> one basically needs to reproduce the thought process of how one would come up with the given model [...] people are much better at deriving the rules from a f

> one basically needs to reproduce the thought process of how one would come up with the given model [...] people are much better at deriving the rules from a few examples than the other way around. Indeed. I don't think this is as mystifying as some people seems to believe. There seem to be at least two errors poor communicators make. The first is that communication doesn't transfer any content from one person to the other. We use signs and symbols with conventional meanings both parties accept to express things which are then interpreted by the other party. If you're not both on the same page, you have to first establish that common ground. Much of education involves building up that common vocabulary and system of signs so that we can even have the conversation. To think of communication as if you were some act of piping the actually semantic content from your mind to another's is to completely misunderstand communication and a recipe for failure and frustration because you will be unable to understand why someone cannot just grasp the content you think you've just poured into their head. "It's right there! I just gave it to you!" This brings us to the second error. Knowing your audience means knowing what their current state of knowledge is. Part of that is knowing the vocabulary and system of signs your interlocutor knows. Explanation is therefore a matter of using what they already know to lead them to the conclusions you already have (introducing claims as necessary). Once the aim of explanation is stated that way, it starts to resemble something like a chain of reasoning...or an argument, which it basically is. I cannot derive certain theorems if I have not yet derived certain prior theorems, much less if I lack the axioms from which they are derived.