Abstract: Problem-solving ability is one of the aspects that is highly needed by students during the mathematics learning process. Cognitive styles are divided into two, namely field independent (FI) and field dependent (FD) cognitive styles. This research was conducted with the aim of describing the mathematical problem-solving abilities of fourth-grade elementary school students based on Field Independent (FI) and Field Dependent (FD) cognitive styles. The type of research used is qualitative descriptive. The data collection techniques included the Group Embedded Figure Test (GEFT), problem-solving ability tests, and interviews. The research subjects consisted of 4 students based on the results of the cognitive style test, namely 2 students with a field-independent cognitive style, and 2 students with a field-dependent cognitive style. The research results show that there is a difference in mathematical problem-solving abilities between subjects with a field-independent cognitive style (FI) and subjects with a field-dependent cognitive style (FD). Subjects with FI cognitive style were able to meet the problem-solving ability indicators according to Polya well in each question, namely understanding the problem, planning the solution, and executing the solution plan. However, there is one indicator that has not been met by the subjects, which is the indicator of rechecking. Subjects with FD cognitive style in each question have not yet been able to meet the problem-solving ability indicators according to Polya. FD subjects have not been able to understand the problem in the question, have not been able to plan the solution, have not been able to execute the solution plan, and have not been able to check the calculation results or final results.  Abstrak: Kemampuan pemecahan masalah merupakan salah satu aspek yang sangat diperlukan oleh peserta didik selama proses pembelajaran matematika. Gaya kognitif dibagi menjadi dua yaitu gaya kognitif field independent (FI) dan field dependent (FD). Penelitian ini dilakukan dengan tujuan untuk mendeskripsikan kemampuan pemecahan masalah matematika siswa kelas IV Sekolah dasar berdasarkan gaya kognitif  Field Independent (FI) dan  Field Dependent (FD). Jenis penelitian yang digunakan ialah deskriptif kualitatif. Teknik pengumpulan data berupa Tes Group Embedded Figure Test (GEFT), tes kemampuan pemecahan masalah dan wawancara. Subjek penelitian terdiri dari 4 siswa berdasarkan hasil tes gaya kognitif, yaitu 2 siswa dengan gaya kognitif field independent, dan 2 siswa dengan gaya kognitif field dependent. Hasil penelitian menunjukkan bahwa adanya perbedaan kemampuan pemecahan masalah matematika antara subjek dengan gaya kognitif FI dan subjek dengan gaya kognitif  FD. Subjek dengan gaya kognitif  FI disetiap soal mampu memenuhi indikator kemampuan pemecahan masalah menurut Polya dengan baik yaitu memahami masalah, merencanakan penyelesaian, melaksanakan rencana penyelesaian, namun ada satu indikator yang belum terpenuhi oleh subjek yaitu indikator memeriksa kembali. Subjek dengan gaya kognitif FD disetiap soal belum mampu memenuhi indikator kemampuan pemecahan masalah menurut Polya subjek FD belum mampu memahami masalah pada soal, belum mampu merencanakan penyelesaian, belum mampu melaksanakan rencana penyelesaian dan tidak mampu memeriksa kembali hasil perhitungan atau hasil akhir.