Penelitian ini bertujuan unutk mengetahui keefektifan guided inquiry approach dan modified free inquiry approach terhadap kemampuan pemecahan masalah matematika siswa, dan manakah yang lebih efektif diantara pembelajaran guided inquiry approach dan modified free inquiry approach terhadap kemampuan pemecahan masalah matematika siswa pada siswa kelas xi mia man tarakan. jenis penelitian yang digunakan dalam penelitian ini adalah eksperimen semu dengan desain penelitian two group pretest and posttest. populasi dalam penelitian ini adalah seluruh siswa kelas xi mia 1, xi mia 3, xi mia 4 man tarakan. pengambilan sampel dilakukan secara simple random sampling. sampel dalam penelitian ini adalah kelas xi mia 1 sebagai kelas eksperimen 1 dan xi mia 2 sebagai kelas eksperimen 2. pengumpulan data digunakan menggunakan tes kemampuan pemecahan masalah matematika. teknik analisis data menggunakan analisis deskriptif dan analisis inferensial. analisis deskriptif meliputi rata-rata hitung dan simpangan baku. analisis inferensial menggunakan uji one sample t-test dan uji independent sample t-test. berdasarkan hasil penelitian menunjukkan bahwa hasil analisis uji one sample t-test diperoleh nilai sig , maka diterima yang berarti model pembelajaran guided inquiry approach dan modified free inquiry approach efektif terhadap kemampuan pemecahan masalah matematika, dan hasil analisis uji independent sample t-test diperoleh nilai sig , maka ditolak yang berarti model pembelajaran guided inquiry approach lebih baik dibandingkan model pembelajaran modified free inquiry approach terhadap kemampuan pemecahan masalah matematika siswa kelas xi mia man tarakan. kata kunci: keefektifan, guided inquiry approach, modified free inquiry approach, kemampuan pemecahan masalah matematika

This research was aims to determine the effectiveness of the guided inquiry approach and modified free inquiry approach to students mathematical problem solving skills, and which are more effective among learning guided inquiry approach and modified free inquiry approach to the ability to solve students ' mathematical problems in grade xi students at mia man tarakan. the type of research used in this study is a pseudo experiment with two group pretests and posttest research designs. the population in this study is all students of class xi mia 1, 3, and 4 at man tarakan. sampling is done in simple random sampling. the samples in this study were xi class 1 as experimental class 1 and xi mia 3 as experimental class 2. data collection is used using mathematical problem solving skills tests. data analysis techniques using descriptive analysis and inferential analysis. descriptive analysis includes the average count and standard deviation. inferential analysis using the one sample ttest of the independent sample t-test. based on the results of the research showed that the results of one sample t-test test obtained the value of sig 0,042 < 0.05 ≥ 0,000, then acceptable which means learning model guided inquiry approach and modified free inquiry approach effective against mathematical problem solving skills, and the results of analysis of independent sample t-test obtained the value of sig 0.032 < 0.05, then rejected which means the learning model guided inquiry approach better than the modified free learning model inquiry approach to the skills of problem solving mathematics student xi at mia man tarakan. keywords: effectiveness, guided inquiry approach, modified free inquiry approach, mathematical problem solving skill