Penalaran Kreatif Siswa SMP dalam Menyelesaikan Masalah Sistem Persamaan Linier Dua Variabel (SPLDV)

Abstract

Abstract: This study aims to describe the creative reasoning of junior high school students in solving the SPLDV problem. The description is based on four indicators. There are novelty, flexibility, plausibility, and mathematical foundation. This research is an explorative research with qualitative approach. This research was conducted on the students of class VIII-C SMP 13 Malang. Subsequently two research subjects were selected that satisfy all the indicators of creative reasoning and also considered the advice of the mathematics teacher. The results of the research that the subjects of S1 and S2 study using creative reasoning in solving the SPLDV problem, S1 and S2 satisfy all the creative reasoning indicators. There are (1) Novelty, S1 and S2 provide a unique strategy different from the standard strategy has been studied (elimination and substitution), which sum two known equations, to obtain an answer. (2) Flexibility, S1 and S2 completed SPLDV with different strategies. S1 and S2 using the method of elimination, mixed methods (elimination and substitution), as well as a unique method that is by summing two known linear equations. (3) Plausibility, S1 and S2 can provide arguments well. namely to provide a logical reason at each stage of completion. But at number 2, S2 uses intuitive intention, the idea that emerges as a guess and test strategy in making decisions based on feeling and intrinsic that produce spontaneous answers. (4) Mathematical foundation, S1 and S2 use the properties of algebraic operations well in completing the given SPLDV. There are operation of addition, subtraction and simplification.

Abstrak: Penelitian ini bertujuan untuk mendeskripsikan penalaran kreatif  siswa SMP dalam menyelesaikan masalah sistem persamaan linier dua variabel (SPLDV). Pendeskripsian tersebut menggunakan empat indikator, yaitu kebaruan (novelty), fleksibilitas (flexibility), hal yang masuk akal (plausibility) dan dasar matematis (mathematical foundation). Penelitian ini merupakan penelitian eksploratif dengan pendekatan kualitatif. Penelitian ini dilaksanakan pada siswa kelas VIII-C SMP 13 Malang. Selanjutnya, dipilih dua subjek penelitian yang memenuhi semua indikator penalaran kreatif dan juga mempertimbangkan saran dari guru matematika. Hasil penelitian menunjukkan subjek penelitian S1 dan S2 memenuhi semua indikator penalaran kreatif, yaitu (1) Kebaruan (novelty), S1 dan S2 memberikan strategi penyelesaian unik (baru) yang berbeda dengan strategi penyelesaian standart yang telah dipelajari. S1 dan S2 menggunakan strategi menjumlahkan 2 persamaan yang diketahui. (2) Fleksibilitas (flexibility), S1 dan S2 dapat menyelesaikan SPLDV dengan tiga strategi. S1 dan S2 menggunakan metode eliminasi, metode campuran (eliminasi dan subtitusi), serta metode yang unik (baru) (3) Hal yang masuk akal (plausibility), S1 dan S2 memberikan argumen dengan baik. S1 dan S2 dapat memberikan alasan logis pada setiap tahap  penyelesain. Namun, pada nomor 2, S2 menggunakan intuitif intensi yaitu ide yang muncul sebagai strategi guess and test dalam membuat keputusan berdasarkan feeling dan intrinsik yang menghasilkan jawaban spontan. (4) Dasar Matematis (mathematical foundation), S1 dan S2 menggunakan sifat-sifat operasi aljabar dengan baik dalam menyelesaikan SPLDV yang diberikan, yaitu operasi penjumlahan, pengurangan, dan penyederhanaan.