Pendekatan Onto-Semiotik Berbasis Problem Solving untuk Memperbaiki Pengetahuan Tanda “Sama Dengan”

Authors

  • Ahmad Hassan Nurdien Universitas Muhammadiyah Sidoarjo
  • Mohammad Faizal Amir Universitas Muhammadiyah Sidoarjo

DOI:

https://doi.org/10.30762/factor_m.v4i2.3349

Keywords:

Knowledge of the equal sign, Onto-semiotic, Problem-Solving, Primary Students

Abstract

Pengetahuan konsep atau simbol penting bagi siswa sekolah dasar sebagai dasar pemahaman untuk mempelajari aljabar pada tingkat lanjutan. Tujuan penelitian ini adalah untuk mengidentifikasi pengetahuan siswa pada tanda sama dengan “=” melalui penerapan pendekatan onto-semiotik berbasis problem solving pada siswa sekolah dasar berdasarkan setiap level pengetahuan dalam konsep kesamaan matematika. Penelitian ini merupakan studi literatur dengan menggunakan pendekatan deskriptif kualitatif. Data sekunder didapat dari literatur yang dianalisis, dikaji, serta terkait dengan fokus penelitian. Analisis studi literatur pengetahuan tanda sama dengan “=” difokuskan pada bilangan cacah yang sesuai dengan kompetensi inti dan kompetensi dasar yang berlaku di kelas satu dan satu sekolah dasar. Hasil penelitian ini menunjukkan bahwa melalui penerapan pendekatan onto-semiotik berbasis problem solving dapat membantu siswa untuk mencapai level secara bertahap pada level pertama, kedua, ketiga, serta keempat pada pengetahuan tanda sama dengan "=".  Level pertama, siswa berhasil untuk menyelesaikan sistem persamaan dengan format standar. Level kedua, siswa tetap fokus dengan sistem persamaan yang fleksibel dan konsisten dengan pandangan operasional tanda sama dengan "=".  Level ketiga, siswa mulai memahami akan relasional dasar meskipun berdampingan dengan pandangan operasional. Level keempat, siswa memiliki pemahaman relasional komparatif pada tanda sama dengan "=".

 

Knowledge of concepts or symbols is important for elementary school students as the basis for understanding algebra at an advanced level. This study aimed to identify students' knowledge of the equal sign "=" through the application of an onto-semiotic approach based on problem-solving in elementary school students based on each level of knowledge in the concept of mathematical similarity. This research is a literature study using a qualitative descriptive approach. Secondary data is obtained from the literature analyzed, reviewed, and related to the research focus. The analysis of the literature study of the knowledge of the equal sign "=" focused on whole numbers that correspond to the core competencies and basic competencies that apply in grade one and one elementary school. The results of this study indicate that applying an onto-semiotic approach based on problem solving can help students reach the level gradually at the first, second, third, and fourth levels of knowledge of the equal sign "=". In the first level, students succeed in solving a system of equations with a standard format. The second level, students stay focused on a flexible and consistent system of equations with an operational view of the equal sign "=". The third level, students begin to understand the basic relational although side by side with an operational view. The fourth level, students have a comparative relational understanding of the equal sign "=".

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References

Afifah, D. S. N., & Nafi’an, M. I. (2019). Analizing of field independent and dependent students’ understanding in solving statistical problems based on onto-semiotic approach. Journal of Physics Conference Series, 1175(1). https://doi.org/10.1088/1742-6596/1175/1/012148

Amin, M. E. I. A., Juniati, D., & Sulaiman, R. (2018). Onto semiotic approach to analyze students’ understanding of algebra based on math ability. AIP Conference Proceedings. United States: American Institute of Physics. https://doi.org/10.1063/1.5054481

Amir, M. F. (2015). Pengaruh pembelajaran kontekstual terhadap kemampuan pemecahan masalah matematika siswa sd. Prosiding Seminar Nasional Pendidikan, 34–42. Retrieved from http://eprints.umsida.ac.id/330/

Burgos, M., & Godino, J. D. (2020). Prospective primary school teachers’ competence for analysing the difficulties in solving proportionality problem. Mathematics Education Research Journal 2020. https://doi.org/10.1007/S13394-020-00344-9

Byrd, C. E., McNeil, N. M., Chesney, D. L., & Matthews, P. G. (2015). A specific misconception of the equal sign acts as a barrier to children’s learning of early algebra. Learning and Individual Differences, 38, 61–67. https://doi.org/10.1016/j.lindif.2015.01.001

Chesney, D. L., McNeil, N. M., Petersen, L. A., & Dunwiddie, A. E. (2018). Arithmetic practice that includes relational words promotes understanding of symbolic equations. Learning and Individual Differences, 64, 104–112. https://doi.org/10.1016/j.lindif.2018.04.013

Fischer, J., Sander, E., Sensevy, G., Vilette, B., & Richard, J. (2019). Can young students understand the mathematical concept of equality ? A whole-year arithmetic teaching experiment in second grade. European Journal of Psychology of Education, 34, 439–456. https://doi.org/10.1007/s10212-018-0384-y

Gade, S. (2012). Teacher-researcher collaboration in a grade four mathematics classroom: Restoring equality to students’ usage of the “=” sign. Educational Action Research, 20(4), 553–570. https://doi.org/10.1080/09650792.2012.727644

Godino, J. D., Batanero, C., & Roa, R. (2005). An onto-semiotic analysis of combinatorial problems and the solving processes by university students. Educational Studies in Mathematics, 60(1), 3–36. https://doi.org/10.1007/s10649-005-5893-3

Godino, J. D., Burgos, M., & Gea, M. M. (2021). Analysing theories of meaning in mathematics education from the onto-semiotic approach. International Journal of Mathematical Education in Science and Technology, 1–28. https://doi.org/10.1080/0020739X.2021.1896042

Godino, J. D., & Font, V. (2010). The theory of representations as viewed from the onto-semiotic approach to mathematics education. Mediterranean Journal for Research in Mathematics Education, 9(1), 189–210.

Gunantara, G., Suarjana, M., & Nanci Riastini, P. (2014). Penerapan model pembelajaran problem based learning untuk meningkatkan kemampuan pemecahan. Mimbar PGSD Undiksha, 2(1). https://doi.org/10.23887/jjpgsd.v2i1.2058

Handayani, K., Sulasmono, B. S., & Setyaningtyas, E. W. (2019). Implementasi metode pembelajaran problem solving dalam meningkatkan kemampuan berpikir kreatif dan hasil belajar matematika siswa sd. Jurnal Penelitian Dan Pembelajaran Matematika, 12(2), 254–270.

Johnson, B. R., Matthews, P. G., Taylor, R. S., & Mceldoon, K. L. (2011). Assessing knowledge of mathematical equivalence: A construct-modeling approach. Journal of Educational Psychology, 103(1), 85–104. https://doi.org/10.1037/a0021334

Kieran, C. (1981). Concept associated with the equality symbol. 12, 317–326.

Matthews, P. G., & Fuchs, L. S. (2020). Keys to the gate ? Equal sign knowledge at second grade predicts fourth-grade algebra competence. Child Development, 91(1), 14–28. https://doi.org/10.1111/cdev.13144

Matthews, P., Johnson, B. R., Mceldoon, K., & Taylor, R. (2012). Measure for measure: what combining diverse measures reveals about children’s understanding of the equal sign as an indicator of mathematical equality. Journal for Research in Mathematics Education, 43(3), 316–350. https://doi.org/10.5951/jresematheduc.43.3.0316

Milinia, R., & Amir, M. F. (2022). Grades four primary students’ learning obstacle on perimeter and area using onto-semiotic approach. Al Ibtida: Jurnal Pendidikan Guru MI, 9(1).

Pino, L. R. F., Guzmán, I., Duval, R., & Font, V. (2015). The theory of register of semiotic representation and the onto-semiotic approach to mathematical cognition and instruction: linking looks for the study of mathematical understanding. Proceedings of 39th Psychology of Mathematics Education Conference, 4, 33–40.

Rachma, A. A., & Rosjanuardi, R. (2021). Students’ obstacles in learning sequence and series using onto-semiotic approach. Jurnal Pendidikan Matematika, 15(2), 115–132. https://doi.org/10.22342/jpm.15.2.13519.115-132

Stephens, A. C., Mcneil, N. M., & Alibali, M. W. (2006). Does understanding the equal sign matter ? Evidence from solving equations. Journal for Research in Mathematics Education, 37(4), 297–312. https://doi.org/10.2307/30034852

Stephens, A., Veltri Torres, R., Sung, Y., Strachota, S., Murphy Gardiner, A., Blanton, M., … Knuth, E. (2021). From “you have to have three numbers and a plus sign” to “it’s the exact same thing”: k–1 students learn to think relationally about equations. Journal of Mathematical Behavior, 62. https://doi.org/10.1016/j.jmathb.2021.100871

Tome, A. O., Purwanto, & Sa’dijah, C. (2019). Students ’ mathematical thinking process involving equal signs. Journal of Physics Conference Series. https://doi.org/10.1088/1742-6596/1227/1/012012

Zed, M. (2014). Metode penelitian kepustakaan. Jakarta: Yayasan Pusaka Obor Indonesia.

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Published

26-06-2022

How to Cite

Nurdien, A. H., & Amir, M. F. . (2022). Pendekatan Onto-Semiotik Berbasis Problem Solving untuk Memperbaiki Pengetahuan Tanda “Sama Dengan”. Journal Focus Action of Research Mathematic (Factor M), 4(2), 65–80. https://doi.org/10.30762/factor_m.v4i2.3349

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