Problem-based learning: Its effect on higher-order mathematical thinking skills in terms of student's initial abilities and mathematical beliefs

The higher-order thinking ability of students in Indonesia is still in the low category. This research aims to see the effect of the application of a problem-based learning model on higher-order mathematical thinking skills in terms of student's initial abilities and mathematical beliefs. This research uses a quasi-experimental design with a Non-Equivalent Control Group Design. Data on students' higher-order mathematical thinking skills were taken using a test instrument. This research was conducted at SMP Negeri 27 Jakarta with a total of 165 students obtained from cluster random sampling. Based on the analysis of the three-way ANOVA test, it was found that the problem-based learning model had a positive effect on students' higher-order thinking skills. Problem-based learning model gives better results than conventional learning models. This also applies to students with the initial ability and mathematical beliefs in the high category. Problem-based learning can be an alternative for teachers to improve students' higher-order mathematical thinking skills.