Proses representasi grounded-abstrak pada pemecahan word-problem perbandingan
DOI:
https://doi.org/10.15575/ja.v7i2.14416Keywords:
representasi grounded-abstrak, word-problem, perbandinganAbstract
Kesulitan dalam pemecahan word-problem perbandingan dialami karena proses representasi yang tidak tepat. Penelitian ini bertujuan mengkaji kasus representasi grounded-abstrak pada pemecahan word-problem perbandingan. Penelitian ini adalah penelitian kualitatif dengan jenis studi kasus. Kasus yang dikaji dalam penelitian ini adalah kasus kolektif. Instrumen penelitian ini adalah Peneliti, word-problem perbandingan, rubrik indikator, lembar validasi, buku catatan dan pedoman wawancara. Hasil penelitian ini adalah proses representasi yang terbagi dua dalam pemecahan word-problem perbandingan, yaitu kategori proses representasi itu adalah proses representasi grounded ke representasi abstrak dan proses representasi abstrak ke representasi grounded. Kesimpulan penelitian ini terdapat empat karakteristik proses representasi grounded-abstrak. Berdasarkan hasil penelitian ini disarankan bagi dosen untuk membelajarkan berbagi bentuk representasi matematis sehingga mahasiswa dapat mengembangkan kemampuan representasinya.
Â
Difficulties in solving word-comparison problems are experienced due to improper representation processes. This study aims to examine the case of grounded-abstract representation in solving word-problem comparisons. This research is a qualitative-research with the type of case study. The case studied in this study is a collective case. The research subjects were two mathematics education students who had studied comparative studies. The research instrument is the researcher, word-problem comparison, indicator rubric, validation sheet, notebook and interview guide. The result of this research is the representation process that categorized into two in solving word-problem comparison, which are grounded representation processes to abstract representations and abstract representation processes to grounded representations. The conclusion of this study is there are four characteristics of the grounded-abstract representation process. Based on the results of this study, it is recommended for lecturers to teach various forms of mathematical representation so that students can develop their representational abilities.
References
Achmetli, K., Schukajlow, S., & Rakoczy, K. (2018). Multiple Solutions for Real-World Problems, Experience of Competence and Students’ Procedural and Conceptual Knowledge. International Journal of Science and Mathematics Education, 10763. https://doi.org/10.1007/s10763-018-9936-5
Al-Saleem, R. M., Al-Hilali, B. M., & Abboud, I. K. (2020). Mathematical Representation of Color Spaces and Its Role in Communication Systems. Journal of Applied Mathematics, 2020. https://doi.org/10.1155/2020/4640175
Amaral, N., & Carreira, S. (2017). Mathematical Creativity in the Solutions of Students Participating in a Problem-Solving Competition. Bolema - Bulletin Mathematics Education Bulletin, 31(59), 880–906.
Chemillier, M. (2004). Musical représentations and mathematical representations. Homme, 171–172, 267–284. https://doi.org/10.4000/lhomme.1381
Darmawan, P. (2017). Berpikir Analitik Mahasiswa Dalam Mengonstruksi Bukti Secara Sintaksis. JPM : Jurnal Pendidikan Matematika, 2(2), 154. https://doi.org/10.33474/jpm.v2i2.196
Darmawan, P. (2020). Students Analytical Thinking in Solving Problems of Polygon Areas. Kontinu: Jurnal Penelitian Didaktik Matematika, 4(1), 17. https://doi.org/10.30659/kontinu.4.1.17-32
Darmawan, P., Purwanto, P., Parta, I. N., & Susiswo, S. (2020a). Interaksi Dual Proses dalam Menyelesaikan Masalah Segibanyak Siswa Sekolah Dasar. Universitas Negeri Malang.
Darmawan, P., Purwanto, P., Parta, I. N., & Susiswo, S. (2021). Teacher Interventions to Induce Students ’ Awareness in Controlling their Intuition. Bolema - Mathematics Education Bulletin, 35(70), 745–765. https://doi.org/http://dx.doi.org/10.1590/1980-4415v35n70a10
Darmawan, P., Purwanto, Parta, I. N., & Susiswo. (2020b). The levels of students’ feeling of rightness (for) in solving polygon perimeter problems. International Journal of Instruction, 13(2), 549–566. https://doi.org/10.29333/iji.2020.13238a
Dwirahayu, G., Tantri K., D., & Afidah, A. (2021). Multimedia Assisted Analogy: Learning Approach to Developing Mathematical Representation Skills. JPI (Jurnal Pendidikan Indonesia), 10(1), 117. https://doi.org/10.23887/jpi-undiksha.v10i1.24371
Giardino, V., & Wöpking, J. (2019). Aspect seeing and mathematical representations. Avant, 10(2), 1–19. https://doi.org/10.26913/AVANT.2019.02.27
Hall, J. (2021). Mathematical Representations in Magazine Advertisements: Have the Messages Changed in a Decade? Journal of Humanistic Mathematics, 11(1), 136–165. https://doi.org/10.5642/jhummath.202101.09
Hanifah, Waluya, S. B., Isnarto, Asikin, M., & Rochmad. (2021). Analysis mathematical representation ability by self-efficacy of prospective mathematics teachers. Journal of Physics: Conference Series, 1918(4). https://doi.org/10.1088/1742-6596/1918/4/042118
Hanifah, Waluya, S. B., Rochmad, & Wardono. (2020). Mathematical Representation Ability and Self -Efficacy. Journal of Physics: Conference Series, 1613(1). https://doi.org/10.1088/1742-6596/1613/1/012062
Hughes, S., Mccormick, M., & Russo, J. (2019). Dilemmas in suggesting mathematics representations to students. December.
Koedinger, K. R., Alibali, M. W., & Nathan, M. J. (2008). Trade-offs between grounded and abstract representations: Evidence from algebra problem solving. Cognitive Science, 32(2), 366–397. https://doi.org/10.1080/03640210701863933
Kolodin, I., & Ryabinin, M. (2019). Mathematical representation of pressure regulator with variable characteristic. IOP Conference Series: Materials Science and Engineering, 589(1). https://doi.org/10.1088/1757-899X/589/1/012018
Kunda, M. (n.d.). The AI Triplet : Computational , Conceptual , and Mathematical Representations in AI Education.
Ma, Z., Wang, Z., Wang, Y., Diao, R., & Shi, D. (2020). Mathematical representation of WECC composite load model. Journal of Modern Power Systems and Clean Energy, 8(5), 1015–1023. https://doi.org/10.35833/MPCE.2019.000296
Mund, S. (2021). Generalization of Various Kinds of Scalar Fields Exist in Universe and Their International Journal of Research Publication and Reviews Generalization of Various Kinds of Scalar Fields Exist in Universe and Their Mathematical Representations Surendra Mund. November.
Musser, G. L., Burger, W. F., & Peterson, B. E. (2011). Mathematics For Elementary Teachers A Contemporary Approach (Ninth Edit). John Wiley & Sons, Inc.
Obersteiner, A., Dooren, W. Van, Hoof, J. Van, & Verschaffel, L. (2013). The natural number bias and magnitude representation in fraction comparison by expert mathematicians. Learning and Instruction, 28, 64–72. https://doi.org/10.1016/j.learninstruc.2013.05.003
Prayitno, S., Lu’luilmaknunn, U., Sridana, N., & Subarinah, S. (2021). Analyzing the Ability of Mathematics Students as Prospective Mathematics Teachers on Multiple Mathematical Representation. Proceedings of the 2nd Annual Conference on Education and Social Science (ACCESS 2020), 556(Access 2020), 309–313. https://doi.org/10.2991/assehr.k.210525.096
Rabi, F., Fengqi, M., Aziz, M., Ullah, M. I., & Abduraxmanovna, N. H. (2021). the Impact of the Use of Geogebra on Student’S Mathematical Representation Skills and Attitude. European Journal of Education Studies, 8(12), 14–28. https://doi.org/10.46827/ejes.v8i12.4007
Rahmah, F., Subanji, & Irawati, S. (2019). Mathematical representation analysis of students in solving mathematics problems. Journal of Physics: Conference Series, 1200(1). https://doi.org/10.1088/1742-6596/1200/1/012011
Rahmawati, D., Purwantoa, P., Subanji, S., Hidayanto, E., & Anwar, R. B. (2021). Process of Mathematical Representation Translation from Verbal into Graphic. International Electronic Journal of Mathematics Education, 12(3), 367–381. https://doi.org/10.29333/iejme/618
Rohilla, D. (2021). Mathematical Logic Behind a Magic Trick. May, 0–2.
Samsuddin, A. F., & Retnawati, H. (2018). Mathematical representation: The roles, challenges and implication on instruction. Journal of Physics: Conference Series, 1097(1). https://doi.org/10.1088/1742-6596/1097/1/012152
Syahputra, E., & Marpaung, R. (2016). Students’ Mathematics Representation and the Alternative Solutions. Proceedings of the 1st Annual International Seminar on Transformative Education and Educational Leadership (AISTEEL), 1, 260–266. https://www.researchgate.net/publication/321382347%0AStudents’
Thalhah, S. Z., Tayeb, T., Raupu, S., & Arifanti, D. R. (2020).
Mathematical Representation Based on Personality Types. Lentera Pendidikan : Jurnal Ilmu Tarbiyah Dan Keguruan, 23(1), 141. https://doi.org/10.24252/lp.2020v23n1i12
Yang, Z. (2020). Mathematical Representation and Explanation: structuralism, the similarity account, and the hotchpotch picture. December. https://philpapers.org/rec/YANMRA
Downloads
Published
Issue
Section
License
Authors who publish in Jurnal Analisa agree to the following terms:
1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Attribution-ShareAlike 4.0 International (CC BY-SA 4.0) License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
3.Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).