Kesulitan Siswa dalam Membuktikan Masalah Kesamaan dan Ketidaksamaan Matematika Menggunakan Induksi Matematika

Abstract

Mathematical similarities and inequalities are common mathematical statements related to numbers whose truth can be proven by mathematical induction. Proving by mathematical induction involves two main steps, namely the basic step and the induction step. The study of mathematical induction related to similarity and inequality is very important and is still relatively limited in quantity. This study aims to determine whether there are significant differences in students' ability to prove mathematical statements using mathematical induction on mathematical similarities and inequalities problems and identify misconceptions. The study was conducted with a mixed method. A sample of 117 students from two high schools in the city of Singaraja was selected by a random cluster technique to obtain quantitative data. Meanwhile, the research subjects were two students selected based on the misconceptions shown to obtain qualitative data. Quantitative data on the ability to prove the similarity and inequality problems using mathematical induction was collected by written tests and qualitative data on misconceptions were collected by interview. Quantitative data were analyzed by a paired group t-test and by z test for proportions. Meanwhile, qualitative data were analyzed by content analysis of students' works to identify their misconceptions. The results showed that proving the mathematical induction of the inequality problem was more difficult than proving the similarity problem. This difficulty occurs both in the basic step and the induction step. Misconceptions arise due to the fallacy of analogies and interpretations of mathematical notation.