Teach Critical Thinking In Math

But few know what it is to think analytically through the content of a subject; few use critical thinking as a tool for acquiring knowledge.(see Nosich)We often talk of knowledge as though it could be divorced from thinking, as though it could be gathered up by one person and given to another in the form of a collection of sentences to remember.When we talk in this way we forget that knowledge, by its very nature, depends on thought.Learning to think historically becomes the order of the day.

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They recognize, for example, what it is to interpret the American Revolution from a British as well as a colonial perspective.

They role-play different historical perspectives and master content through in-depth historical thought. They discuss how their own stored-up interpretations of their own lives’ events shaped their responses to the present and their plans for the future.

Knowledge is produced by thought, analyzed by thought, comprehended by thought, organized, evaluated, maintained, and transformed by thought.

Knowledge exists, properly speaking, only in minds that have comprehended it and constructed it through thought. Knowledge must be distinguished from the memorization of true statements.

Every discipline can be understood only through thinking.

We know mathematics, not when we can recite mathematical formulas, but when we can think mathematically.We forget this when we design instruction as though recall were equivalent to knowledge.Every discipline — mathematics, physics, chemistry, biology, geography, sociology, anthropology, history, philosophy, and so on — is a mode of thinking.They come to understand the daily news as a form of historical thought shaped by the profit-making motivations of news collecting agencies.They learn that historical accounts may be distorted, biased, narrow, misleading.We know science, not when we can recall sentences from our science textbooks, but when we can think scientifically.We understand sociology only when we can think sociologically, history only when we can think historically, and philosophy only when we can think philosophically.The art of learning well illuminates the art of thinking well. For example, to be a skilled thinker in the learning process requires that we regularly note the elements of our thinking/learning: The reflective mind improves its thinking by reflectively thinking about it.Likewise, it improves its reading by reflectively thinking about how it is reading.It prevents them from making the essential connections (both within subjects and across them), connections that give order and substance to teaching and learning.This paper highlights the depth of the problem and its solution — a comprehensive, substantive concept of critical thinking fostered across the curriculum.

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