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Abstract

This study examines the development of learning designs based on Realistic Mathematics Education (RME) on the probability topic at the eighth-grade junior high school level. Probability abounds in everyday life, and the RME approach is believed to develop students’ mathematical communication skills. This learning design development used the Plomp model combined with Gravemeijer and Cobb model. The research phase includes preliminary research, prototyping phase, and assessment phase. The products of this research are a valid, practice, and effective Local Instructional Theory (LIT) and teacher and student books. The results showed that the students who participated in learning using RME-based designs could determine the concept of probability and effectively improve students’ mathematical communication skills.

Keywords

Communication Local Instructional Theory Probability RME

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Armiati, Fauzan, A., Harisman, Y., & Sya’bani, F. (2022). Local instructional theory of probability topics based on realistic mathematics education for eight-grade students. Journal on Mathematics Education, 13(4), 703–722. https://doi.org/10.22342/jme.v13i4.pp703-722
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References

  1. Anggara, B. (2019). Desain pembelajaran matematika pada konsep dasar peluang berbasis kearifan lokal Indramayu [Design of mathematics learning on the basic concept of Indramayu local wisdom-based opportunity]. JNPM (Jurnal Nasional Pendidikan Matematika), 3(2), 223-227. https://doi.org/10.33603/jnpm.v3i2.2377
  2. Anggrayni, D., Haryanto, H., & Syaiful, S. (2021). Analisis epistemic cognition siswa dalam pemecahan masalah matematika ditinjau dari gaya kognitif materi teori peluang [Analysis of students' epistemic cognition in solving mathematical problems in terms of cognitive style of probability theory material]. Jurnal Cendekia: Jurnal Pendidikan Matematika, 5(1), 829–841. https://doi.org/10.31004/cendekia.v5i1.557
  3. Armiati, A., Subhan, M., Nasution, M. L., Aziz, S. Al, Rani, M. M., Rifandi, R., & Harisman, Y. (2020). Profesionalisme guru dalam membuat soal higher order thinking skills [Teacher professionalism in making higher order thinking skills questions]. JNPM (Jurnal Nasional Pendidikan Matematika), 4(1), 75-84. https://doi.org/10.33603/jnpm.v4i1.2587
  4. Asikin, M., & Junaedi, I. (2013). Kemampuan komunikasi matematika siswa SMP dalam setting pembelajaran RME (Realistic Mathematics Education) [Mathematics communication skills of junior high school students in RME (Realistic Mathematics Education) learning settings]. Unnes Journal of Mathematics Education Research, 2(1), 203-213. https://journal.unnes.ac.id/sju/index.php/ujmer/article/view/1483
  5. Astuti, D. (2015). Analisis kesulitan pemahaman konseptual siswa dalam menyelesaikan soal pada materi peluang di MAN Sanggau [Analysis of students' conceptual understanding difficulties in solving questions on opportunities in MAN Sanggau]. Jurnal Pendidikan dan Pembelajaran, 4(10), 1–10.
  6. Batanero, C., Henry, M., & Parzysz, B. (2005). The nature of chance and probability. Exploring Probability in School, 15–37. https://doi.org/10.1007/0-387-24530-8_2
  7. Bilad, D. I., & Ekawati, R. (2022). Development of student worksheet on probability with realistic mathematics education approach using pandemic context. Jurnal Ilmiah Pendidikan Matematika, 11(2), 488-498. https://doi.org/10.26740/mathedunesa.v11n2.p488-498
  8. Borovcnik, M., & Bentz, H.-J. (1991). Empirical research in understanding probability. Chance Encounters: Probability in Education, 73–105. https://doi.org/10.1007/978-94-011-3532-0_3
  9. Cheng, P. C. H. (2011). Probably good diagrams for learning: Representational epistemic recodification of probability theory. Topics in Cognitive Science, 3(3), 475–498. https://doi.org/10.1111/j.1756-8765.2009.01065.x
  10. Cunningham, P., Byrne, S., & Carney, M. (2009). The benefits of using a complete probability distribution when decision making: an example in anticoagulant drug therapy. https://www.researchgate.net/profile/Stephen-Byrne-3/publication/253196186_The_Benefits_of_Using_a_Complete_Probability_Distribution_when_Decision_Making_An_Example_in_Anticoagulant_Drug_Therapy/links/0c960531ed5b8a3c93000000/The-Benefits-of-Using-a-Complete-Probability-Distribution-when-Decision-Making-An-Example-in-Anticoagulant-Drug-Therapy.pdf
  11. Falk, R., & Konold, C. (1992). The psychology of learning probability. Statistics for the Twenty-first Century, 151-164. https://www.srri.umass.edu/sites/srri/files/Falk&Konold1992/index.pdf
  12. Fitri, A., & Abadi, A. M. (2021). Kesulitan siswa SMA dalam menyelesaikan soal matematika pada materi peluang [Difficulties of high school students in solving math problems in the probability subject]. Jurnal Riset Pendidikan Matematika, 8(1), 96–105. https://doi.org/10.21831/jrpm.v8i1.17004
  13. Freudenthal, H. (1968). Realistic models in probability. In Studies in Logic and the Foundations of Mathematics (Vol. 51, Issue C). Academic Press Inc. https://doi.org/10.1016/S0049-237X(08)71041-3
  14. Garfield, J., & Ahlgren, A. (2020). Difficulties in learning basic concepts in probability and statistics: Implications for research. Journal for Research in Mathematics Education, 19(1), 44–63. https://doi.org/10.5951/jresematheduc.19.1.0044
  15. Greer, B. (2001). Understanding probabilistic thinking: The legacy of Efraim Fischbein. Educational Studies in Mathematics, 45(1–3), 15–33. https://doi.org/10.1023/a:1013801623755
  16. Greer, B. (2016). Understanding probabilistic thinking: The legacy of Efraim Fischbein Author (s): Brian Greer Source: Educational Studies in Mathematics, Vol. 45, No. 1 / 3, Constructing Meanings from Published by: Springer Stable URL: http://www.jstor.org/stab. 45(1), 15–33.
  17. Harisman, Y., Kusumah, Y. S., & Kusnandi, K. (2019). How teacher professionalism influences student behaviour in mathematical problem-solving process. Journal of Physics: Conference Series, 1188(1), 012080. https://doi.org/10.1088/1742-6596/1188/1/012080
  18. Harisman, Y., Noto, M. S., Hidayat, W., Habibi, M., & Sovia, A. (2021). Pedagogies and didactic of junior high school teachers on learning process on mathematical problem solving. International Journal of Early Childhood Special Education, 13(2), 807–821. https://doi.org/10.9756/INT-JECSE/V13I2.211123
  19. Haryani, T. M., Putri, R. I. I., & Santoso, B. (2015). Desain pembelajaran dalam memahami konsep luas menggunakan kain motif kotak-kotak di kelas III [Learning design in understanding the concepts of measurement using plaid cloth in third grade]. Kreano, Jurnal Matematika Kreatif-Inovatif, 6(1), 49-57. https://doi.org/10.15294/kreano.v6i1.4503
  20. Hidayanto, T. (2013). Pengembangan bahan ajar berbasis realistic mathematic education untuk membangun kemampuan komunikasi matematis siswa smp kelas viii pada materi fungsi [Developing teaching materials based on realistic mathematical education to build mathematical communication skills for eight grade students on function materials]. Skripsi. Malang: Universitas Negeri Malang
  21. Izzati, N. (2012). Peningkatan kemampuan komunikasi matematis dan kemandirian belajar siswa smp melalui pendekatan pendidikan matematika realistic [Improving mathematical communication skills and learning independence for junior high school students through a realistic mathematics education approach]. Thesis. Bandung: Universitas Pendidikan Indonesia.
  22. Purwanto, E. (2013). Meningkatkan kemampuan pemecahan masalah melalui pembelajaran problem creating materi perbandingan siswa kelas vii SMP Negeri 3 Tulungagung [Improving problem solving ability through problem creating learning with proportion material for seventh grade students at SMP Negeri 3 Tulungagung]. Thesis. Malang: Universitas Negeri Malang.
  23. Kolloffel, B., Eysink, T. H. S., & de Jong, T. (2010). The influence of learner-generated domain representations on learning combinatorics and probability theory. Computers in Human Behavior, 26(1), 1–11. https://doi.org/10.1016/j.chb.2009.07.008
  24. Komarudin. (2016). Analisis kesalahan pemecahan masalah matematika pada materi peluang berdasarkan high order thinking [Analysis of mathematical problem-solving errors in probability material based on high order thinking]. Jurnal Pendidikan, Komunikasi dan Pemikiran Hukum Islam, VIII(1), 202–217.
  25. Komarudin. (2019). Analisis kesalahan siswa dalam pemecahan masalah matematika pada materi peluang berdasarkan high order thinking dan pemberian scaffolding [Analysis of student errors in solving mathematical problems on probability material based on high order thinking and scaffolding]. Journal of Chemical Information and Modeling, 53(9), 1689–1699. https://doi.org/10.1017/CBO9781107415324.004
  26. Madawistama, S. T., Heryani, Y., & Kurniawan, D. (2022). Three zone learning concepts to improve mathematical proof of probability theory. Jurnal Math Educator Nusantara: Wahana Publikasi Karya Tulis Ilmiah Di Bidang Pendidikan Matematika, 8(1), 27–38. https://doi.org/10.29407/jmen.v8i1.17004
  27. Maulida, E., Kasmini, L., & Novita, R. (2015). Peningkatan kemampuan pemecahan masalah melalui pendekatan matematika realistik pada materi peluang [Improving problem solving ability through a realistic mathematical approach in probability material]. Numeracy, 2(2), 72-83.
  28. Mezhennaya, N. M., & Pugachev, O. V. (2019). Advantages of using the CAS Mathematica in a study of supplementary chapters of probability theory. European Journal of Contemporary Education, 8(1), 4–24. https://doi.org/10.13187/ejced.2019.1.4
  29. Misdalina, M., Zulkardi, & Purwoko, P. (2013). pengembangan materi integral untuk sekolah menengah atas (SMA) menggunakan pendekatan pendidikan matematika realistik indonesia (pmri) di palembang [Developing integral materials for senior high schools using the Indonesian realistic mathematics education approach in Palembang]. Jurnal Pendidikan Matematika, 3(1), 61–74. https://doi.org/10.22342/jpm.3.1.321
  30. Mustamin, St. H. (2017). Pembelajaran matematika dengan pendekatan realistic [Learning mathematics with a realistic approach]. Lentera Pendidikan: Jurnal Ilmu Tarbiyah dan Keguruan, 20(2), 231–239. https://doi.org/10.24252/lp.2017v20n2i8
  31. Nodira, S., Gulchekhra, K., Nodira, A., Maprat, R., & Saida, D. (2021). Teaching currently using interactive methods in problem "probability theory and mathematical statistics". Central Asian Journal of Mathematical Theory and Computer Sciences, 2(4), 26-28.
  32. Nurmeidina, R., Lazwardi, A., & Ariyanti, I. (2020). Pengembangan modul teori peluang untuk meningkatkan hasil belajar dan disposisi matematis [Developing probability theory modules to improve learning outcomes and mathematical dispositions]. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 9(2), 440–450. https://doi.org/10.24127/ajpm.v9i2.2824
  33. Plomp, T., & Nieveen, N. (2013). Educational design research part A: An introduction. Enchede: SLO.
  34. Prihartini, N., Sari, P., & Hadi, I. (2020). Design research: Mengembangkan pembelajaran konsep peluang dengan pendekatan pendidikan matematika realistik Indonesia pada siswa Kelas IX di SMPN 220 Jakarta [Design research: Developing learning the concept of probability with an Indonesian realistic mathematics education approach for ninth grade students at SMPN 220 Jakarta]. Jurnal Riset Pembelajaran Matematika Sekolah, 4(8), 1–8.
  35. Putridayani, I. B., & Chotimah, S. (2020). Analisis kesulitan siswa dalam memahami soal cerita matematika pada materi peluang [Analysis of students' difficulties in understanding math story problems on opportunity material]. Jurnal Pembelajaran Matematika Inovatif, 3(6), 671–678. https://doi.org/10.22460/jpmi.v3i6.671-678
  36. Rada, G., & Fauzan, A. (2019). Pengembangan desain pembelajaran berbasis realistic mathematics education untuk topik peluang di Kelas XII SMA [Developing a realistic mathematics education-based learning design for the topic of probability in 12th grade senior high school]. Jurnal Pendidikan Matematika, 8(1), 66–72.
  37. Rahayu, P. T., & Putri, R. I. I. (2021). Project-based mathematics learning: Fruit salad. Journal on Mathematics Education, 12(1), 181–198. https://doi.org/10.22342/jme.12.1.13270.181-198
  38. Rohati. (2015). Pengembangan perangkat pembelajaran berbasis pendekatan realistic mathematics education (RME) pada materi volume bangun ruang sisi datar yang mendukung kemampuan komunikasi matematika siswa di SMP [Developing learning devices based on realistic mathematics education (RME) approach on volume of solid side geometry that support students' mathematical communication skills in junior high schools]. Edumatica: Jurnal Pendidikan Matematika, 5(2), 1-11. https://doi.org/10.22437/edumatica.v5i02.2927
  39. Sagala, P. N., & Andriani, A. (2019). Development of higher-order thinking skills (HOTS) questions of probability theory subject based on bloom’s taxonomy. Journal of Physics: Conference Series, 1188(1), 012025. https://doi.org/10.1088/1742-6596/1188/1/012025
  40. Sahroni, D. (2021). Peningkatan kinerja guru dalam menetapkan kriteria ketuntasan minimal melalui workshop di SDN Pondok Betung 03 [Improving teacher performance in setting minimum completeness criteria through workshops at SDN Pondok Betung 03]. Jurnal Sosial Teknologi, 1(4), 319-334.
  41. Sa’idah, N. (2016). Problematika kesulitan belajar statistic [The problem of difficulty learning statistics]. Proceeding Seminar Nasional PGSD UPY (pp. 54–61). Yogyakarta: Universitas PGRI Yogyakarta
  42. Saniyah, W., & Alyani, F. (2021). Analisis kesulitan belajar siswa dalam pemecahan masalah matematis pada materi peluang [Analysis of students' learning difficulties in solving mathematical problems in the probability material]. ANARGYA: Jurnal Ilmiah Pendidikan Matematika, 4(2), 206-212. https://doi.org/10.24176/anargya.v4i2.6457
  43. Sarvita, L., & Syarifuddin, H. (2020). The developed hypothetical learning trajectory for integral topic based on realistic mathematics education. Journal of Physics: Conference Series, 1554(1), 012032. https://doi.org/10.1088/1742-6596/1554/1/012032
  44. Shodiqin, A., Nuraini, A., & Wulandari, D. (2022). Profil berpikir probabilistik dalam pemecahan materi peluang kejadian berdasarkan self-efficacy [The profile of probabilistic thinking in problem solving based on self-efficacy]. JNPM (Jurnal Nasional Pendidikan Matematika), 6(2), 229-246.
  45. Silvianti, R., & Bharata, H. (2016). Meningkatkan kemampuan komunikasi matematis siswa melalui pendekatan realistic mathematics education (RME) [Improving students' mathematical communication ability through a realistic mathematics education (RME) approach]. Proceedings of Konferensi Nasional Penelitian Matematika dan Pembelajarannya (KNPMP I) (pp. 722-729). Surakarta: Universitas Muhammadiyah Surakarta. https://publikasiilmiah.ums.ac.id/bitstream/handle/11617/7016/78_112_Makalah%20Rev_Rizka%20Silvianti%20Unila%281%29.pdf?sequence=1&isAllowed=y
  46. Sya’bani, F., Armiati, Permana, D., Arnawa, I. M., & Asmar, A. (2021). The practicality of learning design based on realistic mathematics education for probability topic of grade VIII junior high school. Journal of Physics: Conference Series, 1742(1), 012036. https://doi.org/10.1088/1742-6596/1742/1/012036
  47. Tanujaya, B., Prahmana, R. C. I., & Mumu, J. (2018). Designing learning activities on conditional probability. Journal of Physics: Conference Series, 1088(1), 012087. https://doi.org/10.1088/1742-6596/1088/1/012087
  48. Thompson, J. R., & Findlay, M. C. (2002). More realistic paradigms for investment. Wiley Series in Probability and Statistics, 145–170. https://doi.org/10.1002/9780470317099.ch6
  49. Tinungki, G. M. (2015). The role of cooperative learning type team assisted individualization to improve the students’ mathematics communication ability in the subject of probability theory. Proceedings of the Fifth Conference for the Psychology of Mathematics Education, 6(32), 27–31.
  50. Tinungki, G. M., & Nurwahyu, B. (2021). Analysis of ability for understanding the basic concepts of probability theory. Proceedings of the 1st International Conference on Mathematics and Mathematics Education (ICMMEd 2020), 450–456. https://doi.org/10.2991/assehr.k.210508.103
  51. Wilensky, U. (1995). Paradox, programming, and learning probability: A case study in a connected mathematics framework. Journal of Mathematical Behavior, 14(2), 253–280. https://doi.org/10.1016/0732-3123(95)90010-1
  52. Yanti, W., Hartono, Y., & Somakim, S. (2016). Desain pembelajaran peluang dengan pendekatan PMRI menggunakan kupon undian untuk siswa kelas VII [Designing probability learning with PMRI approach using lottery coupons for seventh grade students]. Jurnal Elemen, 2(1), 56-71. https://doi.org/10.29408/jel.v2i1.177
  53. Yunarti, T. (2014). Desain didaktis teori peluang SMA [Didactic design for probability theory at senior high school]. Jurnal Pendidikan MIPA, 15(1), 15–20.
  54. Zeng, L. (2020). Application of MATLAB in the teaching of probability theory and mathematical statistics. Journal of Physics: Conference Series, 1651(1), 012078. https://doi.org/10.1088/1742-6596/1651/1/012078
  55. Zhang, L. (2016). Teaching research in probability theory and mathematical statistics modeling idea. Proceedings of the 3rd International Conference on Education, Management, Arts, Economics and Social Science (pp. 268-272). Atlantis Press.
  56. Zulkardi. (2003). Developing a learning environment on realistic mathematics education for Indonesian student teachers. Thesis. Enschede: University of Twente.
  57. Zulkardi & Putri, R. I. I. (2010). Pengembangan blog support untuk membantu siswa dan guru matematika Indonesia belajar pendidikan matematika realistik Indonesia [Developing a support blog to help Indonesian mathematics students and teachers learn Indonesian realistic mathematics education]. Jurnal Penelitian Inovasi dan Perekayasaan Pendidikan, 2(1), 1–24.
  58. Zulkardi & Putri, R. I. I. (2013). Desain bahan ajar penjumlahan pecahan berbasis pendidikan matematika realistik Indonesia (PMRI) untuk siswa kelas IV Sekolah Dasar Negeri 23 Indralaya [Designing teaching materials for adding fractions based on Indonesian realistic mathematics education for fourth grade students at Sekolah Dasar Negeri 23 Indralaya]. Jurnal Pendidikan Matematika, 4(2). https://doi.org/10.22342/jpm.4.2.818.