EKSPLORASI PEMAHAMAN NILAI MUTLAK MAHASISWA PENDIDIKAN MATEMATIKA BERBASIS THREE WORLDS OF MATHEMATICS

https://doi.org/10.30605/pedagogy.v10i4.7663

Authors

  • Agusalim Juhari Universitas Negeri Makassar
  • Takdirmin Universitas Muhammadiyah Makassar

Keywords:

Pemamaham Nilai Mutlak, Three Worlds of Mathematics, embodied, symbolic–proceptual, formal–axiomatic

Abstract

Penelitian ini bertujuan untuk mendeskripsikan pemahaman mahasiswa Pendidikan Matematika terhadap konsep nilai mutlak berdasarkan kerangka Three Worlds of Mathematics (Tall), yang meliputi embodied world, symbolic–proceptual world, dan formal–axiomatic world. Penelitian menggunakan pendekatan kualitatif deskriptif dengan subjek 15 mahasiswa yang dipetakan ke dalam tiga kategori world melalui tes diagnostik. Tiga subjek utama (M1, M2, dan M3) dipilih secara purposive untuk diwawancarai lebih mendalam. Analisis data dilakukan menggunakan model Miles, Huberman, dan Saldaña (2014). Hasil penelitian menunjukkan bahwa (1) Distribusi pemahaman mahasiswa berdasarkan Three Worlds of Mathematics menunjukkan bahwa symbolic–proceptual world merupakan dunia yang paling dominan, Sebanyak 53.3% mahasiswa berada pada dunia simbolik, 26.7% pada embodied world, dan hanya 20% pada formal–axiomatic world. Hal ini menegaskan bahwa mayoritas mahasiswa lebih menguasai prosedur aljabar nilai mutlak dibandingkan pemahaman visual maupun definisi formalnya, (2) Mahasiswa embodied world memahami nilai mutlak sebagai jarak, tetapi kesulitan mentransformasikan intuisi visual ke representasi simbolik. Mahasiswa mampu menggambar garis bilangan dan menentukan dua solusi berdasarkan jarak, tetapi belum mampu menuliskannya secara simbolik dalam bentuk positif dan negatif secara tepat. Koneksi embodied ke symbolic belum terbentuk secara kuat, (3) Mahasiswa symbolic–proceptual world menguasai prosedur penyelesaian dua bentuk positif dan negatif, tetapi pemahamannya bersifat mekanistik. Mahaisiswa menyelesaikan soal nilai mutlak dengan cepat dan tepat, namun tidak memahami alasan matematis di balik langkah tersebut. Representasi simbolik tidak terhubung dengan makna visual ataupun definisi formal nilai mutlak, dan (4) Mahasiswa formal–axiomatic world memahami definisi formal nilai mutlak, tetapi belum mampu menghubungkannya dengan representasi visual. Mahasiswa dapat menjelaskan fungsi bersyarat dan memberikan justifikasi matematis yang tepat, namun kesulitan menjelaskan grafik nilai mutlak sebagai representasi jarak. Integrasi formal ke embodied belum terjadi secara utuh.

Downloads

Download data is not yet available.

References

Almog, N., & Ilany, B. S. (2012). Absolute value inequalities: High school students' solutions and misconceptions. Educational Studies in Mathematics, 81(3), 347–364. https://doi.org/10.1007/s10649-012-9418-9 DOI: https://doi.org/10.1007/s10649-012-9404-z

Altarawneh, A. F., & Alkhateeb, M. A. (2024). Common misconceptions about absolute value and related thinking strategies. Journal of Curriculum Studies Research, 6(1), 1–17. https://doi.org/10.46303/jcsr.2024.19 DOI: https://doi.org/10.46303/jcsr.2024.19

Anam, K., Hidayati, W. S., & Rozak, A. (2022). Analisis kesalahan mahasiswa dalam menyelesaikan soal nilai mutlak bilangan kompleks. Prosiding Conference on Mathematics Education, 3(1), 45–52.

Aziz, T. A., Supiat, & Soenarto, Y. (2019). Pre-service secondary mathematics teachers’ understanding of absolute value. Cakrawala Pendidikan, 38(1), 112–124. https://doi.org/10.21831/cp.v38i1.21945 DOI: https://doi.org/10.21831/cp.v38i1.21945

Cahyaningtyas, O., & Rahardi, R. (2021). Analisis kesalahan siswa dalam menyelesaikan soal persamaan dan pertidaksamaan nilai mutlak berdasarkan teori Newman. Edumatica: Jurnal Pendidikan Matematika, 11(2), 145–156. DOI: https://doi.org/10.22437/edumatica.v11i03.14201

Dawkins, P. (2015). Students’ understanding of the formal definition of limit: Three teaching experiments. Journal of Mathematical Behavior, 40, 21–37. https://doi.org/10.1016/j.jmathb.2015.03.002 DOI: https://doi.org/10.1016/j.jmathb.2015.03.002

Elia, I., Özel, S., Gagatsis, A., & Özel, Z. E. Y. (2016). Students’ mathematical work on absolute value: Focusing on conceptions, errors and obstacles. ZDM Mathematics Education, 48(6), 837–850. https://doi.org/10.1007/s11858-016-0787-8 DOI: https://doi.org/10.1007/s11858-016-0780-1

Irsyadi, M. K., Sari, A. S. L., & Yunaini, F. (2022). Analisis kesalahan siswa dalam penyelesaian soal persamaan dan pertidaksamaan nilai mutlak berdasarkan kriteria Watson. Numeracy: Jurnal Pendidikan Matematika, 2(1), 12–25. DOI: https://doi.org/10.46244/numeracy.v9i1.1785

Kurudirek, A., Arslan, A., & Tuncer, B. (2025). Math misconceptions: Mistakes, misunderstanding, and confusion. Educenter: Jurnal Ilmiah Pendidikan Matematika, 8(1), 12–27. DOI: https://doi.org/10.55904/educenter.v4i1.1322

Marzano, R. J. (2001). Classroom instruction that works: Research-based strategies for increasing student achievement. ASCD.

Mathaba, P. N., Mhlongo, S., & Sibaya, T. (2024). Error analysis in algebra learning: Exploring misconceptions and cognitive levels. Journal on Mathematics Education, 15(1), 33–48. DOI: https://doi.org/10.22342/jme.v15i2.pp575-592

Miles, M. B., Huberman, A. M., & Saldaña, J. (2014). Qualitative data analysis: A methods sourcebook (3rd ed.). SAGE Publications.

Nisa, Z., Lukito, A., & Masriyah. (2019). Students’ mathematical discourse analysis by commognition theory in solving absolute value equations. Journal of Physics: Conference Series, 1157, 032108. https://doi.org/10.1088/1742-6596/1157/3/032108 DOI: https://doi.org/10.1088/1742-6596/1157/3/032108

Nitko, A. J., & Brookhart, S. M. (2011). Educational assessment of students (6th ed.). Pearson.

Oikkonen, J., & Hannula, M. S. (2022). Students’ mathematical thinking and the development of symbolic and formal understanding: Revisiting Tall's three worlds of mathematics. International Journal of Mathematical Education, 54(3), 367–383.

Papadouris, J. P., Komis, V., & Lavidas, K. (2025). Errors and misconceptions of secondary school students in absolute values: A systematic literature review. Mathematics Education Research Journal. https://doi.org/10.1007/s13394-024-00499-9 DOI: https://doi.org/10.1007/s13394-024-00499-9

Sierpińska, A., Bobos, G., & Pruncut, A. (2011). Teaching absolute value inequalities to mature students. Educational Studies in Mathematics, 78(1), 41–62. https://doi.org/10.1007/s10649-011-9314-9 DOI: https://doi.org/10.1007/s10649-011-9325-2

Syahda, U., & Pujiastuti, H. (2020). Analisis kesalahan siswa dalam menyelesaikan soal persamaan dan pertidaksamaan nilai mutlak berdasarkan teori Polya. JKPM (Jurnal Kajian Pendidikan Matematika), 5(1), 1–10. DOI: https://doi.org/10.30998/jkpm.v6i1.6610

Tall, D. O. (2004). Building theories: The three worlds of mathematics. For the Learning of Mathematics, 24(1), 28–33.

Tall, D. O. (2006). A theory of mathematical growth through embodiment, symbolism and proof. Annales de Didactique et de Sciences Cognitives, 11, 195–215.

Tall, D. O. (2013). How humans learn to think mathematically: Exploring the three worlds of mathematics. Cambridge University Press. DOI: https://doi.org/10.1017/CBO9781139565202

Vhantoria, F. (2022). Analisis kesalahan mahasiswa menyelesaikan soal ketaksamaan yang melibatkan nilai mutlak berdasarkan teori Kastolan. Eksponen: Jurnal Pendidikan Matematika, 4(2), 55–64. DOI: https://doi.org/10.47637/eksponen.v12i1.513

Downloads

Published

2025-12-08

How to Cite

Juhari, A., & Takdirmin, T. (2025). EKSPLORASI PEMAHAMAN NILAI MUTLAK MAHASISWA PENDIDIKAN MATEMATIKA BERBASIS THREE WORLDS OF MATHEMATICS. Pedagogy: Jurnal Pendidikan Matematika, 10(4), 2367–2385. https://doi.org/10.30605/pedagogy.v10i4.7663

Issue

Vol. 10 No. 4 (2025): Pedagogy : Jurnal Pendidikan Matematika

Section

Articles

License

Copyright (c) 2025 Pedagogy : Jurnal Pendidikan Matematika

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

In submitting the manuscript to the journal, the authors certify that:

  • They are authorized by their co-authors to enter into these arrangements.
  • The work described has not been formally published before, except in the form of an abstract or as part of a published lecture, review, thesis, or overlay journal.
  • That it is not under consideration for publication elsewhere,
  • That its publication has been approved by all the author(s) and by the responsible authorities – tacitly or explicitly – of the institutes where the work has been carried out.
  • They secure the right to reproduce any material that has already been published or copyrighted elsewhere.
  • They agree to the following license and copyright agreement.

License and Copyright Agreement

Authors who publish with this journal agree to the following terms:

  1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under Creative Commons Attribution License (CC BY 4.0) 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.