The problem is not so much the purpose of education as how to carry it out.
Literal
Problem [topic-は] education [poss-の] purpose [rather-than-というよりも] education [obj-を] how carry-out [Q-か] [copula-である].
というよりも is a set phrase meaning 'rather than' — it redirects from one characterization to another. The second half embeds a wh-question (どう行うか, 'how to carry out'). 行う is the formal equivalent of する.