Pupil putting all the responsibility on me to gain good grades

Sorry, but I think the biggest issue here is you OP. I say this from the perspective of a teacher trainer. Before anyone starts teaching they need to develop a realistic attitude and a set of boundaries. Asking a group of strangers on a forum if we think you are responsible for this pupil’s situation suggests you need to work on how you see yourself and how you position yourself in relation to your pupils. And that is actually the core of teacher professionalism.

As a teacher you need to do what you can to make sure a pupil learns and it goes without saying that you should care. But often things won’t work out according to expectations. You need to have realistic expectations and it’s up to you to make sure that your pupils and parents do too. Some people don’t get there, or at least not in the time you have. This is not your fault. You need to develop a much more robust understanding of this. Not just for your own protection but to protect your pupils from frustration and disappointment.

But you haven’t just repeated what she says here - you’ve given that as your own opinion, that the teacher is avoiding her.
Of course there are plenty of poor teachers out there… but if you took what she no doubt says about you as the truth, you’d be one of them!

Probably because she’s playing you.
The teacher can’t go to her instead of others every time she has her hand up.
Just like it’s your fault, it’s also his fault.
You know that he’ll be saying things to her just the same as you do, that she’s ignoring.
She’s got tutoring laid on with you, but picks and chooses if she can be bothered. How do you know what efforts and supports he’s given her than she hasn’t bothered with?

Given everything else you’ve said about this girl, that seems like quite an unfair thing for you to say about a fellow teacher.

I can imagine that she isn’t too polite about your professionalism to other people too.

You need a thicker skin - why are you letting a child (who doesn’t bother to even do all the lessons) make you feel it’s your fault?!
If you want the money, I’d repeat one line to her - I can support you, and you will find it helps, but it doesn’t mean you’ll get 100%, we don’t cover everything, and we definitely won’t cover everything if you don’t do all the sessions.

Tbh you lost me at her being rude about the cleaner.

Can you replace the hours with another tutoring pupil? sounds like more trouble than it’s worth. The parents should be making it clear to her that her results are hers and hers alone. If she wants better results she should put in more practice.

During lockdown I gave free maths lessons every day over WhatsApp App to a weak 16year old, don't ask.
I am a mathematician and a retired academic.
We started from first principles and built up with tons of reviews. I set him daily homework for reinforcement. He was fine until I left a topic for a few days when it all disappeared. I finally pointed out to him that there were two things going on. I was teaching but he was also responsible for learning.
I stopped doing it in mid March 21when I ended up in hospital with Covid and my lovely son took it on. The lad got his maths and went to college.

It sounds like you are in a weird place with this. Gone down a rabbit hole perhaps. A 12 year old has an opinion about your teaching and your response is to come onto MN and ask a load of adults if the child is blaming you unfairly.

I think you really need to take a big step back, stick your teacher hat more firmly on your head and move it firmly from the personal to the professional. How would you react if one of your primary class said it was your fault they'd got a low mark? Take it in the same spirit, with much thicker skin and stronger boundaries.

I get the impression that her parents and maths teacher should be talking to each other more on this, and leading it more.

Could it be that she feels inadequate at Maths due to her being ignored by her teacher? Which then undermines her confidence and then results in poor performance?

A word with her in parents' presence, as PP suggested above sounds like a good plan.

I agree with the poster who suggested pre-teaching concepts ready for her to feel confident when she’s learning it in the classroom.

See if there’s a way you can speak to her maths teacher, I’m sure the teacher would appreciate it too.

I'd say for going in yr 8 she is going to need a specific maths tutor, going by my yr 8 and yr 10 DC maths work. I have a degree in science and understand scientific maths (although by no means my strong point) and even I'm a bit frazzled with some of the things they cover now.

she said we didn’t cover X, we didn’t go over it again as it was a very simple concept and with so much to cover, I focused on the more challenging work

I think this is the crux of it.

Maths is iterative.

If you're not secure on the basic, simply concepts, then you will get unstuck with more challenging work.

She might need a separate maths tutor, who is fully familiar with secondary maths curriculum, and who will go right through from the basic concepts, spotting and fixing the gaps in the simple concepts first.

If she excels at all other subjects but maths is a stumbling block where she's getting Es compared to As surely you should signpost her parents to get her assessed by an Ed psych.

Either a WISC V to see how her brain works generally and whether there's a working memory, processing speed or other issues or to specifically look into dyscalculia if it the struggles are limited to maths.

Are you teaching the correct techniques from a Secondary school POV if your training is in Primary Ed?

If she needs to practise outside of tutor sessions then Seneca do paid subscriptions if she doesn't have a account via school or even BBC bitesize for free.

She is going to blame you because she is 12, 12 year olds don't want to accept responsibility for their actions that's quite normal.

What a lot of people fail to acknowledge is that the teacher and tutor are just half of the whole equation. To succeed, it’s also the independent practice and revision that is needed. So, a good teacher is just the beginning and I see it as teamwork. Just because someone has a good coach doesn’t mean they will win the Olympics.

No, it's not down to you.

Do you have a written plan for her development? That way you can both see if she's meeting milestones and you can also add feedback on what she does well and what needs improvement. That way, she can't blame you when she gets an E.

Presumably if maths is the outlier in terms of the pickup in her grades then there could be something else at play eg dyscalculia?

Private tutoring is hard OP. There is a huge culture of 'I pay therefore I expect'. No, it is not your responsibility to get her good grades. It is your responsibility to explain the concepts in a way she understands, answer her questions, set her tasks and correct them. She then has to put in the spadework.
Don't take any crap from her or her parents.

You can teach her maths until the cows come home, but you can't teach her to be more intelligent.

Could it be that she needs to a different maths class in school as she's just not getting things the first time they are taught? Or extra maths support to remain in her current class?

Seems like you're being used to plug the schools gaps for children with less math ability. For a private school that's just bad.

I've accepted I'm crap at maths but if I'd had that I might have managed in o grade in it. Or then again poss not .....🤣

Sounds like the wee soul is a (though spoiled) bag of nerves too so I'd suggest if she gets a new math tutor that if the parents afford it, you keep seeing her too afterwards or next day etc for a while to make sure she's understood him ok and gets it and isn't scared to ask questions. And that he understands what she needs too.

You need to speak honestly to the parents to manage expectations. You can't turn brass into gold