[latte]

> Edit: this might make the kids think you need some 'magical' insights to do math and if they don't see it they are not apt for it, while the opposite might be true.

That's a valid point. However, what's the opposite to having insights? Is that following routines and/or exhaustively exploring the entire problem space (which the first problem in the GP comment seems to teach)?

Teaching those might have higher pedagogical value than conditioning children to find insights (as - at least at first sight - the increase in skill in those is more directly linked to the effort the child invests in learning) However, the von Neumann story in your sibling comment suggests that some people (and so, some children in the class) will perform routines faster than the other children no matter what. Seeing a "shortcut" solution gives a chance to those who are slower at routines to arrive at a solution fast, too.

Moreover, a lot of real-world problems (in academia as well as in business - from my limited experience in both) are exercises in pattern matching and finding shortcuts rather than in an exhaustive exploration of the problem space - and helping children to collect an arsenal of tricks (and more importantly, teaching them to look for insights and patterns by giving them multiple trick-based problems over the years) prepares them to handle those real-world problems.