Proses Validasi Pada Pemodelan Matematis Siswa SMP

Dalam matematika, pemodelan matematis memfasilitasi siswa dalam mengeksplorasi situasi kehidupan nyata dengan konsep matematis. Validasi merupakan tahapan penting dalam proses pemodelan matematis. Hasil validasi akan menentukan pertimbangan munculnya modifikasi model dan mengulangi siklus pemodelan. Penelitian ini merupakan penelitian kualitatif deskriptif dengan tujuan mendeskripsikan proses validasi pada pemodelan matematis siswa SMP. Subjek penelitian merupakan 3 siswa SMP Negeri di Surabaya. Data proses validasi pemodelan matematis didapat melalui wawancara berbasis tugas dan dianalisis menggunakan tipologi validasi Czocher (2018). Secara garis besar tipologi validasi meliputi validasi solusi matematis berdasarkan ekspresi matematis, validasi ekspresi matematis berdasarkan model situasi dan model ideal, dan validasi solusi akhir berdasarkan model situasi dan model ideal.

Hasil penelitian menunjukkan setiap subjek telah memvalidasi solusi matematis dengan mengulang operasi hitung yang dilakukan dan telah berhasil memvalidasi solusi akhir berdasarkan model ideal yang dibangun. Namun terdapat dua kategori subjek dalam memvalidasi solusi akhir berdasarkan model situasi yakni subjek dengan pertimbangan terkait pengaruh aspek konteks nyata dalam memperkuat solusi akhir sedangkan subjek lain tidak karena merasa cukup dengan melihat kesesuaian perintah soal dan solusi akhirnya. Dalam memvalidasi ekspresi matematis berdasarkan model idealnya juga terdapat dua kategori yaitu subjek dengan model ideal yang dibangun berdasarkan model situasi dan berdasarkan intuisi. Meski demikian, setiap subjek gagal dalam memunculkan ragam model sehingga tidak menggeneralisasi solusi.

In mathematics, mathematical modeling facilitates students in exploring real life situations with mathematical concepts. Validation is an important stage in the process of mathematical modeling. The results of the validation will determine the consideration of the emergence of model modifications and repeated modeling cycles. This is a descriptive qualitative research with the aim of describing the validation process in the mathematical modeling of junior high school students. The research subjects were 3 state junior high school students in Surabaya. Data from the mathematical modeling validation process were obtained through task-based interviews and analyzed using Czochers validation typology (2018). In general, the validation typology includes validation of mathematical result based on mathematical expressions, validation of mathematical expressions based on situation model and real model, and validation of real result based on situational model and real model.

The results showed that each subject had validated the mathematical result by repeating the arithmetic operations performed and had succeeded in validating the real result based on the real model that was built. However, there are two categories of subjects in validating the real result based on the situation model, namely subjects with considerations related to the influence of aspects of the real context in strengthening the real result, while other subjects do not because they feel it is enough to see the appropriateness of the question order and the real result. In validating mathematical expressions based on an real model, there are also two categories, namely subjects with an real model built on a situational model and based on intuition. However, each subject failed to generate a variety of models so that they did not generalize the solution.