Going for better school...

What you will read on many threads is that after the initial settling into secondary school there is usually a 'shake-down' of friendships as they all get to know each other, are put into sets, choose extra-curricular activities etc. There is no guarantee his good friends will still be a group by year 8.

If you can get him into a robustly academic school in either sector AS A GENERALISATION he will find a wider circle of potential friends who are also 'bright with quirk', maybe not with his maths prowess but also outliers.

Ds was and still is a social butterfly. He was hugely popular from the minute he entered school with both the children and the staff. He is a person who draws people to him.
Looking back I was stupid to think he needed to be with his friendship group because he had proved consistently from his earliest days that he could establish good social relationships anywhere.
He has friends across the country to this day from past schools,past clubs, past work roles, current work roles, university attendance etc etc.
Ds has no regrets and to be fair neither do I. Going to uni soon after his friend died would,I think,have been a disaster. He was drinking and partying too much and he needed his family near him. That coupled with how little work and studying he needed to do to get his degree and his Masters would have left him too much free time to get wrecked.
As it is he is highly respected in his role and he is flying high and happy and that is what counts.
Coincidentally his role used to involve advising schools on policy and three years after leaving the local comp he was giving presentations advice to his old HT and others to say the HT was surprised was an understatement but it didn't stop him claiming ds as one of his old boys

It sounds like your ds is very much like my ds was exceptionally able at maths (his junior school had a teacher from secondary school come in a couple of times a term to teach him and oversee his work between those times) and able across the board.
Rightly or wrongly I allowed ds to go to the local comp, against my better judgement I suppose, because he had strong friendships and didn't feel he would be happy going to a school where he would be without his friendship group.
In the first few weeks of year seven ds won the whole school maths challenge beating those five years older than him and acquired his nickname "Dexter boy genius"
Suffice to say ds realised at this point that school wasn't going to be much of a challenge for the next five years when it took no effort on his part to get exceptional results.
Ds would say he had the time of his life, his teachers would shudder at the memories and I gained a crop of grey hairs as he used his talents to run rings around the rules and the systems.
He achieved the predicted As and A*s with no effort and no revision and in fact left school three months before GCSEs because school couldn't rein him in. He was bored doing lessons when he was being taught something new, revision was a whole new level of boredom for someone with an eidetic memory with perfect recall.
He went onto six form at a different school. Again he found it easy,he had a fantastic social life that was rarely impeded by studying and put in the bare minimum effort.
His best friend died and ds lost his way a bit. He got A,A,A,B and then decided he wasn't going to uni. I was gutted,he should have been going to Cambridge to study Maths but instead went to work in Local Government.
Fortunately they spotted his potential pretty quickly and funded his degree and his Masters and whilst studying never fulfilled him work does immensely and he's happy with lots of responsibility (tipped to be a future chief exec), a very good salary (he earns more than all of his peers who went the conventional route) and no student debt.
He found his own path I suppose and whilst it wasn't the path I envisaged or hoped for for him it is his life and his happiness is what is most important to me.
So OP in answer to your question in your shoes there is not a cat in hell's chance I would allow ds to attend the sinking school if there were any other alternatives .

I will let him try one of papers this weekend.

As you are looking to research schools it would be worth researching practice material for the entrance tests. I think your DC may enjoy some of the practice papers etc. that are currently available. I don't think he will struggle with the content at all but he will need to be able to work quickly and accurately. You can find information on the schools, entrance exams and practice material here:

www.elevenplusexams.co.uk/forum/11plus/index.php?sid=a0864ebd9edcda7ef1c0f6c028aba125

UKMT questions don't usually require much taught techniques. Usually nothing more than Pythagoras and knowing that the angles within a triangle add up to 180. However, they make you think. The first few are easy but the last 10 are not.
I think they would be a good way of developing your DS's maths skills. There's also a good selection of books on their website apparently.

None of this is a substitution for a suitable school, of course, but it will help your DS develop.

irvine since you are already paying for martial arts and instrument lessons could you add in some online maths tutoring say once a month to have some maths mentoring?
Do not worry about pretests for Eton and Winchester, they do not require any preparation, they are assessing aptitude not learnt material. These tests would also be a way of getting an expert assessment of him to help guide you for the future. If those schools are too far look for others which have similar IQ type pretests. If he is refusing to contemplate any other school than his local comprehensive then adding in some online tutoring may be your best option.

There are 7+ months to grammar/state selection test and 1 year to private/boarding selection test, with your help he wont have any issue to get in Irvine. If you strongly dont want him to go to the nearest comp then try for any grammar school allowed(within catchment or no catchment), apply to boardings/private. You dont have to make decision at all until march next year. Your posts sound sad while it shouldnt. He loves learning and self study and could teach himself then these tests are nothing. He sounds a rounded boy to me and loves learning, he will love to be surrounded by similar peers. Dillusion or not it isnt important, even if he isnt 0.001% whatever, he has nothing to loose.

A good maths tutor would assess him. When we moved to this area I kept getting told my kids "must" have tutoring for 11 plus. I didn't think so but eventually my colleague persuaded me to let her sons tutor assess my daughter. I paid for one hour and she told me I was wasting my money as my child didn't need tutoring. I felt stupid that I had listened to everyone else but it might be worth it for you to find out.

nrich.maths.org/

Would the above website be of interest to your DS?

Obviously it will depend on the school and the child.... But both sets of parents in my example went into the process with the utmost faith in their decision. Sometimes things don't work out as expected. Clearly the drift of day pupils is easier to gauge than that of boarders.

I've seen the same expense bitterly regretted with families sending their DSs to boarding school

That depends on the school and the child. Like everything else with the school system, things are VERY different from one school to another. My son goes to a state school which has a small number of boarders (1/6th of the intake), and he often says he wishes he could board too as his boarding class mates love it.

Have you looked at the admissions policies for state schools 30-45 mins away by bus/train? Do any of the schools have academic banding tests or aptitude tests for music, languages, art, technology etc. where catchment distance is less important? Where do the catholic dc in your area go? Is there a faith school with aptitude places for non-catholics/non-church goers? Even a language aptitude test seems to be based more on logic and memory, not actual language ability.

From your description of him, it’s possible he’d get a bursary even if he didn’t do any prep. I would suggest though that you show him the exam format in advance so he’s familiar with how the booklets will look. And do go to taster days. This will show him that it’s a School just like any other.

If he can do all enough to get even a bronze on the junior challenge when he's only in year 5, then you'll know that he's extremely good

Ds2's prep get quite a few bronze (and some silver) medals in the UKMT Junior Maths Challenge in Year 5 on one practice paper - but yes, the UKMT website/resources would be very useful to gauge his ability.

DC's prep sends boys to private schools such as Hampton, RGS Guildford and KCS Wimbledon - all unfortunately in Surrey/South West London but this tier of private school should be able to cater for him?
hamptonschool.org.uk/academic/departments/maths/
www.rgs-guildford.co.uk/news/2015-01-14/Oxbridge-Success

There must be an online community for gifted mathematicians somewhere. Something where Op's DS can exchange ideas and OP can ask for advice.

I'm not sure it's worth it but you could get an assessment of you wanted to find out whether he is top 25% /10%/1%/0.1% or whatever. I think Mensa do them for not very much money.

I fully understand why you want his maths learning directed by someone who preferably knows maths and knows how to teach. That's not really asking too much but it will challenge many state schools who have other priorities (and frankly, interests). You don't want a school that teaches to the test, and that's most of them.

Have you tried him on the UKMT junior and intermediate challenges? There are some sample questions and solutions on the website. If he can do all enough to get even a bronze on the junior challenge when he's only in year 5, then you'll know that he's extremely good. Any award on the intermediate (which is intended for years 9-11), will mean he has really something special. At any rate, it will give him something to enjoy.

I've seen the same expense bitterly regretted with families sending their DSs to boarding school - two drug related related expulsions spring to mind without even the compensation of decent GCSEs, just ones which would have been at the very low end of the scale at the local comp.

Taffeta I did say I didn't know if it would work the same for everyone but this boy went from a very high achieving 13 year old to a 16 year old with very disappointing GCSE results. At 13 he was talking about university and what he wanted to do but when he got to 18 he had some trouble with the police, had got into debt. He eventually joined up and did OK but his father always regretted that they moved him. Who knows if he would have done better at the original school but I don't think the "best" schools always work out for everyone.

I still went for the school I considered best in my area, it was considered 2nd best by many but I never regretted my choice. I definitely didn't want the failing school. The trouble is we never know what might have been.