PROSES BERPIKIR REFLEKTIF SISWA KELAS X MAN NGAWI DALAM PEMECAHAN MASALAH BERDASARKAN LANGKAH KRULIK DAN RUDNICK DITINJAU DARI KEMAMPUAN AWAL MATEMATIKA

Abstract

Abstract: The aim of this research was to describe reflective thinking process of 10^th grade MAN Ngawi students with different initial mathematics capability (high, normal, low) in solving problems based on Krulik and Rudnick steps. This research was a kind of qualitative research on a case study. The collecting data in this study used task-based on interview method. The analyzed of the data in this study did with reducing the data, presenting the data, and conclusing the data. The results of this research were: 1) on reading and thinking step, students with normal and low initial mathematics capability convince what they read and thought correctly by reading repeatedly. Students with high initial mathematics capability did it by reading and understanding each question sentences repeatedly; 2) on exploring and planing step, selecting and considering information, both students with high and normal initial mathematics capability did these steps by information identification and analysis of main problems and conditions; to convince that initial problem solving planning was right, they did it by organizing problem and deciding the initial steps planned; 3) on selecting a strategy step, to consider confidently the problem solving step based on information obtained, students with high initial mathematics capability did the step by exploring initial problem solving strategy and using representation result by trial-error and guessing test, concerning problem solving pattern, and recheck every step done. Students with normal initial capability did it by exploring initial problem solving strategy and using representation result by trial-error step, making proper initial plan by question stimulation. 4) on finding an answer step, to understand each steps based on selected problem solving strategy, both students with high and normal initial mathematics capability did it by (a) ascertain formula that used for the area of that shapes, triangle area if known two sides which flank an angle, and comparing trigonometry on special angle correctly (students with normal capability used question stimuly); (b) trying repeatedly using selected patterns and recheck every step and calculation done; and (c) aware of each mistakes (computation, formula, way, and writing) and fixed them (students with normal capability needed question stimuly and wrong answering strategy). Student with high initial capability combined the process by paying attention and rechecking every steps and calculation by step back process. 5) on reflecting and extending step, to considering results and problems, students with high initial mathematics capability did it by reflection to get solution and rechecking by verification process. Students with normal capability did it by rechecking and looking back the problem and result obtained. In every steps, students with high initial mathematics capability always used intuition and self-questioning to convince the step done. 10^th grade MAN Ngawi students with low initial mathematics capability did not use reflective thinking in problem solving based on Krulik and Rudnick.

Keywords: Process, reflective thinking, problem solving, and initial mathematics capability.