Bukti yang Membuktikan dan Bukti yang Menjelaskan dalam Kelas Matematika
DOI:
https://doi.org/10.36312/e-saintika.v4i2.253Keywords:
Bukti yang Membuktikan, Bukti yang Menjelaskan, Proofs that Prove, Proofs that ExplainAbstract
Tujuan penelitian ini adalah mendeskripsikan secara komprehensif perbedaan bukti yang membuktikan dan bukti yang menjelaskan berdasarkan pertimbangan implikasi kedua bukti tersebut sebagai dasar konstruksi penalaran dan bukti dalam matematika. Kajian dijalani dengan kegiatan menguraikan perbedaan spesifik antara keduanya serta memberikan contoh kasus kedua bukti, dan memberikan justifikasi atas pentingnya pengenalan kedua bukti dalam kelas matematika. Kedua bukti digambarkan dengan permasalahan konsep barisan bilangan ganjil. Bukti yang membuktikan hanya menunjukkan dengan menggunakan induksi matematis, sementara bukti yang menjelaskan menunjukkan dengan bukti Gauss, representasi geometrik bangun titik, dan garis zig-zag. Perbedaan antara keduanya tampak pada pemberian alasan yang berasal dari bukti itu sendiri. Hasil kajian mengindikasikan bahwa peran bukti dalam kelas matematika pada tingkat perguruan tinggi adalah membuktikan/meyakinkan, pada tingkat menengah atas adalah membuktikan dan menjelaskan, dan pada tingkat sekolah menengah pertama dan dasar peran utamanya adalah menjelaskan. Akibatnya bukti matematis tidak hanya membuktikan/menyakinkan, melainkan juga menjelaskan. Karenanya penting mempertimbangkan implikasi bukti dalam kurikulum matematika di sekolah, serta perlunya menyajikan bab materi kepada mahasiswa pendidikan matematika tidak hanya bukti yang membuktikan, melainkan juga bukti yang menjelaskan.
Proofs that Prove and Proofs that Explain in Mathematics Classroom
Abstract
The purpose of this study was to comprehensively describe the differences of the proofs that prove and proofs that explain based on the consideration of the implications of the two proofs as the basis for the construction reasoning and proofs in mathematics. The study was undertaken with the activity of describing the specific differences between the two and providing examples of cases of both proofs; and provide justification for the importance of introducing both proofs in mathematics classrooms. Both proofs are illustrated by the problem of the odd number sequence concept. Proofs that prove is only shown using mathematical induction, while proofs that explain shows with Gaussian proof, a geometric representation of point shape, and zigzag line. The difference between the two appears to be the reasoning that comes from the proof itself. The results of the study indicate that the role of proof in mathematics classes at the tertiary level is proving/convincing, at the senior secondary level it is proving and explaining, and at the junior and elementary school level its main role is explaining. As a result, mathematical proof does not only prove/convince, but also explain. It is therefore important to consider the implications of proof in the mathematics curriculum in schools, as well as the need to present chapter materials to mathematics education students not only proofs that prove but also proof that explain.
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