ANALISIS PROSES BERPIKIR REFLEKTIF SISWA DALAM MEMECAHKAN MASALAH MATEMATIKA NON RUTIN DI KELAS VIII SMP ISLAMIC INTERNATIONAL SCHOOL PESANTREN SABILIL MUTTAQIEN (IIS PSM) MAGETAN DITINJAU DARI KEMAMPUAN AWAL

Abstract: This study aimed at describing reflective thinking process of eight graders of SMP Islamic International School Pesantren Sabilil Muttaqien (IIS PSM) Magetan viewed from high, moderate, and low initial abilities of Mathematics in solving non routine mathematical problems. Initial abilities of Mathematics influenced problem solving skill of students. Problem solving skill should be developed not only to obtain the solution but also to make students think for explaining the reasons in every problem solving steps. Therefore, one way to develop that skill was by reflective thinking process. This study was qualitative descriptive research. Subjects of this study were eight students from VIII grade of SMP IIS PSM Magetan and represented each mathematics ability categories. Those subjects were determined by purposive sampling. For collecting data, this study used task-based and in-depth interview methods, then time triangulation was used to validate the collected data. Meanwhile, data analysis in this study was qualitative descriptive including data reduction, data display, and verification. The results of this study showed that students with high initial ability in Mathematics had reflective thinking process in four steps of problem solving (Polya), as follows: (a) understanding problem, retelling the problems, and identifying the information, (b) devising strategy, relating the given information and believing that it will find solution, (c) conducting strategy, explaining how to solve the problem based on plan clearly and reasonably, realizing some mistakes and revising it, and believing that those solution are the correct one, and (d) looking back, checking all problem solving steps and the solution based on the constraints or the given information, revising some parts, and giving alternative strategy or solution. In the other hand, students with moderate inital ability in Mathematics had reflective thinking process in three steps of problem solving, as follows: (a) understanding problem, retelling the problems, identify the information, (b) devising strategy, relating the given information for devising a plan by clear consideration, (c) conducting strategy, explaining how to solve the problem based on plan, realizing some mistakes and revising it, and believing that those solution are the correct one. Meanwhile, students with low initial ability in Mathematics only had reflective thinking process in understanding problem, that retelling the problems and identifying the given and asked information of the problems.Key words: reflective thinking, problem solving, non routine problems, inital ability in Mathematic