Friska Ledina Situngkir
Universitas Katolik Santo Thomas, Medan, Indonesia

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Mapping students' mathematical reasoning ability in solving systems of linear equations in two variables based on NCTM indicators Mei Yanti Purba; Friska Ledina Situngkir
Eduvista: Journal of Education and Innovation Vol. 1 No. 1 (2026): Eduvista: Journal of Education and Innovation
Publisher : Eduvista: Journal of Education and Innovation

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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.
Transforming mathematical representations: A process-based analysis of junior high school students' problem solving Prasita Manginar Tesalonika Napitupulu; Friska Ledina Situngkir
Eduvista: Journal of Education and Innovation Vol. 1 No. 1 (2026): Eduvista: Journal of Education and Innovation
Publisher : Eduvista: Journal of Education and Innovation

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

Mathematical representation is an essential competency in mathematics learning because it enables students to transform information into visual, symbolic, and verbal forms throughout the problem-solving process. However, previous studies have primarily focused on assessing the achievement of representation indicators, providing limited insight into how representation transformation occurs and at which stage errors begin to emerge. This study aims to analyze junior high school students' mathematical representation transformation during problem solving on circle topics. A descriptive qualitative approach was employed involving three eighth-grade students purposively selected from high, medium, and low representation ability categories based on the results of a mathematical representation test. Data were collected through a four-item mathematical representation test and students' written work, then analyzed descriptively. The findings revealed that the greatest difficulty occurred in transforming visual representation into symbolic representation, which subsequently affected verbal representation and problem verification. This study proposes a mathematical representation transformation model consisting of problem comprehension, visual representation, symbolic representation, verbal representation, and problem verification, providing a conceptual contribution to understanding students' mathematical thinking processes. Abstrak Kemampuan representasi matematis merupakan kompetensi penting dalam pembelajaran matematika karena membantu siswa mentransformasikan informasi ke dalam bentuk visual, simbolik, dan verbal selama proses penyelesaian masalah. Namun, sebagian besar penelitian terdahulu lebih berfokus pada pengukuran ketercapaian indikator representasi sehingga belum banyak mengungkap bagaimana proses transformasi representasi berlangsung dan pada tahapan mana kesalahan mulai muncul. Penelitian ini bertujuan menganalisis transformasi representasi matematis siswa SMP dalam proses penyelesaian masalah pada materi lingkaran. Penelitian menggunakan pendekatan kualitatif deskriptif dengan melibatkan tiga siswa kelas VIII yang dipilih secara purposive dari kategori kemampuan tinggi, sedang, dan rendah berdasarkan hasil tes kemampuan representasi matematis. Data diperoleh melalui tes tertulis dan dokumentasi hasil pekerjaan siswa, kemudian dianalisis secara deskriptif. Hasil penelitian menunjukkan bahwa hambatan terbesar terjadi pada transformasi visual representation menuju symbolic representation, yang selanjutnya memengaruhi verbal representation dan problem verification. Penelitian ini menghasilkan model transformasi representasi matematis yang terdiri atas problem comprehension, visual representation, symbolic representation, verbal representation, dan problem verification sebagai kontribusi konseptual dalam menjelaskan proses berpikir matematis siswa.