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Critical thinking plays an important role for students in solving open-ended problems. This research is qualitative descriptive, which aimed at exploring and describing the student’s critical thinking in solving open-ended problems on geometry based on the personality type. Four boys’ students of the 8th grade of the Labschool of Universitas Negeri Surabaya, were selected from the higher rank in the mathematics’ test and represent for personality type of Keirsey. The chosen students were asked to solve problem and were interviewed. The rational performs critical thinking by providing logically and objectively arguments in choosing such strategies for solving the problems. In contrast, the idealist provides only subjectively reasons, the artisan shows inconsistently implement his chosen plan, and the guardian can correctly execute his plan as described by Russo (2012). In regard FRISCO’s criteria, the rational and idealist satisfy all FRISCO’s criteria in every stage of the Polya’s schemes. However, it could not be find in guardian and artisan type. This study emphasizes that teachers should give more exercises to guardian and artisan to develop their critical thinking skills through the teaching and learning.

Critical thinking; FRISCO criteria; open-ended problem; problem solving; personality type