Proses Berpikir Mahasiswa Pendidikan Matematika Dalam Pemecahan Masalah Pembuktian Tahun Akademik 2014/2015

Abstract

This research aimed to describe the thinking process in proof problem solving using direct, contraposition, and contradiction methods in 2 nd semester mathematic education students of Nusantara PGRI University of Kediri with (1) high, (2) moderate, and (3) low learning achievements. The research method employed was qualitative approach. Subject of research was selected using purposive sampling technique, consisting of 6 2 nd-semester mathematic education students: 2 students with high, 2 with moderate, and 2 with low learning achievements. Data collection was carried out using interview based on proof problem solving assignment. Data validation was carried out using time triangulation, and the valid data was analyzed using data reduction, data display, and conclusion drawing. The result of research showed that: (1) The thinking process of students with high learning achievement. The proof problem solving in direct contraposition, and contradiction ways. In entry phase, the subjects understood the problem by writing antecedent as they know and consequence to be proved. In finishing phase, the subjects explained antecedent into premise correctly and completely, did algebraic operation to connect consequence to premise, in order to prove the consequence. In review phase, the subjects check their answer and were sure with their answer after seeing the process and proof result. (2) The thinking process of students with moderate learning achievement. The proof problem solving in direct, contraposition, and contradiction ways. In entry phase, the subjects understood the problem by writing antecedent as they know and consequence to be proved. In finishing phase, the subjects explained antecedent into premise correctly, did algebraic operation with summing procedure and distributive property to connect consequence to premise in order to prove the consequence. In review phase, the subjects did not check their answer and were sure with their answer when their proved. (3) The thinking process of students with low learning achievement. The proof problem solving in direct, contraposition, and contradiction ways. In entry phase is the same, the subjects understood the problem by writing antecedent as they know and consequence to be proved. In finishing phase, the subjects explained antecedent into premise difficultly, did algebraic operation with summing procedure and distributive property to connect consequence to premise using number example, thereby could not prove the consequence. Then in review phase, the subjects did not check their answer and were sure with their answer after seeing their proof result.

Analisis Kemampuan Pemecahan Masalah Soal Cerita Ditinjau Dari Gaya Kognitif Siswa

“…Pemecahan masalah matematika adalah proses menerapkan pengetahuan yang diperoleh sebelumnya ke situasi baru yang tidak biasa (Rismen et al, 2022) (Aisyah, 2018). Seseorang yang menganggap suatu masalah bukanlah suatu masalah, yaitu ketika orang tersebut telah mengetahui suatu cara atau proses untuk mencari pemecahannya (Yohanie et al, 2016).…”

Systematic Literature Review: Kemampuan Pembuktian Matematis

“…Berdasarkan studi literatur ini ditemukan bahwa sebagian mahasiswa maupun siswa sudah mampu melakukan pembuktian matematis (Adamura & Susanti, 2018;Faizah et al, 2022;Firmasari & Sulaiman, 2019;W. O. Handayani & Rahaju, 2018;Hermanto et al, 2016;Hidayati & Wahyuni, 2020;Maulana et al, 2021;Muliawati, 2018;Multahadah & Mardhotillah, 2022;Novyta, 2022;Perbowo & Pradipta, 2017;Sutiarso, 2019;Waluyo & Sari, 2017;Wulandari & Lestari, 2021;Yohanie et al, 2016) meskipun masih diungkapkan beberapa kesulitan yang dialami siswa maupun mahasiswa seperti pada penelitian (Dadan Sundawan et al, 2018; U. F. Handayani et al, 2022;Kiik et al, 2021;Novyta, 2022;Perbowo & Pradipta, 2017;Waluyo & Sari, 2017;Yazidah et al, 2022).…”

“…Beberapa contoh hasil penelitian sebelumnya mengungkapkan bahwa kemampuan pembuktian matematis rendah menunjukkan ketidakmampuan memahami alur pembuktian serta menyusun rencana pembuktian (Firmasari & Sulaiman, 2019;Hendana & Lestari, 2021), kemampuan pembuktian matematis tinggi dan sedang sudah mampu melakukan pembuktian dengan benar meski untuk kategori sedang masih ada beberapa pembuktian yang kurang lengkap (Firmasari & Sulaiman, 2019;Muliawati, 2018;Multahadah & Mardhotillah, 2022;Novyta, 2022;Sutiarso, 2019;Suwanti & Fayeldi, 2018;Yohanie et al, 2016).…”