn, JT, & Holling, H. (2015). Interventions for children with mathematical difficulties. Zeitschrift Für Psychologie, 223(2), 129–144. Doi: 10.1027/2151-2604/a000211.

Dahar, R. W. (2011). Teori-teori belajar dan pembelajaran. Jakarta: PT. Rineka Cipta.

Dickinson, P., Eade, F., Gough, S., Hough, S., & Solomon, Y. (2020). Intervening with realistic mathematics education in england and the cayman islands—the challenge of clashing educational Ideologies. International Reflections on the Netherlands Didactics of Mathematics, 341.

Fauzan, A., & Diana, F. (2020). Learning trajectory for teaching number patterns using the RME approach in junior high schools. Journal of Physics: Conference Series, 1470(1), 012019.

Fauzan, A., Yerizon, Y., & Yolanda, RN (2020). Learning trajectory for teaching division using rme approach at elementary schools. Journal of Physics: Conference Series, 1554(1), 012079.

Fessakis, G., Karta, P., & Kozas, K. (2017). The math trail as a learning activity model for m-learning enhanced realistic mathematics education: A case study in primary education. In International Conference on Interactive Collaborative Learning (pp. 323-332). Springer, Cham.

Fitri, Y. (2016). Realistic mathematics learning model. THEOREMS (THE jOuRnal of mathEMatics), 1(2), 185-195.

Fosnot, C. T., & Dolk, M. (2001). Young mathematicians at work: Constructing multiplication and division. Heinemann. Heinemann, 88 Post Road West, PO Box 5007, Westport, CT 06881.

Geary, D. C., & Hoard, M. K. (2001). Numerical and arithmetical deficits in learning-disabled children: Relation to dyscalculia and dyslexia. Aphasiology, 15(7), 635-647. Doi: 10.1080/02687040143000113.

Gifford, S., & Rockliffe, F. (2012). Mathematics difficulties: Does one approach fit all?. Research in Mathematics Education, 14(1), 1-15.

Gillum, J. (2012). Dyscalculia: Issues for practice in educational psychology. Educational psychology in practice, 28(3), 287-297. DOI: 10.1080/02667363.2012.684344.

Gravemeijer. (2004). Mathematical thinking and learning local instruction theories as means of support for teachers in reform mathematics education. Mathematical thinking and learning, 6(2), 105–128.

Gravemeijer. (2020). Emergent modeling: An RME design heuristic elaborated in a series of examples. Educational Designer, 4(13), 1–31.

Gravemeijer, K., & Cobb, P. (2006). Design research from a learning design perspective. In J. van den Akker, K. Gravemeijer, S. McKenney & N. Nieveen (Eds.), Educational Design Research (pp. 17-51). London: Routledge.

Gravemeijer, K., & Van Eerde, D. (2009). Design research as a means for building knowledge base for teaching in mathematics education. The Elementary School Journal, 109(5), 510-524.

Guardian, N. (2013). Handbook of qualitative research methods in entrepreneurship. Gender in Management: An International Journal, 28(7), 441–44.

Hadi, S. (2017). Realistic mathematics education (theory, development, and implementation). Jakarta: Rajawali Press.

Henik, A., Rubinsten, O., & Ashkenazi, S. (2011). The “where” and “what” in developmental dyscalculia. The Clinical Neuropsychologist, 25(6), 989-1008. DOI: 10.1080/13854046.2011.599820.

Karso. (2019). Pembelajaran matematika di SD. Pendidikan Matematika I, 1–66.

Kucian, K., Loenneker, T., Martin, E., & von Aster, M. (2011). Non-symbolic numerical distance effect in children with and without developmental dyscalculia: A parametric fMRI study. Developmental neuropsychology, 36(6), 741-762. DOI: 10.1080/87565641.2010.549867.

Koh, C. (2020). A qualitative meta-analysis on the use of serious games to support learners with intellectual and developmental disabilities: What we know, what we need to know and what we can do. International Journal of Disability, Development and Education, 69(3) 1-32.

Luneta, K. (2016). Mathematical cognition: Understanding how children acquire mathematical knowledge and skills. Wulfenia Journal, 23(4), 291–296.

Mammarella, I. C., Hill, F., Devine, A., Caviola, S., & Szűcs, D. (2015). Math anxiety and developmental dyscalculia: A study on working memory processes. Journal of clinical and experimental neuropsychology, 37(8), 878-887. DOI: 10.1080/13803395.2015.1066759

Marlina. (2019). Asesmen kesulitan belajar (I). Jakarta: Prenada Media Group.

Maryati, M., & Prahmana, R. C. I. (2021). Learning trajectory of dilation and reflection in transformation geometry through the motifs of bamboo woven. Journal of Didactic Mathematics, 8(2), 134-147.

McCloskey, M., Caramazza, A., & Basili, A. (1985). Cognitive mechanisms in number processing and calculation: Evidence from dyscalculia. Brain and Cognition, 4(2), 171–196.

Monei, T., & Pedro, A. (2017). A systematic review of interventions for children presenting with dyscalculia in primary schools. Educational Psychology in Practice, 33(3), 277-293. DOI: 10.1080/02667363.2017.1289076.

Morsanyi, K., van Bers, B. M., O’Connor, P. A., & McCormack, T. (2018). Developmental dyscalculia is characterized by order processing deficits: Evidence from numerical and non-numerical ordering tasks. Developmental Neuropsychology, 43(7), 595-621. DOI: 10.1080/87565641.2018.1502294.

Munro, J. (2003). Dyscalculia: A unifying concept in understanding mathematics learning disabilities. Australian Journal of Learning Difficulties, 8(4), 25-32. DOI: 10.1080/19404150309546744.

NCTM. (2000). Principles and standards for school mathematics. Virginia: The National Council of Teachers of Mathematics, Inc.

Neergard. (2013). Educational Design Research Educational Design Research. Netherlands Institute for Curriculum Development: SLO 1–206.

Nelwan, M., Friso-van den Bos, I., Vissers, C., & Kroesbergen, E. (2021). The relation between working memory, number sense, and mathematics throughout primary education in children with and without mathematical difficulties. Child Neuropsychology, 28(2), 143-170.

Putrawangsa, S., & Hasanah, U,. (2018). Strategi dan tingkat kepekaan bilangan siswa sekolah dasar dalam menyelesaikan masalah operasi bilangan bulat. Jurnal Pendidikan Matematika.12(1):15–28.

Rahayu, Tika. (2010). Pendekatan RME terhadap peningkatan prestasi belajar matematika siswa kelas 2 SDN penaruban I purbalingga. Yogyakarta: UNY.

Rajaie, H., Allahvirdiyani, K., Khalili, A., & Sadeghi, A. (2011). Effect of teaching attention to the mathematical performance of the students with dyscalculia in the third and fourth grade of elementary school. Procedia-Social and Behavioral Sciences, 15, 3024-3026.

Saga, M., Rkhaila, A., Ounine, K., & Oubaha, D. (2021). Developmental dyscalculia: The progress of cognitive modeling in the field of numerical cognition deficits for children. Applied Neuropsychology: Child, 1-11.

Simon, M. A., Kara, M., Placa N., & Avitzur, A. (2018). Towards an integrated theory of mathematics conceptual learning and instructional design: The Learning Through Activity theoretical framework. The Journal of Mathematical Behavior, 52, 95–112. doi: 10.1016/j.jmathb.2018.04.002.

Simon, M. A., & Tzur, R. (2004). Explicating the role of mathematical tasks in conceptual learning: an elaboration of the hypothetical learning trajectory. Mathematical thinking and learning, 6(2), 91–104. , doi:10.1207/s15327833mtl0602_2.

Shalev, R. S., Manor, O., & Gross‐Tsur, V. (2005). Developmental dyscalculia: A prospective six-year follow-up. Developmental Medicine & Child Neurology, 47(2), 121–125. doi:10.1017/ S0012162205000216.

Syafriandi, S., Fauzan, A., Lufri, L., & Armiati, A. (2020). Designing a hypothetical learning trajectory for learning the importance of hypothesis testing. Journal of Physics: Conference Series, 1554(1), 012045. IOP Publishing.

Taufina, T., Chandra, C., Fauzan, A., & Syarif, M. I. (2019). Development of statistics in elementary school based rme approach with problem solving for revolution industry 4.0. In 5th International Conference on Education and Technology (ICET 2019) (pp. 716-721). Atlantis Press.Doi: 10.2991/icet-19.2019.172

Temple, C. M. (1992). Developmental Dyscalculia. In SJ Segalowitz & I. Rapin (Eds.), Handbook of neuropsychology (pp. 211–222). New York, NY: Elsevier

Tran, T., Nguyen, T., Le, T., & Phan, T. A. (2020). Slow learners in mathematics classes: The experience of vietnamese primary education. Education 3-13, 48(5), 580-596. DOI: 10.1080/03004279.2019.1633375

Treffers, A. (1991). Realistic mathematics education in the Netherlands 1980-1990. Freudenthal Institute, Utrecht University.

Van den Heuvel-Panhuizen, M., & Drijvers, P. (2020). Realistic mathematics education. Encyclopedia of mathematics education, 713-717.

Wijaya, A. (2009). Permainan (tradisional) untuk mengembangkan interaksi sosial, norma sosial dan norma sosiomatematik pada pembelajaran matematika dengan pendekatan matematika realistik. Seminar Nasional Aljabar, 31, 1–10.

Williams, A. (2013). A teacher's perspective of dyscalculia: Who counts? An interdisciplinary overview. Australian Journal of Learning Difficulties, 18(1), 1-16. DOI:10.1080/19404158.2012.727840.

Yeni, F., Yarmis, H., & Tarmansyah. (2013). Efektifitas game edukasi untuk meningkatkan kemampuan penjumlajan bagi anak kesulitan belajar di MIN koto luar, kecamatan pauh. E-JUPEKhu (Jurnal Ilmiah Pendidikan Khusus), 2(3),501–513.



  • There are currently no refbacks.

Copyright (c) 2022 Ahmad Fauzan

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Jurnal Didaktik Matematika

ISSN 2355 – 4185 (print) | 2548 – 8546 (online)

Published by:

Master Program of Mathematics Education incorporated with Himpunan Matematika Indonesia (Indonesian Mathematical Society/IndoMs)

Faculty of Teacher Training and Education

Universitas Syiah Kuala

Darussalam, Banda Aceh, Indonesia - 23111

Website : 
Email     : 

Creative Commons License

Jurnal Didaktik Matematika by Program Studi Magister Pendidikan Matematika FKIP Universitas Syiah Kuala is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Based on a work at