Rules for Deductive Reasoning – Modus Tollens

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Modus Tollens Modus tollens is another deductive rule of inference frequently used in mathematics including beginning algebra. The general expression for modus tollens is the following: P → Q  (First premise is a conditional statement) ¬ Q  (Second premise is the negation of the consequent) ¬ P   (Conclusion deduced is the negation of the

A Dramatic Transformation

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I taught my first math class in 1965.  I taught my last class in 2017.  A disturbing transformation has occurred in those 52 years. In those early years of my career we taught concepts, generalizations, abstractions, deductive reasoning, and critical thinking (although Richard Paul had not yet invented the term). The same things were taught