In this chapter, we are setting a number of goals for the cognitive development of the student. The most fundamental construction that we are after is that the student should have a mental model of proposition. This should take the form of a representation of Boolean valued variables that can be combined by logical connectives to form Boolean expressions corresponding to logical statements in English. When the variables are replaced by specific Boolean values (true or false), then the expression has a Boolean value. We will try to stimulate this construction by having the student experience the interaction between a logical statement in English, an ISETL (or mathematical) expression that represents the statement, and the computer activities involved in storing and evaluating the expression. Translation back and forth between English and ISETL will be an important activity that will also contribute to the student’s ability to work with formal notation.
KeywordsMathematical Notation Boolean Function Direct Proof Propositional Calculus Predicate Calculus
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