A Learning Trajectory for Statistics Through the Traditional Game of Congklak to Enhance Mathematical Reasoning Skills

Yemi Kuswardi, Farida Nurhasanah, Nabilla Uristu Al Firdaus, Budi Usodo, Henny Ekana Chrisnawati, Sutopo Sutopo, Masitah Shahrill

Abstract


The purpose of this study is to design a learning trajectory (develop mathematics reasoning skills) for junior high school statistics material to be used in eighth-grade classrooms. This design research study comprises three stages: preliminary design, experimental design and Retrospective Analysis. The subjects in this study were eighth-grade learners in a public junior-high school in Wonogiri City. Data collection methods included observation, interview and tests. Based on the results of the retrospective analysis, a learning trajectory for statistics material with the traditional Congklak game in application combines both informal and formal activities. In informal activities, through the Congklak game experiments conducted. These helped to form, mode, medium, examination, quartiles and semi-interquartile range interpretation concepts. In formal activities, based on the experimental results learners decided how to define mean (average), mode (the number of times a value appears in given data), medium and quartiles. The statistical results show that there are differences in mathematics reasoning skills between teaching with a learning trajectory assisted by Congklak and the direct method. The marginal mean for learning path is 71.57, while it is 62.66, and this outside the margin of error. This suggests that by application of a realistic mathematics approach using learning path driven Congklak traditional game of so can improve learners' mathematics reasoning ability.


Keywords


design research, mathematical reasoning ability, learning trajectory, congklak game.

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References


Antoni, M., Natalia, S., María, J. R., & Iris, M. (2022). Advancing the conceptualization of learning trajectories: A review of learning across contexts. Learning, Culture and Social Interaction, 37, 1-14. https://doi.org/10.1016/j.lcsi.2022.100658

Arnellis, Suherman, & Amalita. (2019). Implementasi learning trajectory kalkulus berbasis realistic mathematics education untuk meningkatkan kemampuan berpikir matematis tingkat tinggi peserta didik SMA Kota Padang. MENARA Ilmu, 13(6), 11-18. https://doi.org/10.33559/mi.v13i6.1399

Brodie, K. (2010). Teaching Mathematical Reasoning in Secondary School Classrooms. New York: Springer. https://doi.org/10.1007/978-0-387-09742-8

Clements, D. H., & Sarama, J. (2009). Learning and Teaching Early Math: The Learning Trajectories Approach. New York: Routledge. https://doi.org/10.4324/9781003083528

Collins, A., Joseph, D., & Bielaczyc, K. (2004). Design Research: Theoretical and Methodological Issues. Journal of the Learning Sciences, 13(1), 15–42. https://doi.org/10.1207/s15327809jls1301_2

Fakhmi, L., Sampoerno, P., & Meiliasari, M. (2021). Design research: lintasan pembelajaran statistika untuk menumbuhkan kemampuan literasi statistik siswa. Histogram: Jurnal Pendidikan Matematika, 5(2), 249-265. http://dx.doi.org/10.31100/histogram.v5i2.1164

Fowler, S., Cutting, C., Fiedler, S.H., et al. (2023). Design-based research in mathematics education: trends, challenges and potential. Mathematics Education Research Journal, 35, 635–658. https://doi.org/10.1007/s13394-021-00407-5

Garfield, J., & Ben-Zvi, D. (2008). The Discipline of Statistics Education. Developing Learner’s Statistical Reasoning: Connecting Research and Teaching Practice (1st ed., pp. 1–408). Springer Netherlands. https://doi.org/10.1007/978-1-4020-8383-9

Goos, M. (2004). Learning Mathematics in a Classroom Community of Inquiry. Journal of Research in Mathematics Education, 35, 258-291. https://doi.org/10.2307/30034810

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_3

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/10.1086/596999

Herbert, E., & Bragg, L. A. (2020). Factors in a professional learning program to support a teacher’s growth in mathematical reasoning and its pedagogy. Mathematics Education Research Journal, 33(1), 409–433. http://dx.doi.org/10.1007/s13394-020-00310-5

Herbert, E., & Bragg, L. A. (2021). Elementary teachers’ planning for mathematical reasoning through peer learning teams. International Journal for Mathematics Teaching and Learning, 22(1), 24-43. https://doi.org/10.4256/ijmtl.v22i1.291

Hilton, A., Hilton, G., Dole, S., & Goos, M. (2016). Promoting middle school learner’s proportional reasoning skills through an ongoing professional development programme for teachers. Mathematics Education Research Journal, 92, 193–219. https://doi.org/10.1007/S13394-013-0083-6

Lithner, J. (2008). Learner’s mathematical reasoning in university textbook exercises. Educational Studies in Mathematics, 52, 29–55. https://doi.org/10.1023/A:1023683716659

Marande, G. M. S., & Diana, H. A. (2023). Design Research: Development of Learning Trajectories in Realistic Mathematics Education on Relation and Function Materials. Indo-MathEdu Intellectuals Journal, 4(1), 10-28. http://doi.org/10.54373/imeij.v4i1.50

McKenney, S., & Reeves, T. (2018). Conducting Educational Design Research (2nd ed.). Routledge. https://doi.org/10.4324/9781315105642

Nickerson, S. D., & Whitacre, I. (2010). A Local Instruction Theory for the Development of Number Sense. Mathematical Thinking and Learning, 12(3), 227–252. https://doi.org/10.1080/10986061003689618

Rodríguez-Consuegra, F.A. (1991). The principles of mathematics. In: The Mathematical Philosophy of Bertrand Russell: Origins and Development. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7533-2_5

Sugiyono, D. (2018). Metode Penelitian Kuantitatif, Kualitatif dan R & D. Bandung: Alfabeta.

Surya, Z., Zulkardi, & Somakim. (2017). Desain Pembelajaran Statistika Menggunakan Konteks Mal. Jurnal Elemen, 3(2). https://doi.org/10.29408/jel.v3i2.344

Vale, C., Widjaja, W., Herbert, S., Bragg, L. A., & Loong, E. Y. K. (2015). A framework for primary teachers’ perceptions of mathematical reasoning. International Journal of Educational Research, 74, 26-37. https://doi.org/10.1016/j.ijer.2015.09.005

Vale, C., Widjaja, W., Herbert, S., Bragg, L. A., & Loong, E. Y. K. (2017). Mapping variation in children’s mathematical reasoning: the case of ‘what else belongs?’. International Journal of Science and Mathematics Education, 15(5), 873-894. https://doi.org/10.1007/s10763-016-9725-y

Van den Akker, J., Gravemeijer, K., McKenney, S., & Nieveen, N. (Eds.). (2006). Educational Design Research (1st ed.). Routledge. https://doi.org/10.4324/9780203088364




DOI: https://doi.org/10.20961/ijpte.v8i1.90547

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Copyright (c) 2024 Yemi Kuswardi, Farida Nurhasanah, Budi Usodo, Henny Ekana, Sutopo Sutopo, Masitah Shahrill

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International Journal of Pedagogy and Teacher Education

Print ISSN: 2597-7792
Online ISSN: 2549-8525
Website: https://jurnal.uns.ac.id/ijpte/index
Email: ijpte@mail.uns.ac.id
Published by: Faculty of Teacher Training and Education, Universitas Sebelas Maret
Ir. Sutami Street, No. 36A, Surakarta, Jawa Tengah Indonesia

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