THE REVIEW OF WAYS OF UNDERSTANDING IN PROVING CONGRUENCE OF TWO TRIANGLES
Abstract
This study aims to reviewing ways of understanding of prospective mathematics teacher students in the process of proving the triangle congruence theorem deductively. Deductive proof is a process that is quite difficult to do if students do not know the postulates, theorems, definitions, and properties that can be used as references in the proof process. The mathematical critical thinking process needs to be reviewed to determine the relevance of students' considerations in choosing the various references needed. The study used a case study to investigate the phenomenon specifically. The participants involved in the study were five students from a university in West Java. Theory of ways of understanding is needed to examine students' understanding of postulates, theorems, definitions, and other properties that have been studied previously so that it can be known to what extent students can validate the proof process carried out. The results of the study showed that based on the ways of understanding they have, students can prove the congruence theorem of two triangles by formulating the main problems, expressing facts, choosing logical arguments, detecting information bias with different points of view, and being able to draw conclusions. Thus, in the deductive proof process, a good way of understanding is required regarding postulates, theorems, definitions, and other relevant properties to reach systematic conclusions.
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References
Aiyub, A. (2023). Ways of thinking siswa dalam menyelesaikan masalah pola bilangan non rutin: Suatu penelitian fenomenologi hermeneutik. Journal of Didactic Mathematics, 4(2), 65-76. http://dx.doi.org/10.34007/jdm.v4i2.1851
Budiarto, M. T., & Artiono, R. (2019). Geometri dan permasalahan dalam pembelajarannya (suatu penelitian meta analisis). Jurnal Magister Pendidikan Matematika (JUMADIKA), 1(1), 9-18. http://dx.doi.org/10.30598/jumadikavol1iss1year2019page9-18
Creswell, J. W. (2007). Qualitative inquiry & research design: Choosing among five approaches (Second Eds). Sage Publication, Inc. https://psycnet.apa.org/record/2006-13099-000
Ennis, R. H. (2011). The nature of critical thinking: An outline of critical thinking dispositions and abilities. University of Illinois, 2(4), 1-8.
Harel, G. (2008). What is mathematics? A pedagogical answer to a philosophical question. In B. Gold & R. A. Simons (Eds.), Proof and Other Dilemmas: Mathematics and Philosophy. United States of America: The Mathematical Association of America, Inc.
Harel, G. (2007). Students' proof schemes revisited. In Theorems in school (pp. 65-78). Brill. https://doi.org/10.1163/9789087901691_006
Harel, G. (2013). Intellectual need. In Vital directions for mathematics education research (pp. 119-151). New York, NY: Springer New York.
Harel, G. (1998). Two dual assertions: The first on learning and the second on teaching (or vice versa). The American Mathematical Monthly, 105(6), 497-507. https://doi.org/10.2307/2589401
Harel, G., & Sowder, L. (1998). Students’ proof schemes: Results from exploratory studies. In A. Schoenfeld, J. Kaput, & E. Dubinsky (Eds.), Research in collegiate mathematics education III (pp. 234-283). Providence, RI: American Mathematical Society.
Ikhsan, M., Munzir, S., & Fitria, L. (2017). Kemampuan Berpikir Kritis dan Metakognisi dalam Menyelesaikan Masalah Matematika Melalui Pendekatan Problem Solving. Aksioma: Jurnal Program Studi Pendidikan Matematika, 6 (2), 234-245. http://dx.doi.org/10.24127/ajpm.v6i2.991
Karakoç, M. (2016). The Significance of Critical Thinking Ability in Terms of Education. International Journal of Humanities and Social Science, 6 (7), 81-84.
Lusiyana, D. (2024). Systematic Literatur review: Satu Dekade Penelitian Kemampuan Spasial dan ICT. JUMLAHKU: Jurnal Matematika Ilmiah STKIP Muhammadiyah Kuningan, 10(1), 177-189. https://doi.org/10.33222/jumlahku.v10i1.3692
Maarif, S. (2016). Mengkonstruksi bukti geometri melalui kegiatan eksplorasi berbantu Cabri II Plus. Euclid, 3(2). http://dx.doi.org/10.33603/e.v3i2.331
Masfingatin, T., Murtafiah, W., & Krisdiana, I. (2018). Kemampuan mahasiswa calon guru matematika dalam pemecahan masalah pembuktian teorema geometri. Jurnal Mercumatika: Jurnal Penelitian Matematika Dan Pendidikan Matematika, 2(2), 41-50. https://doi.org/10.26486/jm.v2i2.272
Prayitno, A. (2018). Characteristics of Students' Critical Thinking in Solving Mathematics Problems. The Online Journal of New Horizons in Education, 8 (1), 46- 55. http://www.tojned.net/journals/tojned/articles/v08i01/v08i01-06.pdf
Prihandhika, A., Prabawanto, S., Turmudi, T., & Suryadi, D. (2020, April). Epistemological obstacles: an overview of thinking process on derivative concepts by apos theory and clinical interview. In Journal of Physics: Conference Series (Vol. 1521, No. 3, p. 032028). IOP Publishing. https://dx.doi.org/10.1088/1742-6596/1521/3/032028
Rasiman. (2015). Leveling of Critical Thinking Abilities of Students of Mathematics Education in Mathematical Problem Solving. IndoMS-JME (IndoMS-Journal of Mathematics Education), 6 (1), 40-52. http://dx.doi.org/10.22342/jme.6.1.1941.40-52
Rich, B. 2004. Geometri Schaum’s Easy Outlines. Ed. Wibi Hardani. Jakarta: Erlangga.
Santosa, C. A. (2013). Mengatasi Kesulitan Mahasiswa Ketika Melakukan Pembuktian Matematis Formal. Jurnal Pengajaran MIPA, 18 (2), 152- 160. https://doi.org/10.18269/jpmipa.v18i2.36130
Suandi, B. (2017). Bukti Informal dalam Pembelajaran Matematika. Al-Jabar: Jurnal Pendidikan Matematika, 8 (1), 13-24. https://dx.doi.org/10.24042/ajpm.v8i1.1160
Susanah & Hartono. 2004. Geometri. Surabaya: Unesa University Press
Yazidah, N. I. (2017). Analisis kesalahan menyelesaikan soal pembuktian geometri Euclid ditinjau dari gender pada mahasiswa IKIP Budi Utomo Malang. Kalamatika: Jurnal Pendidikan Matematika, 2(1), 71-80. http://dx.doi.org/10.22236/KALAMATIKA.vol2no1.2017pp71-80
Yerizon. (2011). Peningkatan Kemampuan Pembuktian dan Kemandirian Belajar Matematik Mahasiswa Melalui Pendekatan M-APOS. Bandung: Disertasi Universitas Pendidikan Indonesia.
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