ITT was a method favoured by a few 'progressive' types of schools in the early 60's. Basically it meant that everything was spelt phonetically, which you'd think would make perfect sense only we're talking of the englsih language and not finnish (which I am told is an almost perfectly phonetic written language). So I wos tawt to rite evrything just as it sownds. this was fine til I left that school and started to attend a forces school (dad in the RAF) where they were somewhat more formal and I found myself the only 8 year old who could not spell, know her alphabet etc, though I was a very good reader but more down to good luck and my mother's intervention! the forces school was in germany but we still learnt pounds shillings and pence and feet and inches!
The standard of teachers grammar and spelling today is down to the abandoning of teaching useful grammar during my teens and beyond for probably a full generation fo kids, who are now all adult. I learnt more british grammar learning classical greek when I was 40 than I ever did at school, and then learnt some more when I did my teacher training a few years a go. I can remember sitting in my no. 2 son's class about 9 years ago and listening to the teacher talking about parts of written language I had never heard of and these were 6 year kids! So grammar is better taught now in schools than it was when I was growing up, which given the tone of your observation of your daughter's class is probably not a huge comfort!!!
I am trying to teach my no.2 son some basic grammar and spelling at the moment. he has severe learning difficulties and it's really not til you try to break things down into real small steps and try to see them from his point of view that you realise just how stupid the written part of our language is and I have a lot of sympathy for the chinese who simplified their written language some years ago.