Path magic is where a spellcaster must learn types of magic in strings. Fire is an easy one, so I will use it as an example. When a caster wants to learn fire magic, he must start at the beginning (i.e. 0 or 1st level) and work his way up. He can not learn fireball until he has mastered 0,1st and 2nd level fire related spells. And so on and so forth. The path magic is APM is a bit more complex, but all the important features are there.
The current hodgepoge of spell learning is bizzare as the caster needs no foundation to base his learning on. It is like getting a PhD in astronomy when your BS is in music and Masters is in economics.