Logic in University Mathematics Education
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Mathematical logic generally addresses questions of reference and validity of inference. Questions of reference concern how statements in language refer to mathematical objects and under what conditions those statements are true or false.
Questions of inference concern how various statements in language are related to each other – such as equivalence, negation, and implication – and how statements in language may be verified by arguments, i.e., standards of proof.
Modern logic is in many ways the study of formal languages, which have been developed to deal with questions of reference and inference by taking in consideration the relationships between syntax and semantics. Part of the study of logic in undergraduate mathematics education should include students’ learning of such formal systems in model theory, proof theory, or computability. However, we are aware of no research-based evidence on the teaching and learning of such topics. Current research also...
KeywordsUniversity Mathematics Education Reference Inference Syntax Semantics Truth Validity
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