Learning Trajectory of Whole Numbers using the Context  of Muara Enim Melemang Based on Realistic Mathematics Education (PMRI)

Arbella Sri Marleny M.; Zulkardi Zulkardi; Ratu Ilma Indra Putri; Yusuf Hartono

doi:10.31764/jtam.v10i1.34937

Learning Trajectory of Whole Numbers using the Context of Muara Enim Melemang Based on Realistic Mathematics Education (PMRI)

Arbella Sri Marleny M., Zulkardi Zulkardi, Ratu Ilma Indra Putri, Yusuf Hartono

Abstract

Learning whole numbers in the early grades of elementary school often poses challenges because students must understand abstract concepts and represent them symbolically. This study focuses on developing a Local Instructional Theory (LIT) for learning whole numbers using the Muara Enim melemang cultural context within the Pendidikan Matematika Realistik Indonesia (PMRI) framework. The research contributes both to the development of learning theory (LIT) and to improving the effectiveness of culturally based mathematics learning in Indonesian primary schools. The study employed design research (validation study) consisting of three stages: (1) the preliminary design formulated a Hypothetical Learning Trajectory (HLT) through curriculum analysis and contextual task design; (2) the teaching experiment tested the HLT in classroom practice to explore students’ strategies and interactions; and (3) the retrospective analysis compared the HLT and the Actual Learning Trajectory (ALT) to refine the emerging instructional theory. Findings reveal that the predicted HLT aligned with the ALT. Students successfully developed number sense counting, comparing, ordering, and performing simple operations through concrete representations of lemang. Difficulties mainly appeared in symbolic notation, such as using inequality signs and subtraction symbols. The study’s novelty lies in establishing a local culture-based LIT that bridges PMRI principles with ethnomathematics. Practically, it provides a contextual model teachers can adopt to enhance meaningful mathematics learning in early grades.

Keywords

Learning Trajectory; Whole Numbers; PMRI; Melemang; Ethnomathematics.

Full Text:

DOWNLOAD [PDF]

References

Alangui, W. V. (2020). Beyond songs and dances: Ethnomathematics and the challenge of culture. Revista Latinoamericana de Etnomatemática, 13(3), 88–107. Retrieved from https://www.redalyc.org/journal/2740/274065861006/274065861006.pdf

Askew, M. (2019). Transforming primary mathematics: Understanding classroom tasks, tools and talk. Routledge. https://doi.org/10.4324/9780203806746

Bakker, A. (2018). Design research in education: A practical guide for early career researchers. Routledge. Retrieved from api.taylorfrancis.com

Carpenter, T. P., & Moser, J. M. (1984). The acquisition of addition and subtraction concepts. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 7–44). Academic Press. https://doi.org/10.5951/jresematheduc.15.3.0179

Clarke, D. (2015). Early number sense: The key to later mathematics learning. Australian Primary Mathematics Classroom, 20(4), 4–9. https://primarystandards.aamt.edu.au/

Clements, D. H. (2020). Linking research and practice: The case of learning trajectories in early mathematics education. ZDM Mathematics Education, 52(1), 33–45. https://doi.org/10.1007/s11858-019-01122-z

Clements, D. H., & Sarama, J. (2014). Learning and teaching early math: The learning trajectories approach (2nd ed.). Routledge. https://www.taylorfrancis.com/books/mono/10.4324/9780203520574/

Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9–13. https://doi.org/10.3102/0013189X032001009

Confrey, J., Maloney, A. P., & Corley, A. K. (2014). Learning trajectories: A framework for connecting standards with curriculum. ZDM Mathematics Education, 46(5), 719–733. https://doi.org/10.1007/s11858-014-0632-0

Doorman, M., Drijvers, P., Gravemeijer, K., Boon, P., & Reed, H. (2012). Design research: A powerful tool to improve education. ZDM Mathematics Education, 44(3), 501–512. https://doi.org/10.1007/s11858-012-0418-4

Fuson, K. C. (2019). Early whole number learning and development. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 423–456). NCTM. https://doi.org/10.1007/s11858-012-0418-4

Gravemeijer, K. (1994). Developing realistic mathematics education. Freudenthal Institute. https://research.tue.nl/en/publications/developing-realistic-mathematics-education?utm_source=chatgpt.com

Gravemeijer, K. (2004). Local instruction theories as means of support for teachers in reform mathematics education. Mathematical Thinking and Learning, 6(2), 105–128. https://doi.org/10.1207/s15327833mtl0602_2

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). Routledge. https://www.fi.uu.nl/publicaties/literatuur/EducationalDesignResearch.pdf?utm_source=chatgpt.com

Gravemeijer, K., & van Eerde, D. (2009). Design research as a means for building a knowledge base for teachers and teaching in mathematics education. The Elementary School Journal, 109(5), 510–524. https://doi.org/10.1086/597397

Jordan, N. C., Glutting, J., & Ramineni, C. (2013). The importance of number sense to mathematics achievement in first and third grades. Learning and Individual Differences, 23, 123–128. https://doi.org/10.1016/j.lindif.2012.11.003

Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. National Academy Press. https://www.nap.edu/catalog/9822/adding-it-up-helping-children-learn-mathematics

National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. NCTM. https://www.nctm.org/standards/

Rosa, M., & Orey, D. C. (2011). Ethnomathematics: The cultural aspects of mathematics education. Revista Latinoamericana de Etnomatemática, 4(2), 32–54. https://revista.etnomatematica.org/index.php/RevLatEm/article/view/32

Rosa, M., & Orey, D. C. (2016). Ethnomathematics and its pedagogical action in mathematics education. Journal of Mathematics and Culture, 10(3), 75–102. DOI: https://doi.org/10.1007/978-3-319-30120-4_3

Seah, W. T. (2020). Values in mathematics education: Its place and potential. International Journal of Science and Mathematics Education, 18(1), 1–18. https://doi.org/10.1007/s10763-019-09983-0

Sembiring, R. K., Hadi, S., & Dolk, M. (2008). Reforming mathematics learning in Indonesian classrooms through RME. ZDM Mathematics Education, 40(6), 927–939. https://doi.org/10.1007/s11858-008-0125-9

Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26(2), 114–145. https://doi.org/10.2307/749877

Sowder, J. T. (2021). Developing number sense in young children: A research-based approach. Early Childhood Research Quarterly, 54, 25–38. https://doi.org/10.1016/j.ecresq.2020.101021

Van den Heuvel-Panhuizen, M. (2020). Didactical phenomenology applied to mathematics education. In M. van den Heuvel-Panhuizen (Ed.), National reflections on the Netherlands didactics of mathematics (pp. 75–92). Springer. DOI: https://doi.org/10.1007/978-3-030-33824-4

Yang, D. C. (2022). Using visual scaffolds to support young children’s understanding of mathematical symbols. Early Childhood Education Journal, 50(5), 865–878. https://doi.org/10.1007/s10643-021-01274-2

DOI: https://doi.org/10.31764/jtam.v10i1.34937