I'm afraid I have yet another question for the experienced teachers. For those of you who have answered previous questions, please skip the first paragraph.

My nine-year-old has been learning the cello for a bit over three years and the trombone since September. At the French music school she goes to she has an hour a week compulsory solfege lesson which covers what we would call theory and aural. There are five of them in the class at the moment, three pianists, a guitarist and my daughter.

Daughter came out of her lesson yesterday saying that during the holidays she has to learn to identify in written music major and minor seconds and major and minor thirds and she didn't understand how it worked. They don't use a theory book and all she had written down were four examples in the treble clef (which she reads very laboriously): E/F labelled minor second, F/G major second, E/G minor third, F/A major third. After talking to her for a bit it turned out that her first problem was that she doesn't actually understand what a semi-tone is. The teacher said (or at least my daughter understood) that a semi-tone was two notes side by side and a tone was when you missed a note out. The problem for my daughter as a cellist is that she doesn't actually know how to play a chromatic scale yet as she has not yet learnt extensions, so for example the four lowest notes for her are C, D, E, F. As far as she is concerned C and D are adjacent notes and so (following teacher's definition) should be a semi-tone. I showed her on the piano what the teacher meant by missing notes out but am at a loss as to what to do next as I have always thought about intervals in relation to the keyboard.

Do I just get her to memorise that there is a semi-tone between E/F and B/C and then everything else is a tone unless the second note has got a flat or a sharp in front of it?

And how do you work out major/minor thirds before you have learnt all the key signatures? I can't remember trying to work out intervals without knowing scales and counting the number of semi-tones seems rather laborious.

Not very helpful but I agree with you on that.
I think that the basic problem seems to be the separation between practical and theory and that they seem to be being taught at very different levels.

Yes I agree too. Seems to me a bit like putting the cart before the horse - but that doesn't help you either.
I would be unlikly to try to teach things in this order so not best placed to advise.

I think showing on the keyboard was a useful move. Would it help to write a chart with note-names set-out like the keyboard (but no note-shapes round them - not sure if I'm describing it very clearly) to help give your daughter more practice in counting semitones ? I know she can do it on the keyboard, but if she can take a chart away and work out a few examples ? Just a thought.

You have hit the nail on the head but I don't know what to do about it. How I long for the ABRSM system with clearly defined contents for each theory grade and the choice to decide when you want to do theory.

A fortnight ago I did actually show my daughter's cello teacher what she was doing in the solfege class because my daughter was finding basic 6/8 time confusing and her cello teacher asked if she had seen it yet in solfege. I jumped on the occasion to point out that my daughter hasn't been doing anything as useful as the difference between simple and compound time and that they had jumped straight in with dotted quavers, semi-quavers and triplets. Cello teacher agreed that there was no way my daughter could understand the rhythm exercises and not to worry but my daughter is a perfectionist and (understandably I think) doesn't like feeling completely out of her depth.

I know this might not help immediately but why don't you explain to her cello teacher what is happening in these theory lessons and maybe that teacher can use exercises at the beginning of each lesson that will help her. And perhaps the teacher can teach her some extensions so she understands what a chromatic scale is.

I would approach it from a piano perspective as you have done kerioboe, and continue to keep it seperate from her instrument until she understands the concepts on the piano completely. I would stress the semitone between e-f and b-c, and get her to draw a keyboard on the top of the page with the note names on it so that she can count up the tones & semitones. My students find that it helps to have a visual aid.

Once she gets the concept, I'd get her with her cello in front of a mirror, so that she can see the distance between her fingers on the string with tones & semitones. Perhaps she could also play some chromatic notes with her first finger, just sliding her finger up the string, with you playing the notes on piano so that she can pitch them. Even if she hasn't done shifting or extensions, at least she would have an understanding of how the concept of semitones & tones relates to her instrument.

Good luck with it