Representasi Semiotik Mahasiswa Calon Guru Matematika dalam Pemodelan Matematika dengan Scaffolding Berdasarkan Level Kompetensi Pemodelan Matematika

Semiotics Representation of Prospective Mathematics Teachers in Mathematical Modelling with Scaffolding Based on Mathematics Modelling Competency Level

Sri Irawati, 2025. Representasi Semiotik Mahasiswa Calon Guru Matematika dalam Pemodelan Matematika dengan Scaffolding Berdasarkan Level Kompetensi Pemodelan Matematika. Disertasi, Fakultas Matematika dan Ilmu Pengetahuan Alam. S3 Pendidikan Matematika, Universitas Negeri Surabaya. Promotor: (I) Prof. Dr. Manuharawati, M.Si. (II) Prof. Dr. Abadi, M.Sc.

Kata Kunci: Representasi Semiotik, Mahasiswa Calon Guru Matematika, Pemodelan Matematika, Scaffolding, Level Kompetensi Pemodelan Matematika

Pemodelan matematika memiliki peranan penting dalam pembelajaran matematika. Namun sayangnya banyak peserta didik yang mengalami kesulitan dalam menyelesaikan masalah pemodelan matematika. Salah satu penyebabnya karena peserta didik kesulitan dalam representasi semiotik. Untuk mengatasi hal tersebut maka peserta didik perlu diberi bantuan seperti scaffolding sesuai dengan level kompetensi pemodelannya. Selain itu, perlu siapkan calon guru matematika yang kompeten untuk menghasilkan peserta didik yang sukses dalam pemodelan matematika. Sehingga tujuan yang ingin dicapai pada penelitian ini adalah untuk mendeskripsikan representasi semiotik mahasiswa calon guru matematika dalam pemodelan matematika berdasarkan level kompetensi pemodelan matematika, bentuk scaffolding yang diberikan berdasarkan level kompetensi pemodelan matematika dan representasi semiotik mahasiswa calon guru matematika dalam pemodelan matematika berdasarkan level kompetensi pemodelan matematika dengan scaffolding.

Penelitian ini merupakan penelitian kualitatif. Subjek dalam penelitian ini adalah 6 mahasiswa calon guru matematika yang dipilih berdasarkan level kompetensi pemodelan matematika yaitu level 0 sampai level 5. Instrumen yang digunakan terdiri dari Tugas Pemodelan Matematika (TPM), Tugas Representasi Semiotik Pemodelan Matematika (TRSPM), Pedoman wawancara dan Panduan scaffolding pemodelan matematika. Hasil data TPM dianalis berdasarkan level kompetensi pemodelan matematika dengan merujuk indikator  dari Ludwig & Xu (2010) sedangkan hasil data TRSPM sebelum dan setelah diberi scaffolding dianalisis berdasarkan analisis data dari Miles et al., (2014) yang terdiri dari kondensasi data, penyajian data dan penarikan kesimpulan serta verifikasi.

Mahasiswa pada setiap level kompetensi menunjukkan variasi dalam penggunaan jenis register (bahasa, simbol, grafik/tabel, gambar) dan transformasi antar register. Mahasiswa dengan level 2, 3, 4 dan 5 mampu menggunakan berbagai jenis register, namun hanya level 3, 4 dan 5 yang mampu melakukan transformasi register dengan tepat pada hampir semua tahap pemodelan matematika, sedangkan level 2 mengalami kesulitan dalam hal transformasi register. Di sisi lain, mahasiswa pada level 0 dan 1 cenderung terbatas pada register bahasa dan simbol numerik sehingga transformasi yang digunakan hanya sebatas pada kedua register tersebut. Mahasiswa level 0 menunjukkan kesulitan pada semua tahapan pemodelan matematika sementara level 1 menunjukkan kesulitan dimulai dari tahapan membuat asumsi dan model matematika. Scaffolding diberikan berdasarkan kesulitan yang dialami mahasiswa pada tahap-tahap pemodelan. Mahasiswa level 0 menerima scaffolding mulai tahap awal yaitu understanding, Mahasiswa level 1 dan 2 mendapatkan scaffolding mulai dari tahap simplifying, sedangkan Mahasiswa level di atasnya hanya membutuhkan scaffolding pada tahap akhir yaitu validating. Bentuk scaffolding yang diberikan antara lain: membimbing membaca situasi masalah, membuat asumsi, membuat model matematika, melakukan perhitungan, menginterpretasi hasil, hingga memvalidasi dan memberikan rekomendasi. Setelah mendapatkan scaffolding, terjadi peningkatan kualitas representasi semiotik pada semua level. Mahasiswa mulai menggunakan lebih banyak jenis register dan melakukan transformasi yang lebih tepat dalam menyelesaikan pemodelan matematika. Mahasiswa level rendah (level 0 dan 1) yang awalnya hanya menggunakan simbol numerik dan bahasa, mulai dapat menggunakan gambar dan tabel/grafik, serta membuat model matematika menggunakan simbol aljabar yang lebih sesuai dengan masalah.

Sri Irawati, 2025. Semiotics Representation of Prospective Mathematics Teachers in Mathematical Modelling with Scaffolding Based on Mathematics Modelling Competency Level. Dissertation. Faculty of Mathematics and Natural Sciences. Doctorate Program in Mathematics Education, Surabaya State University. Supervisors: (1) Prof. Dr. Manuharawati, M.Si. (II) Prof. Dr. Abadi, M. Sc.

Keywords: ​ Mathematics Modelling, Mathematics Modelling Competency Level, Prospective Mathematics Teacher, Scaffolding, Semiotics Representation

Mathematical modelling plays an important role in mathematics learning. Unfortunately, many students have difficulty in solving mathematical modelling problems. One of the reasons is because students have difficulty in semiotic representation. To overcome this, students need to be given assistance such as scaffolding according to their modelling competency level. In addition, it is necessary to prepare competent prospective mathematics teachers to produce students who are successful in mathematical modelling. So that the objectives to be achieved in this study are to describe the semiotic representation of prospective mathematics teacher in mathematical modelling based on the level of mathematical modelling competency, the form of scaffolding given based on the level of mathematical modelling competency and the semiotic representation of prospective mathematics teacher students in mathematical modelling based on the level of mathematical modelling competency with scaffolding.

This research is a qualitative research. The subjects in this study were 6 prospective mathematics teacher selected based on the level of mathematical modelling competency, namely level 0 to level 5. The instruments used consisted of Mathematical Modelling Tasks (TPM), Mathematical Modelling Semiotic Representation Tasks (TRSPM), Interview Guidelines and Mathematical Modelling Scaffolding Guidelines. The results of the TPM data were analyzed based on the level of mathematical modelling competency by referring to indicators from Ludwig & Xu (2010) while the results of the TRSPM data before and after being given scaffolding were analyzed based on data analysis from Miles et al., (2014) which consisted of data condensation, data presentation and drawing conclusions and verification.

Students at each competency level showed variations in the use of register types (language, symbols, graphs/tables, images) and transformations between registers. Students at levels 2, 3, 4 and 5 were able to use various types of registers, but only levels 3, 4 and 5 were able to perform register transformations correctly at almost all stages of mathematical modelling, while level 2 had difficulty in register transformations. On the other hand, students at levels 0 and 1 tended to be limited to language registers and numeric symbols so that the transformations used were limited to these two registers. Students at level 0 showed difficulties at all stages of mathematical modelling while level 1 showed difficulties starting from the stages of making assumptions and mathematical models. Scaffolding was given based on the difficulties experienced by students at the modelling stages. Students at level 0 received scaffolding starting from the early stages, namely understanding, students at levels 1 and 2 received scaffolding starting from the simplifying stage, while students at the level above only needed scaffolding at the final stage, namely validating. The forms of scaffolding provided include: guiding reading problem situations, making assumptions, making mathematical models, performing calculations, interpreting results, to validating and providing recommendations. After receiving scaffolding, there was an increase in the quality of semiotic representation at all levels. Students began to use more types of registers and make more precise transformations in solving mathematical modelling. Low-level students (levels 0 and 1) who initially only used numeric symbols and language, began to be able to use images and tables/graphs, and create mathematical models using algebraic symbols that were more appropriate to the problem.