Hi Amanda
It is perfectly normal for beginners to be playing hands separately after 5 weeks. I do not know 'Tunes for 10 Fingers', but it sounds as though it introduces ideas gradually, which you need.
My favourite beginners' books are the John Thompson 'Easiest Piano Course' (4 volumes - I use 1 to 3). I back these up where necessary, with Fanny Waterman's 'Me and my Piano'. Other contributors will chip in with their favourites.
Some basic principles for teaching beginners (these are the basic principles behind any good teaching):
- introduce each new idea one at a time; a note at a time, a rhythm value at a time etc. Reiterate the new info over and again by questioning your pupil - what is that note called?; where is it on the piano; how many beats does that note last for? - that kind of thing.
- accept that beginners will absorb info at differing rates. Don't be worried by the slower learners. Enjoy the quick ones.
- be patient. Never get cross. Try not to feel impatient.
- laugh a lot.
- listen to everything the pupil has practised at the start of the lesson and work outwards from there.
- do not keep beginners on the same material for more than a week (except for special reasons). They will have made mistakes; this does not matter. A common mistake amongst inexperienced piano teachers is to imagine that everything has to be perfect before a pupil can tackle the next idea. It doesn't; children make mistakes (actually, so do adult beginners).
Ways to help beginners learn new pieces:
- clap the rhythm, first with you then without.
- say the names of the notes.
- identify the direction of movement as up or down ('up' and 'down' can cause problems at the piano, as it is horizontal. Memo to myself: try using 'higher' and 'lower' instead - why didn't I think of that years ago. Hey-ho

)
- along with the previous point, try to get them to see that line to line (and space to space) on the music = miss out a note on the piano. All this, after all, is how we all read music; note names are only there to help beginners who get stuck.
- identify repeated sections\passages.
Others will contribute with their own successful tips. Enjoy you teaching, Amanda. It is the best work in the world.
Steve