Abstract
This study aims to describe and analyze students' mathematical problem solving abilities based on theory of APOS (Action, Peocess, Object, Schema) in terms of Field Dependent and Field Independent Cognitive Style. It is descriptive research with qualitative approach. The research subjects are 34 students in class XI MIPA 1 SMA Nurul Islam Jember, they are grouped on cognitive style, they are 24 students having field independent cognitive style and 10 students having field dependent cognitive style. The method of data collection use a GEFT (Group Embedded Figure Test), test of problem solving abilities, , and interviews. The results of the data analysis of the problem solving ability test and interviews showed that at the action stage, students with the independent field cognitive style (FI) tended to be able to explain the meaning and information on the questions even though they did not write down what they knew. Students with the field dependent cognitive style (FD) tend to be able to write down the information contained in the questions, but have difficulty explaining the meaning of the questions. At the process stage, FI and FD students are able to model and explain the stages well, but FD still has errors in the resulting mathematical model. At the object stage, FI students tend to work on questions freely, while FD students tend to work on questions in detail or are fixated on completely arranged steps, FD students also have difficulty in explaining back the results of their work. At the schema stage, FI and FD students tend to be able to explain how to use the information contained at the object stage to be used at the schema stage. In general, students with a field independent cognitive style in solving mathematical problems tend to be free or not fixated on complete and detailed steps, and have an analytical nature, so they are able to sort out the important information contained in the questions. Students with a field dependent cognitive style in solving math problems tend to be bound or fixated with steps that are arranged in a complete and detailed manner.
 Keywords: mathematics problem solving, APOS theory, cognitive style
Highlights
This study aims to describe and analyze students' mathematical problem-solving abilities based on the APOS (Action, Peocess, Object, Schema) theory in terms of Field Dependent and Field Independent Cognitive Style
Prosiding Seminar Nasional Matematika Dan Pendidikan Matematika UNS 2011, 95–172
Summary
Berdasarkan uraian di atas, maka dilakukan penelitian dengan tujuan untuk mengetahui kemampuan pemecahan masalah matematika siswa khususnya materi persamaan linear tiga variabel berdasarkan teori APOS pada masing-masing siswadengan gaya kognitif yang berbeda. Instrumen penelitian yang dibuat pada penelitian ini yaitu tes kemampuan pemecahan masalah yang berupa dua soal uraian materi Sistem Persamaan Linear Tiga Variabel, dan pedoman wawancara untuk meninjau kembali jawaban siswa. Subjek yangtelah terpilih untuk mewakili masing-masing gaya kognitif diberikan soal tes kemampuan pemecahan masalah untuk mengetahui kemampuan pemecahan masalah siswa berdasarkan teori APOS dan dilakukan wawancara untuk memperoleh informasi yang lebih dalam dari hasil pekerjaan siswa dalam menyelesaikan tes kemampuan pemecahan masalah. Kemampuan pemecahan masalah matematika siswa berdasarkan teori APOS pada ditinjau dari gaya kognitif field dependent dan field independent dideskripsikan dengan memperhatikan kesesuaian dan kecenderungan siswa sebagai sampel penelitian yang mewakili kedua tipe gaya kognitif dan dilihat dari indikator pemecahan masalah berdasarkan teori APOS, yaitu aksi, proses, objek dan skema. Deskripsi Hasil Tes Kemampuan Pemecahan Masalah dan Hasil WawancaraSiswa pada Tahap
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