Critical thinking is a mode of higher-order thinking that is focused on deciding what to think or do. In contrast to the way that many people think much of the time, critical thinking involves thinking logically about the subject matter, considering other points of view, questioning assumptions, and evaluating evidence, while trying to avoid drawing conclusions based on incomplete information, irrelevant factors, or biased data.
Critical thinking can be thought of as having two parts: First, a set of skills for evaluating information and beliefs and, second, the habit of using those skills to guide thinking and decision making. It is not simply acquiring knowledge or a set of skills; it involves habitually using that knowledge and skills.
While critical thinking may not be specifically mathematical, it is a skill that can be used in every domain of thought, which would include mathematical reasoning. Critical thinking is not automatically grasped by learning about mathematics, but mathematics teaching that incorporates critical thinking skills can help students pick up critical thinking skills. Being able to think critically is an important part of number sense.
Critical thinking is an important component in mathematical problem solving. Being able to apply a logical process to solving problems, to analyze a problem so as to determine what assumptions are being made, what information is available, and what the answer should be, and to be able to evaluate the reasonability of an answer and to justify that answer all demonstrate critical thinking.
Another part of learning critical thinking involves having an intuitive understanding of the rules of logic, and being aware of many common ways in which we can be deceived (these include logical fallacies, but there are also many errors in thought that we can make that do not fall under the heading of fallacies).
Related articles: Critical thinking can be considered to be the complement of lateral thinking.
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