I haven't had my coffee yet, but here's an observation, at least with guitar:
When boys hit puberty I think they become a lot more interested in their own identity and expressing themselves (or just being a cool guitar player,) and they'll get a lot more motivated to play on their own.
For most kids, before the 12/13 mark, the guitar may just be another activity that they do, and it holds no real special meaning.
Once they reach that age I also think they become able to listen to something and really "feel it" on a deeper level.
Since I started playing guitar when I was twelve, I wasn't aware of this huge difference. And my first few years of teaching kids under ten or so were pretty bad. I pushed them too hard, I expected too much interest, I got dissapointed and frustrated too easily.
Now I realize with kids that young I have to do a lot of work to keep things bright and fun, but I also have the liberty of being more structured with how I want them to practice.
I don't feel right telling a parent of a fourteen or fifteen year old kid that he/she has to get their kid to practice. At that age, the kids either gonna be into guitar or not. For a nine year old, I think it's much more useful to get the parents involved.
My observations of different age groups were pretty clearly echoed in a little book I just read called "Making Money Teaching Music." A good and easy read: http://www.amazon.com/Making-Money-T.../dp/0898796571
the gist (this is all regarding the average beginner for the first year or two)-
5-8, lots of structure, games, keep parents involved
8-11, structure, ez rewarding songs that are fun, have parents keep an eye on what's going on
12-15, treat the more as adults, be a "cool" older person if you can, be relatable, focus on their goals and who they are and what they want to do with music. There's often very little point (or success) in pushing them to do something they really don't want to do. They either want to be better musicians or they don't.
15-20, with guitar, at this age I'm basically just helping them with whatever they're working on, and their lives often get in the way of them being consistent with the instrument.
20-60, regarding beginning students, good f**cking luck, haha! Unless if they're really serious (which they very rarely are) I've just come to decide to give them whatever has the most short term gratification. It's been noted before that for an adult, playing an instrument can be an escape from work, so it's realistic to expect them to just play for fun and not ever really practice or anything.
I've had several situations where this wasn't the case, even three adult students right now who are pretty hard workers, but historically this observatioin has been true, especially if they get my name from a flyer or card. maybe I've just gotten better at working with adults ::