"Higher order" sounds pretty functional to me. Higher order functions and all. Although I guess the term higher order function is hardly even spoken of in real functional languages because they're taken for granted.
As do all abstractions.
> If you can solve something first order, then that is much more preferable to a higher order solution.
a.k.a. "To abstract, or not to abstract?". It really depends, of course. But I know for certain I would not want to solve "mapping over an array" without the Array.prototype.map higher-order function.