Oh OP this is horrid. DS1 (now y11) was very badly bullied when he was y3-4, and the 'outstanding' primary school was rubbish. It was only when I started writing letters of complaint (Ofsted get to see letters of complaint), with copies of their bullying policy highlighted, and annotated that they took the issue seriously, and it all stopped.
I am sceptical of the secondary school's stance of: 'it happened outside school, so not our responsibility'. Well, sure if it happened at 20.30 outside the chicken shop 5 blocks away. But surely just after school, just outside school is a different matter. Most schools do try and push the message that whilst students are in school uniform, they are school ambassadors, so creditable behaviour is expected both in and out of school.
When DS1 was in y8 another boy ran across traffic without looking, and a taxi had to brake hard, just about hitting him. There was a special assembly a couple days later: the taxi company had sent the dashcam footage to the school, showing the boy sprawled on the bonnet. The school did not say 'oh, this was after hours', but used it as a reminder to the boys to consider road safety, and also how their behaviour reflects upon the school.
You've had great advice on here. As others have said, I would make a careful note of everything that has happened (the assault, the threats, school responses). Take pictures of DS's black eye if still visible/ have not already.
Check school website for their anti-bullying policy, or email school office and ask them to email it. Go through it and - hopefully - there are examples you can give of when things that happened to your son are listed in their policy as bullying. State clearly that as a school's statutory duty of care is to keep your child safe: and repeated threats mean he is not safe, they are failing in this duty. You look forward to meeting with the appropriate member of staff so they can outline how they are going to address this issue, and let you know what action they are going to take to ensure this does not happen again. And, whilst you have not wanted to bother the police with this criminal assault at this stage, if there were to be a repeat, you would be reporting to the police.
Good luck, you have got this - and your son will feel empowered seeing that this situation is not ok, and someone, his mum, is doing something about it.
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