This research was conducted to obtain empirical evidence about the impact of Problem Based Learning learning models to improve students' mathematical reasoning abilities in Vocational High Schools (SMK). This study used a quasi-experimental research design, to determine the increase in students' reasoning abilities used test instruments in the form of descriptions. The results of the study were obtained as follows. (1) There are differences in mathematical reasoning between students who learn using the Problem Based Learning model with students learning with conventional learning models in high group students. (2) There are differences in mathematical reasoning between students who learn using the Problem Based Learning model with students learning with conventional learning models in the middle group students. (3) There are differences in mathematical reasoning between students who learn using the Problem Based Learning model with students learning with conventional learning models in low group students. (4) There is a difference in the increase in mathematical reasoning abilities between students who study using the Problem Based Learning model and students who learn to use conventional learning models in group students as a whole are accepted.
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