The House of Lords is being asked to rule on two cases concerning children's right not to be denied an education.
Shabina Begum said her exclusion was typical of Western attitudes
One case involves Abdul Ali, excluded from Lord Grey School in Milton Keynes, Bucks, over a fire in a waste bin.
The other involves the refusal of Denbigh High School in Luton, Beds, to allow Shabina Begum to wear a jilbab.
The Court of Appeal held previously that the human rights of both students had been violated. Their former schools have appealed against those judgements.
Both students are represented by human rights lawyers Cherie Booth QC and Carolyn Hamilton.
They are backed by the Children's Legal Centre, which said the cases were the first of their kind to reach the highest court since the introduction of the Human Rights Act 1998.
Out of school
Abdul Ali's exclusion happened in 2001 when he was 13, after he and two other boys were accused of causing smoke damage.
Edward Faulks QC, for Lord Grey School, told the panel of five judges that when police finally announced there would be no prosecution, neither Abdul nor his parents attended a meeting to discuss his reinstatement.
Mr Faulks said the school permanently excluded him after he failed to return. Only then did the parents decide they wanted him to.
The Court of Appeal had held that from the end of the temporary exclusion to the time he started a new school, the following January, Lord Grey had been in breach of its duty to provide an education under the European Convention on Human Rights.
Mr Faulks said: "This case raises for the first time the role of the Human Rights Act in educational disputes and the meaning of the so-called right to education."
Pupils and parents had the right challenge exclusion orders, he said.
"More than a year after his exclusion, rather than seeking any remedies by statute or judicial review, they commenced a claim for damages alleging infringement of various articles of the convention."
He said the Human Rights Act was never intended to be used in that way.
The hearing is expected to last two days, after which the Law Lords will hear the Shabina Begum appeal.
Shabina began wearing full-length Muslim religious garb in September 2002. She was told it did not comply with the school's uniform policy and was a health and safety hazard.
She was out of school for almost two years before attending another, wearing the full-length jilbab.
When she won her Court of Appeal case she said the school's attitude was part of an atmosphere created in Western societies since the attacks on the US in 2001, "in which Islam has been made a target for vilification in the name of the 'war on terror'."