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They say that it is discriminatory and is also against several laws, including equality and human rights laws.
Daniel Jillings has been raising money for a while now to bring a legal challenge to the government and try to get BSL added to the curriculum.
According to Daniel and his mother, the government has said that they would introduce such an exam before, but they currently have no plans to do so.
The 12-year-old said: "I feel that it is wrong that deaf children cannot achieve a GCSE in a signed language.
"My mother has been speaking to lawyers who have advised that the lack of a GCSE in BSL may well be discriminatory and unlawful."
British Sign Language has been accepted as a language for 15 years already, but despite all children having to take a modern language at school throughout Key Stage 3 and Key Stage 4, no such assessment is available to Daniel.
Most schools only offer French, German, and Spanish. However, Daniel is unable to take those courses because of his inability to take a speaking or listening test.
Daniel's mum, Ann, who lives with him in Lowestoft, Suffolk, said: "Ministers have said the GCSE could be a possibility in the future but at this point that just feels like lip service.
"We not only want reassurances that this will happen, but also some indication that action will be taken to address the matter once and for all.
"It feels like we have been left with no choice but to take this route and we would appreciate any support as we push on.
"The introduction of a BSL GCSE could have a huge impact on so many lives and we simply believe that is far more important than the idea that schools need a 'period of stability'.
"The government's stance on the issue is denying deaf children across the country the same opportunities as other school pupils and that simply cannot be right."
The Jillings family are being represented by Alex Rook, of Irwin Mitchell solicitors. He said: "The delay and ultimate failure to introduce a BSL qualification amounts to a breach of a number of legal duties and this issue requires urgent attention.
"It is simply not right that thousands of deaf children across the UK are unable to achieve a GCSE in their first language."
They've already raised £6,000 ($7,900) to pay for legal costs, and are now taking it to the courts.
Fai play, Daniel LAD.
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