The purpose of this study was to: (1) describe the application of the free inquiry learning model in improving students' initiative thinking. (2) Describing the application of the free Iinquiry learning model in improving student learning achievement and (3) Describing the effectiveness of free inquiry learning to improve student mathematics learning achievement in class X Automotive Engineering at SMKN 4 Bengkulu City. In this study, the Classroom Action Research (CAR) method was used and continued with experimental research. The subjects of this study were X grade students of the Automotive Engineering Skills Competency at SMKN 4 Bengkulu City. The data collection techniques used in the study were the observation sheet and the student test method. The data analysis used values were (1) analysis of the ability to think initiative, (2) analysis of the pre-test and post-test, (3) analysis of the t test of student learning achievement. The material validation instrument and students' initiative thinking in the study used was the likert scale model. The conclusions of this research are; (1) The application of free inquiry learning can improve students' initiative thinking in Mathematics. (2) The application of the free inquiry learning model can improve student achievement in Mathematics at SMKN 4 Kota Bengkulu for the 2020/2021 academic year and (3) The application of the free inquiry learning model is effective in increasing student learning achievement compared to conventional learning models
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