Berpikir siswa level deduksi dalam membuktikan teorema kesebandingan segitiga dan konversnya berdasarkan langkah-langkah Polya
Thinking of deduction level students in proving theorem of triangle and its convers based on the steps of Polya
Abstract
Proving ability is rarely homed in mathematics learning. Thus, this becomes interesting when examined and associate it with van Hiele’s level of geometrical thinking, namely the level of deduction. This study aims to determine the thinking process of student’s level deduction in proving Triangle Proportionally Theorems and its convers. This type of research is qualitative research. Deduction level students were given a theorem proving test consist of two questions, then conducted interviews to find out more about the thinking process. The results are students level deduction can prove the theorem by utilizing the knowledge possessed both undefined terms (point and line), parallel and similarity AAA postulates, definitions of angle and congruence, parallel and similarity SAS~ theorems, corollary CSSTP and CASTC. It can be known from the student’s proving scheme and interviews that is conducted by researcher towards student.
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References
Agostino, S. D. (2011). A math major, polya , invention, and discovery. Journal of Humanistic Mathematics, 1(2), 51–55.
Alexander, D. C., & Koeberlein, G. M. (2011). Elementary Geometry for College Students. Canada: Cengage Learning.
Aminudin, M., & Kusmaryono, I. (2019). Upaya Guru Matematika Dalam Mengembangkan Kemampuan Berpikir Kritis Siswa. MATH Didactic : Jurnal Pendidikan Matematika, 5(3), 248–258. Retrieved from http://jurnal.stkipbjm. ac.id/index.php/math.
Ben-Ari, M. (2012). Mathematical Logic for Computer Science. In Theory and Practice of Logic Programming (Vol. 2). https://doi.org/10.1017/S1471068402001187.
Bulut, N., & Bulut, M. (2012). Development of Pre-Service Elementary Mathematics Teachers’ Geometric Thinking Levels Through an Undergraduate Geometry Course. Procedia - Social and Behavioral Sciences, 46, 760–763. https://doi.org/10.1016/j.sbspro.2012.05.194.
Coronado, W. A., Luna, C. A., & Tarepe, D. A. (2017). Improving students van Hiele and proof-writing ability using Geometer’s sketchpad. Journal of Social Sciences (COES&RJ-JSS), 6(2S), 55–74. https://doi.org/10.25255/jss.2017.6.2s.55.74.
Falupi, D. V., & Widadah, S. (2016a). Profil Berpikir Geometris pada Materi Bangun Datar Ditinjau dari Teori Van Hiele. Jurnal Pendidikan Matematika STKIP PGRI Sidoarjo, 4(1), 1–8.
Falupi, D. V., & Widadah, S. (2016b). Profil BerpikirGeometris Pada Materi Bangun Datar Ditinjau Dari Teori Van Hiele. Jurnal Pendidikan Matematika STKIP PGRI Sidoarjo, 4(1), 1–8.
Feza, N., & Webb, P. (2012). Assessment standards, Van Hiele levels, and grade seven learners’ understandings of geometry. Pythagoras. https://doi.org/ 10.4102/pythagoras.v0i62.113.
Fitriyani, H., Yudianto, E., Maf’Ulah, S., Fiantika, F. R., & Hariastuti, R. M. (2020). Van Hiele’s Theory: Transforming and Gender Perspective of Student’s Geometrical Thinking. Journal of Physics: Conference Series, 1613(1). https://doi.org/10.1088/1742-6596/1613/1/012070.
Fuys, D., Geddes, D., & Tischler, R. (1988). The Van Hiele Model of Thinking in Geometry among Adolescents. Source: Journal for Research in Mathematics Education. Monograph. https://doi.org /10.2307/749957.
Haviger, J., & Vojkůvková, I. (2015). The van Hiele Levels at Czech Secondary Schools. Procedia - Social and Behavioral Sciences, 171(May), 912–918. https://doi.org/10.1016/j.sbspro. 2015.01.209.
Hock, T. T., Tarmizi, R. A., Aida, A. S., & Ayub, A. F. (2015). Understanding the primary school students’ van Hiele levels of geometry thinking in learning shapes and spaces: A Q-methodology. Eurasia Journal of Mathematics, Science and Technology Education, 11(4), 793–802. https://doi.org/10.12973/eurasia.2015.1439a.
Kemendikbud. (2017). Matematika SMP/MTs Kelas VII. Jakarta: Pusat Kurikulum dan Perbukuan, Balitbang, Kemdikbud.
Kivkovich, N. (2015). A Tool for Solving Geometric Problems Using Mediated Mathematical Discourse (for Teachers and Pupils). Procedia - Social and Behavioral Sciences, 209, 519–525. https://doi.org/10.1016/j.sbspro.2015.11.282.
Martyanti, A. (2019). Profil Kemampuan Berpikir Kritis Siswa Tunanetra dalam Menyelesaikan Masalah Geometri Ditinjau dari Tingkat Kemampuan Akademik. Math Didactic: Jurnal Pendidikan Matematika, 5(3), 296–304.
Mason, M. (2014). The van Hiele Levels of Geometric Understanding. The Professional Handbook for Teachers: Geometry: Explorations and Applications.
Mccammon, J. E. (2018). Preservice Teachers ’Understanding Of Geometric Definitions And Their Use In The Concept Of Special Quadrilaterals. Georgia State University.
Noor, F., & Ranti, M. G. (2019). Hubungan antara kemampuan berpikir kritis dengan kemampuan komunikasi matematis siswa SMP pada pembelajaran matematika. Math Didactic: Jurnal Pendidikan Matematika, 5(1), 75–82. https://doi.org/10.33654/math.v5i1.470.
Noto, M. S., Priatna, N., & Dahlan, J. A. (2019). Mathematical Proof: the Learning Obstacles of Pre-Service Mathematics Teachers on Transformation Geometry. Journal on Mathematics Education, 10(1), 117–126. https://doi.org/10.22342/ jme.10.1.5379.117-126.
Nuthall, P. L., & Old, K. M. (2018). Intuition, the farmers’ primary decision process. A review and analysis. Journal of Rural Studies, 58(December 2017), 28–38. https://doi.org/10.1016/j.jrurstud.2017.12.012
Pavlovicova, G., & Zahorska, J. (2015). The Attitudes of Students to the Geometry and Their Concepts about Square. Procedia - Social and Behavioral Sciences, 197, 1907–1912. https://doi.org/10.1016/j. sbspro.2015.07.253.
Pegg, J. (2014). The van Hiele Theory. In Encyclopedia of Mathematics Education. https://doi.org/10.1007/978-94-007-4978-8_183
Polya, G. (2020). Physical Mathematics. In Mathematics and Plausible Reasoning, Volume 1. https://doi.org/10.2307/j.ctv 14164db.13.
Rinaldi, E. N. Z., Supratman, & Hermanto, R. (2019). Proses Berpikir Peserta Didik Ditinjau Dari Kemampuan Spasial Berdasarkan Level Berpikir Van. Journal of Authentic Research on Mathematics Education, 1(1), 38–45.
Senk, S. L. (1989). Van Hiele Levels and Achievement in Writing Geometry Proofs. Journal for Research in Mathematics Education, 20(3), 309–321. https://doi.org/10.2307/749519.
Sunardi. (2002). Hubungan antara Tingkat Penalaran Formal dan Tingkat Perkembangan Konsep Geometri Siswa. Jurnal Ilmu Pendidikan, 9(1), 43–54.
Sunardi, Yudianto, E., Susanto, Kurniati, D., Cahyo, R. D., & Subanji. (2019). Anxiety of students in visualization, analysis, and informal deduction levels to solve geometry problems. International Journal of Learning, Teaching and Educational Research, 18(4). https:// doi.org/10.26803/ijlter.18.4.10.
Todd, R. M. (2010). A Direct Proof of the Theorem: If a Line Divides Two Sides of a Triangle Proportionally, Then it is Parallel to the Third Side. School Science and Mathematics. https://doi.org/10.111 1/j.1949-8594.1966.tb13641.x.
Usiskin, Z. (1982). Van Hiele Levels and Achievement in Secondary School Geometry. CDASSG Project. United States of America: Chicago University.
Yuan, S. (2013). Incorporating Polya’s problem solving method in remedial math. Journal of Humanistic Mathematics, 3(1), 96–107.
Yudianto, E., Trapsilasiwi, D., Sunardi, Suharto, Susanto, & Yulyaningsih. (2019). The process of student’s thinking deduction level to solve the problem of geometry. Journal of Physics: Conference Series, 1321(2). https:// doi.org/10.1088/1742-6596/1321/2/0220 78.
Yulyaningsih. (2018). Proses Berpikir Siswa Peraih Medali Olimpiade Matematika dalam Memecahkan Masalah Geometri. Universitas Jember.
Zhumni, A. I., & Misri, M. A. (2013). Pengaruh Tingkat Berpikir Geometri (Teori Van Hiele) Terhadap Kemampuan Berpikir Siswa Dalam Mengerjakan Soal Pada Materi Garis Dan SUDUT. Eduma : Mathematics Education Learning and Teaching. https://doi.org/10.24235/EDU MA.V2I2.44.
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