Mapping students' mathematical reasoning ability in solving systems of linear equations in two variables based on NCTM indicators
Keywords:
Mathematical reasoning ability, Systems of linear equations in two variables, NCTM, SLETV, Mathematics educationAbstract
Abstract
Mathematical reasoning is an essential competency in mathematics education because it enables students to understand concepts, construct logical arguments, and solve problems effectively. This study aimed to analyze the mathematical reasoning ability of ninth-grade students in solving SLETV problems based on the five reasoning indicators proposed by the National Council of Teachers of Mathematics (NCTM). A descriptive quantitative approach was employed involving 30 ninth-grade students of SMP Negeri 1 Baktiraja. Data were collected using essay tests and analyzed through descriptive statistics based on percentage achievement. The findings revealed that mathematical manipulation achieved the highest percentage (50.00%), whereas providing mathematical justification (26.67%) and verifying solutions (20.00%) were the weakest indicators. These results indicate that students' reasoning remains predominantly procedural rather than argumentative and reflective. The novelty of this study lies in developing a comprehensive profile of students' mathematical reasoning based on NCTM indicators and proposing two conceptual models, namely the Conceptual Hierarchy of Mathematical Reasoning Ability and the Reasoning Pathway in Solving SLETV Problems, to explain the characteristics of students' mathematical reasoning.
Abstrak
Kemampuan penalaran matematis merupakan kompetensi esensial dalam pembelajaran matematika karena mendukung siswa dalam memahami konsep, menyusun argumentasi, dan menyelesaikan masalah secara logis. Penelitian ini bertujuan menganalisis kemampuan penalaran matematis siswa kelas IX pada materi SPLDV berdasarkan lima indikator National Council of Teachers of Mathematics (NCTM). Penelitian menggunakan pendekatan deskriptif kuantitatif dengan subjek 30 siswa kelas IX SMP Negeri 1 Baktiraja, sedangkan data dikumpulkan melalui tes uraian dan dianalisis menggunakan statistik deskriptif berbasis persentase. Hasil penelitian menunjukkan bahwa kemampuan melakukan manipulasi matematika memperoleh persentase tertinggi (50,00%), sedangkan kemampuan memberikan alasan atau bukti (26,67%) dan memeriksa kebenaran solusi (20,00%) menjadi indikator terendah. Temuan ini menunjukkan bahwa kemampuan siswa masih didominasi aspek prosedural dibandingkan argumentatif dan reflektif. Penelitian ini berkontribusi melalui penyusunan profil kemampuan penalaran matematis berdasarkan indikator NCTM serta pengembangan model konseptual Conceptual Hierarchy of Mathematical Reasoning Ability dan Reasoning Pathway in Solving SPLDV Problems sebagai sintesis hasil penelitian.
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