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Not proud of my Polish heritage [110]
A true Gaeltacht man would say his family were from Tír Chonaill ;) I wouldn't say I was fluent but I'll tabhair cabhair duit if you have any more problems :D Your family is 'as' not 'ón'. We come 'out' of a place in Irish, not 'from'. If you haven't guessed by now, I'm a teacher :)
Home schooling is the only option, but there is a Montessori too.
Forget the home schooling. It might be ok for a short time but it's not sustainable in the long run in a foreign country. It takes a lot of time and energy and research to do it properly and if you're not a trained teacher, you need some kind of support group or network of other home schoolers who are experienced. The few people who homeschool in Ireland generally don't do it in complete isolation.
It won't do the kids any harm to attend a Polish state school for a year or so but it's a bit late in the day to be thinking about whether you want to raise them in Poland. You'll have to accept that if you settle in provincial Poland there's a high possiblity that they will grow up more Polish than Irish in outlook in many ways. If you don't want that, then give them a year here for the experience but don't settle here permanently.
Btw I'm a Montessori teacher myself, but I trained to teach 3-12 year olds so after my training I pretty much always taught in mainstream Irish primary schools. Montessori, if it's done properly and authentically is second to none as a system of education but it's a relatively new thing in Poland and the standards are very variable. Also if your kids are attending Polish primary school, they are at least six years old and that complicates matters because the authentic Montessori curriculum for that age (if you can find a school that runs it and isn't just nursery level) works on the basis that your child has already completed the three year programme preceding it. So without the foundation at 3-6 years it can be difficult to adapt. Very often what you'll find in so-called Montessori primary schools is a half-baked mish-mash that's neither mainstream nor Montessori. Finally you need to consider your childrens' literacy in English. Will that be catered for in a Polish Montessori school to the level it needs to be for their age group considering English is their native language. So there's a lot for you to chew over.
I presume your wife is from the area of Poland where you've settled? Would you be willing to share what motivated you to bring your family here and how old are the children?