A password is a type of (usually partial) extensive definition (a list of the members of a set). What we want to teach is intensive definitions (the defining characteristics of sets). An extensive definition is not entirely useless as a learning aid, because an student could, in theory, work out the related intensive definition. Unfortunately, this is extraordinarily difficult when the definitions relate to wave dynamics, for example.
A password is an extensive definition being treated like the objective—a floating definition, where the intensive definition is no longer being sought. Extensive definitions do not restrict anticipation, and so can only ever be a step towards teaching intensive definitions. Learning passwords is wrong by definition—if it’s useful, it’s no longer a password.
In the case of a student learning a foreign language, providing extensive definitions is very useful because there is no difference between saying “the set {words-for-apple} includes apfel” and “apfel means apple, and the set {words-for-apple} contains all words meaning apple” - the intensive and extensive definitons are provided together, assuming the student knows what what an apple is.
A password is a type of (usually partial) extensive definition (a list of the members of a set). What we want to teach is intensive definitions (the defining characteristics of sets). An extensive definition is not entirely useless as a learning aid, because an student could, in theory, work out the related intensive definition. Unfortunately, this is extraordinarily difficult when the definitions relate to wave dynamics, for example.
A password is an extensive definition being treated like the objective—a floating definition, where the intensive definition is no longer being sought. Extensive definitions do not restrict anticipation, and so can only ever be a step towards teaching intensive definitions. Learning passwords is wrong by definition—if it’s useful, it’s no longer a password.
In the case of a student learning a foreign language, providing extensive definitions is very useful because there is no difference between saying “the set {words-for-apple} includes apfel” and “apfel means apple, and the set {words-for-apple} contains all words meaning apple” - the intensive and extensive definitons are provided together, assuming the student knows what what an apple is.