If your school book you on a training course on your day off are you entitled to a day in lieu or to be paid extra for it or do you just have to do it as part of the extra duties expected of a teacher?
Of course you are entitled to be paid, or have a day not working in lieu! And you are entitled to say no.
Did they not check with you first? If you work part time hours, you could well have a job somewhere else on the days you don't work, so the school should never simply assume you are available.
Pay and condition are very clear on this for part time teachers. Schools can ask you to attend INSET or training on days you don't work, but must pay you, and you definitely have the right to say no if it's not convenient.
I work .6 and I don't work anywhere else on the .4 left, so always try to be accommodating with this type of thing, if I can organise childcare, as it's in my and the school's interest for me to be up to date, training wise, but that's my choice. As it is yours