Analisis Kemampuan Siswa dalam Pembuktian Kesebangunan Dua Segitiga

Yayan Eryk Setiawan

Abstract


Abstract:

Mathematics learning in junior high is inseparable from proof, including of congruence of two triangles. This study analyzes the ability to prove the similarity of two triangles. The procedure used (1) grouped the answers of 51 students based on categories of able, underprivileged and unable, (2) analyzing the ability of evidence-based basic mathematical knowledge, representation of evidence, and assumptions used. The result (1). students who can prove have basic knowledge of the Pythagoras theorem, algebra operations, and the principle of equality, the representations used are symbolic and formal evidence, the assumptions used are logical. (2) Students who are unable to prove to have basic knowledge of congruence, comparison, and the principle of equality, the representation used is visual and formal evidence, the assumptions used are logical. (3) Students who have not been able to prove to have the basic knowledge that is not relevant in supporting evidence, the representation used is symbolic evidence but is wrong in algebraic manipulation and informal evidence, students' assumptions are lacking or illogical.

Abstrak:

Pembelajaran matematika di SMP tidak terlepas dari pembuktian termasuk kesebangunan dua segitiga. Penelitian ini menganalisis kemampuan siswa dalam membuktikan kesebangunan dua segitiga. Prosedur yang digunakan (1) mengelompokkan jawaban 51 siswa berdasarkan kategori mampu, kurang mampu dan belum mampu, (2) menganalisis kemampuan pembuktian berdasarkan pengetahuan matematis dasar, representasi bukti, serta asumsi yang digunakan. Diperoleh hasil bahwa (1). siswa yang mampu membuktikan memiliki pengetahuan dasar teorema Pythagoras, operasi aljabar, dan prinsip kesetaraan, representasi yang digunakan berupa bukti simbolis dan formal, asumsi yang digunakan adalah logis. (2) Siswa yang kurang mampu membuktikan memiliki pengetahuan dasar kesebangunan, perbandingan, dan prinsip kesetaraan, representasi yang digunakan adalah bukti visual dan formal, asumsi yang digunakan adalah logis. (3) Siswa yang belum mampu membuktikan memiliki pengetahuan dasar yang tidak relevan dalam mendukung pembuktian, representasi yang digunakan adalah bukti simbolis, tetapi salah dalam manipulasi aljabar dan bukti tidak formal, asumsi siswa kurang atau tidak logis.


Keywords


Similarity of two triangles.; The ablitiy to Prove.

Full Text:

PDF

References


Chartouny, Madona, Iman Osta, and Nawal Abou Raad. “A Framework for Failed Proving Processes in a Dynamic Geometry Environment.” Mathematics and Technology, 2017, 225.

Djumanta, Wahyudin, and Dwi Susanti. Belajar Matematika Aktif Dan Menyenangkan. Jakarta: Grasindo, 2008.

Ernest, Paul, Ole Skovsmose, Jean Paul Van Bendegem, Maria Bicudo, Roger Miarka, Ladislav Kvasz, and Regina Moeller. “The Philosophy of Mathematics Education,” 1991.

Fujita, Taro, and Keith Jones. “Reasoning-and-Proving in Geometry in School Mathematics Textbooks in Japan.” International Journal of Educational Research 64 (2014): 81–91.

Knuth, Eric J. “Secondary School Mathematics Teachers’ Conceptions of Proof.” Journal for Research in Mathematics Education, 2002, 379–405.

Mathematics, Research Advisory Committee of the National Council of Teachers of. “NCTM Curriculum and Evaluation Standards for School Mathematics: Responses from the Research Community.” Journal for Research in Mathematics Education 19, no. 4 (1988): 338–44. https://doi.org/10.2307/749544.

Solfitri, Titi, and Yenita Roza. “Analisis Kesalahan Dalam Menyelesaikan Soal-Soal Geometri Siswa Kelas IX SMPN Se-Kecamatan Tampan Pekanbaru.” SEMIRATA 2015 1, no. 1 (2015).

Stylianou, Despina A., Maria L. Blanton, and Eric J. Knuth, eds. Teaching and Learning Proof Across the Grades: A K-16 Perspective. 1 edition. New York: Routledge, 2009.

Subchan, Winarni, Lukman Hanafi, M. Syifa’ul Mufid, Kistosil Fahim, and Wawan Hafid Syaifudin. Matematika SMP/MTs Kelas IX - Semester 1 - Kurikulum 2013 - Edisi Revisi 2015. Jakarta: Kementerian Pendidikan dan Kebudayaan, 2018. https://www.myedisi.com/bse/25202/matematika.

Tall, David. “Cognitive Development, Representations and Proof.” In Proceedings of the Conference Justifying and Proving in School Mathematics, 27:38, 1995.

Yayan Eryk Setiawan. “Ketercapaian Indikator Keterampilan Dasar Dalam Berpikir Kritis Pada Siswa SMP.” Jurnal Pendidikan Dan Pengembangan Profesi 6, no. 2 (2016): 242–51.

Yayan Eryk Setiawan, and Sunardi. “Profil Keterampilan Berpikir Kritis Siswa SMP,” 1:933–42. Malang: Program Studi S2-S3 Pendidikan Matematika Pascasarjana Universitas Negeri Malang, 2016. https://scholar.google.co.id/citations?user=-eo91IMAAAAJ&hl=en#d=gs_md_cita-d&u=%2Fcitations%3Fview_op%3Dview_citation%26hl%3Den%26user%3D-eo91IMAAAAJ%26citation_for_view%3D-eo91IMAAAAJ%3A9yKSN-GCB0IC%26tzom%3D-480.

Zhang, Dake. “Effects of Visual Working Memory Training and Direct Instruction on Geometry Problem Solving in Students with Geometry Difficulties.” Learning Disabilities: A Contemporary Journal 15, no. 1 (2017): 117–138.




DOI: https://doi.org/10.24256/jpmipa.v8i1.800

Article Metrics

Abstract view : 41 times
PDF - 17 times

Refbacks

  • There are currently no refbacks.


View My Stats