Well, I've been playing pure mages for quite a long time, and I don't find the problem that the above posters mention. I have a Level 1 Bosmer in the University right now. I suspect the problem is a matter of...
1. ...Raising Alchemy too fast. Alchemy is a double-edged sword; it adds powerful effects that are hard to get other ways, but it levels too fast. The key is to never use Alchemy as a money-maker, never make spells you won't use, and never, never, never brew a Restore Fatigue potion.
2. ...Relying too heavily on Conjuration. This is the other crazy-fast riser in the Intelligence department. There's nothing wrong with Intelligence, but most Mage characters are already chock-full of it. You don't need to raise anything fast, unless you're a Nord, in which case, maybe you'd better rethink the whole thing...
2a. ...Likewise Alteration. Stop opening all those locks with it; there's nothing in there but a few septims, two lockpicks, and another Iron Cuirass.
3. ...Pretending to be a Warrior in disguise. This is where you run into a fight instead of away from it. You end up taking more damage, and thus restoring more health, using more potions, etc. More potions and restoration means casting more spells and brewing more potions, which means increasing skills faster, which means, yes, you're level 18 before you finish the recommendations. Mages hate pain, unless it's the other guy feeling it. They run away and hide, cast destruction from a safe distance, blast enemies with a staff.
4. ...Misplaced priorities. This is when you don't attend to the business of learning to be a mage in the first place, and you go all over the map, dungeon diving and exploring "since you're going in that direction anyway." This is great for the Hybrid character, but it doesn't fit the Mage class. You want power. You've been told from early on that you can make your own spells and enchantments when you get to the Arcane University. You want that. You want to be able to make spells that will take out an enemy in one blast, or that will turn him against his friends. The spells you can buy don't do that. You have to make them.
5. ...Failure to update spells and enchanted gear. Blasting away at a level 6 enemy with a novice Fireball spell, which has to be cast more times to kill (raising the skill faster.) Healing with the novice spell. Summoning a skeleton 5 times before the bad guy finally goes down, instead of using a more durable zombie. Trying to protect yourself with that novice Shield spell.
These same observations could be directed at other class choices. The problem of leveling too fast is the problem of wasted effort and useless training. It's not a bad thing to develop skills, but there should be purpose to it. If "Skill X" is rising too fast, find a way to use it less.