Grammatically speaking, the last two examples are quite different. In the first example, *what* substitutes the predicative

> The wisdom behind education is **something**. 
>
> **What** is the wisdom behind education? (question is about the predicative)
>
> I don't know **what** the wisdom behind education **is**. <-- correct
>
> <s>I don't know what is the wisdom behind education.</s> <-- too colloquial, unacceptable in formal writing.

Now, in the second example, *what* substitutes the subject. 

> **Something** is on her mind.
>
> **What** is on her mind? (question is about the subject)
>
> I don't know **what is** on her mind. <-- correct
>
> <s>I don't know what on her mind is</s> <-- incorrect