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[https://byorgey.wordpress.com/2009/01/12/abstraction-intuition-and-the-monad-tutorial-fallacy/ This blog post] on the "monad tutorial fallacy" is I think insightful; there's really no substitute for doing the hard work of understanding, and once you've done it, your insight is still hard (impossible?) to communicate with others, because the hard work simply cannot be avoided. -- [[User:The Anome|The Anome]] ([[User talk:The Anome|talk]]) 13:25, 8 June 2020 (UTC)
:Except that's only true in a limited way. Mathematics pedagogy has known for a long time that often the best way to get someone to understand something is to begin by describing concrete instances and only once the intuition has been developed for the concrete do we generalize and abstract. Think about how you learned about the real numbers. Did you start by sayings its the unique Dedekind complete ordered field or hand you a definition in terms of equivalence classes of Cauchy sequences? Of course not! You started by learning to manipulate concrete examples of reals, first the rationals and then you started to add some special definable real numbers like pi which you can approximate and then we say ok now it's like that but we generalize even to values which you can't define and give a fully formal definition.
:I think the linked article does have a good point but I'd phrase it as this. When introducing a new abstraction it's important to be clear on whether you are giving a concrete example of a type of thing that falls under the concept or something that can kinda motivate the concept or if you are suggesting that a description captures the complete nature of the concept. [[User:Peter M Gerdes|Peter M. Gerdes]] ([[User talk:Peter M Gerdes|talk]]) 16:25, 2 October 2021 (UTC)
== "f returns a defined value of type Maybe U" ==
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