<![CDATA[This research was carried out with the aim of knowing: (1) whether students' mathematical problem solving abilities in the online-based PME learning model achieved classical learning completeness; (2) is the average mathematical problem solving ability in the online-based PME learning model better than the online-based expository learning model; (3) is there any effect of metacognition performance on students' mathematical problem solving abilities in online-based PME learning models; (4) how is the description of mathematical problem solving abilities in terms of the metacognitive performance of Vocational High Schools Perdana Semarang students on the online-based PME learning model. This research uses the mix method. This research is a Quasi Experimental Design with Pre-Test-Post-Test Control Group Design. The population of this research is all students of class XI Vocational High Schools Perdana Semarang. The results of this study indicate that: (1) students' mathematical problem solving abilities in the online based PME learning model can achieve classical learning completeness; (2) the average mathematical problem solving ability of students in the online-based PME learning model is better than the online-based expository learning model; (3) there is a positive influence on the level of metacognition performance on students' mathematical problem solving abilities in the online PME learning model; (4) students with high metacognition performance have better mathematical problem solving abilities than students with moderate and low metacognition performance levels, then students with moderate metacognition performance have better mathematical problem solving abilities than students with low metacognition performance levels.]]>
