Transforming mathematical representations: A process-based analysis of junior high school students' problem solving
Keywords:
Mathematical representation, Problem solving, Representation transformation, Thinking process, Junior high school studentsAbstract
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.
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Copyright (c) 2026 Prasita Manginar Tesalonika Napitupulu, Friska Ledina Situngkir (Author)
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