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When you give your students the facts they require, they will memorize the facts and use them to serve their short-term goals of passing tests and graduating to a higher class. When you give them critical thinking skills, they will be able to find the necessary information for themselves; they will be able to evaluate the merits and consequences of that information; and they will be able to utilize that information to solve any problems at hand.
Critical thinking is a meta-skill - it governs a person's facility to process information in a logical manner. A person with critical thinking skills is capable of upgrading his own knowledge and can easily engage in independent self-learning. He can find connections between diverse streams and pieces of knowledge and can assess the value of the information he acquires.
Someone with critical thinking skills can judge what pieces of information are important and discard data that is not useful to him. He can weigh various facts and points of view and identify logical errors. This helps him in solving problems. Critical thinking brings about a clarity of perception that also makes a person capable of re-appraising his own core values, opinions and calculations. With critical thinking, thus, a person can continually reach new planes of self-improvement and self-actualization.
In practical terms, critical thinking has many daily applications and advantages for your students. It is obvious that solving mathematical problems and testing scientific theories would require critical thinking, but If a student can think clearly and and solve problems independently and systematically, he can do well in all subjects.
For instance, I could use my critical thinking faculties when reading a literary text in order to understand it, examine its structure, its characters and themes and then apply my knowledge when analyzing other texts I may be reading now or will read in the future.
I can use my critical thinking abilities to improve my communication skills and to express myself better - to become a better speaker, to make better predictions about my audience, to use language in interesting ways, to arrange my thoughts in a rational format and ultimately, to become a better listener.
I can use critical thinking to make educated decisions, negotiate better options for myself, and to get myself into win-win situations through creative problem-solving.
When I approach any issue with an open mind, a general curiosity, an attitude of inquiry and the wherewithal to put two and two together without necessarily coming to a single, pre-determined answer, I can make innovations and positive changes in my world and in myself.
By answering the question, "Why is critical thinking important," I can discover for myself that great transformations can be achieved if I don't stop at the first correct answer I get; that there can be many right answers to any problem that may present itself. That realization, in itself, can be a tremendously liberating experience.