MENGGUNAKAN CONTOH DALAM PEMBUKTIAN

Christina Kartika Sari; Mohamad Waluyo; Citra Maharani Ainur; Eka Nurhayati Darmaningsih

doi:10.26877/jipmat.v2i1.1475

MENGGUNAKAN CONTOH DALAM PEMBUKTIAN

Christina Kartika Sari, Mohamad Waluyo, Citra Maharani Ainur, Eka Nurhayati Darmaningsih

Abstract

Penelitian ini bertujuan mengidentifikasi bukti-bukti yang dihasilkan mahasiswa dalam memecahkan soal-soal Pengantar Analisis Riil, khususnya bukti yang memanfaatkan contoh spesifik. Pendekatan yang digunakan adalah kualitatif. Subyek diambil dari 54 mahasiswa yang menempuh mata kuliah Pengantar Analisis Riil. Seluruh subjek dihadapkan pada dua soal pembuktian. Dari 54 mahasiswa, tidak lebih dari 15% yang mampu menuliskan bukti yang valid. Sekitar 30% masih belum memiliki pengetahuan yang cukup untuk dapat dirangkai menjadi sebuah bukti yang valid, sehingga mereka gagal dalam membuktikan. Hampir 30% mahasiswa tampak berhasil menyelesaikan pembuktian, tapi ternyata bukti tersebut tidak valid, salah satunya Putri. Putri memilih satu contoh spesifik untuk membuktikan suatu pernyataan implikasi yang general. Contoh yang dipilih Putri pun mengabaikan asumsi-asumsi yang diminta oleh soal. Selain itu, Putri tampak mencampuradukkan definisi dan teorema yang sekiranya terkait dengan soal. Oleh karena itu, pembelajaran Pengantar Analisis Riil hendaknya menekankan pemahaman definisi, teorema, lemma, maupun pernyataan matematika lainnya dengan lebih bermakna.

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DOI: https://doi.org/10.26877/jipmat.v2i1.1475