The children, two girls aged eight and five and a boy aged seven, who may not be named by order of the High Court, are fighting a test case against Dyfed CC.
Through their mother, the children challenge the decision of the Council's Schools and School Services Sub-Committee on May 27 this year to refuse them free transport for the ten-mile trip from their home to the school chosen for them by their parents.
Their counsel, Mr David Pannick QC, told the court that the case raised 'the important issue of whether an education mainly in Welsh is suitable for children whose main language is English and who wish to continue to be educated mainly in English, leaving Welsh as a second language as they do at present'.
Since that date Dyfed schools had been categorised either A, B, or C, according to the priority they placed on the teaching of the Welsh language.
Category A schools were situated in what were designated as 'traditionally Welsh-speaking areas' and, at infant and junior levels, the whole life and work of such schools were mainly conducted in Welsh.
The object of the policy, which Mr Pannick said the council was 'entitled to make', was to ensure that pupils were 'thoroughly bi-lingual' in both English and Welsh by the time they were aged 11.
The county firmly believed that school-children from traditionally Welsh areas should be instilled with an appreciation of native culture and should leave school prepared to form a part of the Welsh society in which they lived, he told the court.
The case continues.