Critical thinking ability is used as a basis for analyzing an argument and the emergence of interpretation in developing a consistent logical pattern of reasoning, the ability to understand assumptions, formulate problems, make deductions and make informed decisions. The identification of students' critical thinking portraits can be done through a mathematical problem-solving process that is closely related to the student's real life with an ill-defined problem structure that aims to get the solution. Students with field independent cognitive style tend to receive information that is analytical. In contrast the field dependent cognitive style that is more impulsive and receive information in general which is a component in creative thinking skills. Men and women can have different cognitive styles. Men in thinking are more analytical and flexible than women, while women are less skilled in abstract and logical thinking. From the point of view it can be argued that men are more inclined to think critically than women considering that critical thinking activities are logical, analytical, evaluative and reflective, but the importance of good emotional control in carrying out these activities carefully also makes women has possibility to be superior to men in critical thinking.