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I have been teaching a few girls who seem to have an interest in writing their own music. Some can notate their ideas quite accurately, others seem to struggle to do that.

So far here are some of the things I have done:

- Improvisation at the piano on different chords (I normally start with I and V and then move onto ii, IV then vi, iii - etc)
- Improvisation with singing (we sing a broken chord pattern over and over and then take turns making up a melody on top - very Orff)
- Explore texture by doing ostinato patterns and adding things on top (body percussion, singing rounds, adding piano parts, etc)
- Taught a bit of directional harmony and general harmony (e.g. one student had chord I, II, III in root position under her melody and the melody was D, E, F - seemed to be in dorian mode) so I talked about directional harmony and suggested I, V6 and I - and we talked about different ways to play the chord (broken, full, etc)
- Assigned things in modes - e.g. Dorian

I'm not a composer... these students come for piano lessons, but I want to nurture their interest to the best of my ability. I would love to get any suggestions

There are too many factors to give a good answer. How old are these girls? How often are they taking lessons? How long are the lessons? How much of the lesson time are you using for composition? How long have they been taking piano? What type of compositions are they writing? How complex is it? Can they improvise? How difficult is the repertoire they play? Have they been exposed to a large amount of music of the type they are trying to compose? Can you compose at all yourself? Can you improvise? What is your level of experience in these things? How long have they been your students?

You might want to answer some of these questions so we can help you out better.

How old are these girls? 5-10 (there are a few of them, actually I do also have an 11 year old boy)
How often are they taking lessons? once a week
How long are the lessons? half an hour, to an hour (depends on their age)
How much of the lesson time are you using for composition? five-ten minutes (most of the work is done at home)
How long have they been taking piano? 1-4 years
What type of compositions are they writing? How complex is it? 4 bar pieces in one hand for the younger ones, 16-32 bar pieces in both hands for the older ones.
Can they improvise? Yes, but to a limited extent.
How difficult is the repertoire they play? Beginner to early intermediate.
Have they been exposed to a large amount of music of the type they are trying to compose? Yes and no ... hard to say
Can you compose at all yourself? Can you improvise? I do it leisurely, I do not regard myself as a composer, I mean I can do it, but most of the time, if I want something to be written, I just get my composer friends to do it. I can arrange music and I understand harmony pretty well. I am able to notate my ideas quite accurately.
What is your level of experience in these things?
I'm a musicology major at a goodish music school, I have studied harmony and I have written things that are in the style of (essentially copying) other composers.
How long have they been your students? 6 months, some 2 months

Here are some really fun things I've done:

You can make a secret code by writing down all the letters of the regular alphabet. Then underneath is you can either write the musical alphabet over and over again, or you can write scale degrees repeatedly until all the letters of the alphabet are used up:

ABCDEFGHIJK
1234567123

Preferably you can do scale degrees, which will be helpful for them to learn that. Then you have them write down a sentence for a phrase that you will put into your secret code. Be sure it's not too long, just a few words. Then translate it into the scale degrees or note names. Then take your notes to the piano and play them. This is a lot of fun to hear how it comes out, and it's really cute to see what phrase the student chooses to "say".

Another thing you can do is write down note names on little strips of paper and then throw them into a hat. You will want to have probably more Cs and Gs than anything else in there. Then have the student draw from the hat and write them down in the order they're drawn. Maybe just do 4 at a time. Then they can play it and decide if they like it, or if they want to put them back and draw another 4.

These are fun ways of coming up with ideas. Once they get an idea they like, you can certainly practice notating them which is great to help their reading skills. And then ask them what kind of things can they do to change what they have? The best thing is to think opposites: what might be the opposite way to write this phrase? Try to come up with a bunch of variations on their theme. You can even use their current repertoire to come up with ideas. What did this composer do with their theme?

Composing can be a lot of fun, but not all students enjoy it. It's great that you have so many that are interested!

The sections in the Music Pathways books on musical questions and musical answers are fun for young pianists to play with. They're mostly in the level B Discoveries book if you're interested.

I also like to have older composing enthusiasts play around with chords vs. melodies first, improvising-wise. It can be fun to develop a melody and flesh it out with chords, or to start with a chord progression and find a melody to go with it. I have also found a short poem and had a student write music to go with it.

The students sound like they're beginners, so Morodiene's suggestions seem like good ideas. I'd add that they should be familiar with basic harmony (at least I, IV, and V chords in all keys).

For beginners of all ages, there are three foundational aspects to "composing".
[1] Get your students in the habit of writing down what they create. For the real young ones, this will require some guidance from you.
[2] Focus on melody. Everything hinges upon melody.
[3] Keep students working upon (developing) the same piece until it has some sense of completion.

Ed

And if they object, tell them that's what Bach and Beethoven did.

It sounds like you've been doing some very valuable things with them already, and several people have suggested good ideas. I'll just add this-

Improvisation is key. Try to expand their improvisation, have them develop a simple ostinato and improvise over it, as they get the hang of it, have them develop more complex ostinatos (they can also be rhythmic ostinatos). Just one example. As someone else said, have them write a melody alone first, then develop an accompany
(and vice versa), not necessarily just block chords... a simple bass line alone can teach them more about harmony if they get good at this. Think of all the simple two part baroque dances, single melody, single bass line. Have them think of this as writing two melodies that work together, this can start as a simple slow moving bass line and eventually develop into free counterpoint.

Starting simple and short is always best. For the youngest have them notate the pitch alone, and work with them to figure out the rhythm later... doing too much at once can be frustrating.

Have them think of a place, a mood, a scene from a story, an animal, etc. Have them improvise something to match this idea. That can lead to a seed for a composition. The more variety the better, for the techniques that they seem to do best with have them write more pieces using these techniques, always trying to incorporate new ideas, new scales, new textures, etc.

I gave a very basic introduction to teaching composition to piano students which is currently on youtube. It was a first draft and so is a bit rough, but might provide some ideas. I'm working on refining it and expanding certain aspects- http://www.youtube.com/watch?v=eI_04Gz1gV8

All the best,