### PENALARAN MATEMATIS SISWA DALAM PEMECAHAN MASALAH PADA MATERI POKOK FAKTORISASI BENTUK ALJABAR DI KELAS VIII SMP NEGERI 1 SURAKARTA

#### Abstract

**Abstract:** The purposes of this study were to describe: (1) the students with high-ability mathematical reasoning on problems solving of algebra factorization in eighth grade students of SMP Negeri 1 Surakarta, (2) the students with moderate-ability mathematical reasoning in problem solving of algebra factorization of eighth grade students of SMP Negeri 1 Surakarta, (3) the students with low-ability mathematical reasoning in problem solving of the algebra factorization material in eighth grade students of SMP Negeri 1 Surakarta. This research was a qualitative case study type. The research subjects were taken from eighth grade students of SMP Negeri 1 Surakarta. The subjects amounted to 9 students consisting of 3 students with high ability, three students with moderate ability, and 3 students with low ability. The research data were in the form of written and oral data. Written data were obtained from the research subject test on written test instruments. The oral data obtained from the *think aloud* verbal conducted by researchers to the study subject. The techniques of analyzing the data were: (a) data reduction (b) presention of data (c) conclusion. The results showed that the students with high-ability reasoning mathematical were: (a) understand the problem, the students read the questions carefully and write down the information that is known of the problem and write down what was being asked of the problem; (b) present the mathematical expressions and perform calculations, students write a mathematical equation to calculate by used the operations of addition, subtraction and multiplication algebra fluently; (c) submit the notion and manipulation of mathematics, students write the answer to determine the length and width of the rice field by factoring and write down the factoring results that obtained; (d) drawn the conclusions, students write the length and width of the rice fields and multiplying the factoring results obtained to convince answers that obtained. The students with moderate-ability reasoning mathematical were: (a) understand the problem, students read the question after it write down the information that was known from the problem and write down what was being asked of the problem; (b) present the mathematical expressions and perform calculations, students write a mathematical equation to calculate by using the operations of addition, subtraction and multiplication algebra although this was used long time to write mathematical expressions and perform calculation, but students were get the expected rice fields wide. The students with low-ability mathematical reasoning were: understand the problem, students read again and again but still confused after it write down the information that was known from the problem and write down what was being asked of the problem.

**Keywords: **mathematics, reasoning, problem solving

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