Analysis of Studentsr Mathematical Reasoning Ability in Solving Mathematics Problem

Abstract

The purpose of this study is to describe students' mathematical reasoning abilities in solving mathematical problems. This study used descriptive qualitative method. The subjects of the study consisted of 10 XI grade students of SMA Muhammadiyah 3 Surakarta, selected by purposive sampling. The instrument used to explore the ability of mathematical reasoning is a description test, followed by an interview. Based on the results of this study it can be concluded that the reasoning of SMA Muhammadiyah 3 Surakarta students in solving mathematical problems is more dominant using inductive reasoning of 70%, which is far greater than deductive reasoning which is only 30%. Another interesting finding from this study, students tend to use the inductive reasoning and the difficulty or not thought of using deductive reasoning in solving mathemathics problem, but when interviews are given guidance it turns out that some of them are capable of using deductive reasoning. The tendency of inductive reasoning, associated with students who are easier to think with real specific facts in solving abstract mathematics problems. This inductive reasoning is formed because inlearning, to facilitate students' understanding in the mastery of abstract mathematical concepts, the teacher provides spesific concrete examples to conclude a more general concept. To build a deductive mindset, it should teach an understanding of bastract mathematical concepts, although starting from a spesific example but the teacher must deliver gradually so that the correct logic can conclude a general concept.

Analyzing of Student’s Mathematical Reasoning Ability in Solving Mathematical Problem Based on Higher Order Thinking Skill (HOTS)

“…The results of this study are in line with [13], [14] statement that reasoning and proofing abilities are very important for building students' understanding of mathematical concepts. Leithner in [8] mentions that reasoning is the foundation of mathematics, unfortunately, students at all grade levels find it difficult in mathematical reasoning problem including undergraduate students of mathematical majors. Therefore, mathematical reasoning skills must be given attention during the lecturing process of real analysis courses and should be regularly improved with proving mathematical theorems.…”

“…Mathematical reasoning is important because it makes unique features applied in mathematics as a subject [8]. Once students are able to apply some of the unique features of mathematics, then they are able to solve problems that require them to generalize, apply abstract thinking and also simplify.…”

Students’ Statistical Reasoning in Statistics Method Course

“…One of the abilities that must be possessed by students to compete against the challenges nowadays is reasoning ability. Muller & Maher (Rahmawati, Mardiyana, & Triyanto, 2018) stated that reasoning as a process for making a conclusion base on evidence or other assumptions. This reasoning is useful for a person in the process of building and comparing ideas from various situations faced, so that he can make the right decision in solving his life's problems.…”

Kemampuan Penalaran Matematis Siswa SMP dalam Kegiatan Penugasan Dosen di Sekolah (PDS)

“…Penalaran matematis memiliki peranan penting dalam memecahkan masalah maupun dalam menyampaikan ide saat belajar matematika (Ayal et al, 2016) (Sandy et al, 2019). Siswa yang mempunyai kemampuan penalaran matematis dapat menyampaikan ide matematikanya dengan keterampilan pemecahan masalah yang lebih baik ( (Rahmawati et al, 2018) ( Baroody, 1993) menemukan bahwa pengalaman yang nyata dalam melihat pola, memformulasi dugaan tentang pola yang telah diketahui dan mengevaluasinya bersifat lebih informatif, sehingga siswa lebih memahami proses pada doing mathematics dan eksplorasi dari matematika. (Sumarmo, 2013) menyatakan indikator kemampuan penalaran matematis diantaranya: 1) Menarik kesimpulan logis, 2) Memberi penjelasan terhadap model, fakta, sifat, hubungan, atau pola, 3) memperkirakan jawaban dan proses solusi, 4) Menggunakan pola hubungan untuk menganalisis situasi, atau membuat analogi, generalisasi, dan menyusun konjektur.…”