Even where she would confine its teaching to a highly-talented mathematics class, she sees it being of value in introducing students to "a way of thinking that encourages carefulness and precision".That makes its value rest on an assumption of transfer of skills from one area to another, an assumption for which there is no current evidence.Another justification for the teaching of formal logic was thought to be that it was a description of the rules by which a competent mind naturally works.
The huge importance of the possibility system is largely ignored.Others have suggested that while the formal rules of logic provide a tether for reason, the process of formalising everyday language, of standing aside from it to look at the patterns is enough to achieve the purpose of "objective" reflection and that one does not have to
The methods of teaching critical thinking currently favoured are critical analysis and metacognition. The former denies the place of interactive contextual judgment in reasoning, the latter devalues human purposes and quality. A metacognitive lesson on classification is shown to be too didactic to allow children to think in any but a passive sense. Splitter’s categorization of questions shows how moving away from closed substantive questions to open ones through dialogue can encourage children to think for themselves. Some consequences for pedagogy and evaluating children’s thinking are briefly examined.
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