Kemampuan Mengkonstruksi Bukti Geometri Mahasiswa Calon Guru Matematika Pada Perkuliahan Geometri
DOI:
https://doi.org/10.29408/jel.v6i2.2012Keywords:
construct the proof of geometry, geometry proof, proofAbstract
This study aims to analyze and describe the ability to construct proofs of perspective teacher mathematics students in basic geometrical lectures on the concepts of alignment, triangles, and concordance of two triangles. This research uses a descriptive qualitative method involving 35 prospective mathematics students at the Universitas PGRI Semarang. This study uses a qualitative descriptive method involving 35 students. The results of this study show that: (1) 28% of students sketched diagrams and used geometric labels appropriately on the constructed evidence; (2) 28.57% of students have the correct initial step of proof; (3) 28.57% of students can determine the exact conjecture that leads to the correct proof; (4) 25.71% of students are correct in compiling proof arguments by the correct postulate and theorem; (5) 25.71% of the thought flow process used by coherent students leads to valid evidence; and (6) 22.86% of students mastered theorems and concepts used in compiling constructing proof.
References
Arnawa, I. M., Sumarno, U., Kartasasmita, B., & Baskoro, E. T. (2007). Applying the Apos Theory to improve students ability to prove in elementary abstract algebra. Journal of the Indonesian Mathematical Society, 13(1), 133–148. https://doi.org/10.22342/jims.13.1.80.133-148.
Asyhar, B. (2015). Analisis kemampuan mahasiswa dalam menyelesaikan soal pembuktian tentang isomorfisma grup. Jurnal Tadris Matematika, 2(2). 127–135. https://doi.org/10.21274/jtm.2019.2.2.111-126.
Azrou, N., & Khelladi, A. (2019). Why do students write poor proof texts? A case study on undergraduates’ proof writing. Educational Studies in Mathematics, 102(2), 257-274. https://doi.org/10.1007/s10649-019-09911-9.
Bieda, K. N., Ji, X., Drwencke, J., & Picard, A. (2014). Reasoning-and-proving opportunities in elementary mathematics textbooks. International Journal of Educational Research, 64, 71–80. https://doi.org/10.1016/j.ijer.2013.06.005.
Cervantes-Barraza, J. A., Hernandez Moreno, A., & Rumsey, C. (2020). Promoting mathematical proof from collective argumentation in primary school. School Science and Mathematics, 120(1), 4–14. https://doi.org/10.1111/ssm.12379.
Daguplo, M. S., & Development, H. R. (2014). How well do you write proof? characterizing students proof - writing skill vis - à - vis van hiele’s model in geometrical proving. Journal of Educational and Human Resource Development, 2, 104-114.
Dimakos, G., Nikoloudakis, E., Ferentinos, S., & Choustoulakis, E. (2007). Developing a proof-writing tool for novice lyceum geometry students. The Teaching of Mathematics, 10(2), 87–106.
Fiallo, J., & Gutiérrez, A. (2017). Analysis of the cognitive unity or rupture between conjecture and proof when learning to prove on a grade 10 trigonometry course. Educational Studies in Mathematics, 96(2), 145–167. https://doi.org/10.1007/s10649-017-9755-6.
Firmasari, S., & Sulaiman, H. (2019). Kemampuan pembuktian matematis mahasiswa menggunakan induksi matematika. Journal of Medives : Journal of Mathematics Education IKIP Veteran Semarang, 3(1), 1-9. https://doi.org/10.31331/medivesveteran.v3i1.642.
Harini, L. P. I., & Oka, T. B. (2016). Penggunaan mind map dalam matematika. Jurnal Matematika, 6(1), 56–67.
Heinze, A., & Reiss, K. M. (2002). Reasoning and proof: methodological knowledge as a component of proof competence. European Research in Mathematics Education, III, 1–10.
Hilbert, T. S., Renkl, A., Kessler, S., & Reiss, K. (2008). Learning to prove in geometry: Learning from heuristic examples and how it can be supported. Learning and Instruction, 18(1), 54–65. https://doi.org/10.1016/j.learninstruc.2006.10.008.
Hodds, M., Alcock, L., & Inglis Loughborough, M. (2014). Self-explanation training improves proof comprehension. Journal for Research in Mathematics Education, 45(1), 62–101. https://doi.org/10.5951/jresematheduc.45.1.0062.
Isnarto, (2014). Kemampuan konstruksi bukti dan berpikir kritis matematis mahasiswa pada perkuliahan struktur aljabar melalui guided discovery learning pendekatan motivation to reasoning and proving tasks. Disertasi tidak dipublikasikan, Bandung, Universitas Pendidikan Indonesi.
Jones, K. (2010). Proving in geometry. Proceedings of the British Society for Research into Learning Mathematics, 30(2), 62-67.
Komatsu, K., & Jones, K. (2019). Task design principles for heuristic refutation in dynamic geometry environments. International Journal of Science and Mathematics Education, 17(4), 801–824. https://doi.org/10.1007/s10763-018-9892-0.
Kuusi, T., Mingione, G., & Nyström, K. (2014). Sharp regularity for evolutionary obstacle problems, interpolative geometries and removable sets. Journal Des Mathematiques Pures et Appliquees, 101(2), 119–151. https://doi.org/10.1016/j.matpur.2013.03.004.
Leech, N. L., & Onwuegbuzie, A. J. (2007). An array of qualitative data analysis tools: a call for data analysis triangulation. School Psychology Quarterly, 22(4), 557–584. https://doi.org/10.1037/1045-3830.22.4.557.
Lindsay, R. K. (1998). Using diagrams to understand geometry. Computational Intelligence, 14(2), 238–272. https://doi.org/10.1111/0824-7935.00062.
Maarif, S., Perbowo, K. S., Noto, M. S., & Harisman, Y. (2019). Obstacles in constructing geometrical proofs of mathematics-teacher-students based on Boero’s proving model. Journal of Physics: Conference Series, 1315, 012043. https://doi.org/10.1088/1742-6596/1315/1/012043.
Maarif, S., Wahyudin, Noto, M. S., Hidayat, W., & Mulyono, H. (2018). Geometry exploration activities assisted with Dynamic Geometry Software (DGS) in a teacher education classroom. Infinity Journal, 7(2), 133-146. https://doi.org/10.22460/infinity.v7i2.p133-146.
Magajna, Z. (2013). Overcoming the obstacle of poor knowledge in proving geometry. CEPS journal, 3(4), 99-116.
Magro, T. D. (2019). On Euclidean diagrams and geometrical knowledge. Theoria 34(2), 255-276. https://doi.org/10.1387/theoria.20026.
Mariotti, M. A., & Pedemonte, B. (2019). Intuition and proof in the solution of conjecturing problems’. ZDM - Mathematics Education, 51(5), 759-777. https://doi.org/10.1007/s11858-019-01059-3.
Masters, J. (2010). Automated scoring of an interactive geometry item: A proof-of-concept. Journal of Technology, Learning, and Assessment, 8(7), 1-38.
Michael, P., Gagatsis, C., & Gagatsis, A. (2013). Geometrical figures in geometrical task solving: an obstacle or a heuristic tool?. Acta Didactica Universitatis Comenianae. Mathematics, 2013(13), 17–32.
Middleton, T. J. (2009). Development of scoring rubrics and pre-service teachers ability to validate mathematical proofs. Digital Library The University Mexico. Diambil dari https://digitalrepository.unm.edu/math_etds/30.
Ningrum, R., & Mega, T. . (2015). Alur berpikir siswa SMP dalam membuktikan teorema Pythagoras melalui tugas pengajuan soal ditinjau dari perbedaan jenis kelamin. MATHEdunesa Jurnal Ilmiah Pendidikan Matematika, 3(3), 59–66.
Otten, S., Gilbertson, N. J., Males, L. M., & Clark, D. L. (2014). The mathematical nature of reasoning-and-proving opportunities in geometry textbooks. Mathematical Thinking and Learning, 16(1), 51–79. https://doi.org/10.1080/10986065.2014.857802.
Ozturk, B. M. (2020). Cognitive and metacognitive skills performed by math teachers in the proving process of number theory. Athen Journal of Education, 7(1).1–19.
Pegg, J., Gutiérrez, A., & Huerta, P. (1998). Assessing reasoning abilities in geometry. New ICMI Studies Series, 5. 275–295.
Reiss, K., & Renkl, A. (2002). Learning to prove: The idea of heuristic examples. ZDM - International Journal on Mathematics Education, 34(1), 29–35. https://doi.org/10.1007/BF02655690.
Sommerhoff, D., & Ufer, S. (2019). Acceptance criteria for validating mathematical proofs used by school students, university students, and mathematicians in the context of teaching. ZDM, 51(5), 717-730.
Tripathi, P. N. (2020). Exploring the use of deductive logic in geometry AS. International Conference to Review Research in Science, Technology and Mathematics Education (2), 91–100.
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. https://doi.org/10.22236/KALAMATIKA.vol2no1.2017pp71-80.
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