It starts with her making a mistake, and me correcting it.

So don't correct her. Especially her schoolwork should be hers and hers alone. A teacher does not expect 100% correct work, they want to see how well a student has understood the current topic. Leave the corrections to the teacher. And she may even go back to school without complete homework (but trying is a must), tell the teacher that she didn't understand or couldn't solve some of it and get another explanation.

Failure is a part of life. Accepting one's own limitations and dealing with failures or mistakes can be hard, but every child must learn it at some point. And yes, this may mean tantrums and tears, but the less you try to solve it, the better. You can be a sounding board if she needs to vent or someone to console her if that's what she needs, but don't try to solve her problem - unless she explicitly asks for help. Taking her work to another place is for me a sign that she wants to be left alone and work through it on her own. Give her the freedom to take responsibility - think how much more proud she'll be if she solved it alone and without you correcting and improving her work.

Most of the answers (as well as your question) here make it sound as if your daugther was unable or unwilling to accept her own mistakes.

But when I read these sentences

It starts with her making a mistake, and me correcting it. [...] I've tried variations on "stop", "no", "wait", "hang on" and "just a second" but they all have the same result

it sounds as if you are sitting right next to her watching over her shoulder and immediately correting whatever error she makes immediately (why else would you need phrases like "stop" or "hang on"?).

Let me tell you: this is the perfect way to create frustration.

Having someone point out every flaw within seconds of it occurring and without any chance to recognize and correct the error yourself is just downright demoralizing. Over longer periods of time it sucks out your self-esteem and gives you a feeling of incapability and helplessness (especially if the mistake you made is a small one which you just know you would have recognized yourself if given the chance).

This way everything, even fun things like videogames, can becom a frustrating nightmare if someone like a parent or older sibling points out what you are doing wrong all the time.

So step back a little.

When she is doing her homework do not sit next to her but be in the room next door.

Make sure she knows that whenever she needs help she can come to you and ask, but do not interfere until she herself thinks its done.

Of course you can still check her work and point out all the flaws at once and ask her to correct them (like "Your solutions on excercise 1, 5 and 7 are wrong. Do you think you can correct them yourself?")

Stephie's point is valid - and it makes me wonder if she reacts the same way at school when she is not perfect. If it is only an at home problem, then I think her advice is bang on. That doesn't mean you cannot help.

If she is having problems everywhere, perhaps she feels like making a mistake is a bad thing. So many children feel this way. We can try to build them up and gain confidence.

• When you or your partner makes a mistake -- point it out. "Opps! I dropped the papers all over the floor! It's no big deal but will you help me clean them up?" "I made a mistake. Today is Sunday, not Saturday. Silly me! Oh well!"

• Show her that she is important to you no matter what. Ask her opinion -- especially about things that you cannot correct. Look through a nature book and ask which images she likes best, or what colour she likes, and then praise her for those ideas.

• Ask her how to solve a problem -- TV is great for this. Stop her show and help brainstorm what the characters will do to fix their problem.

• Deep pressure -- like a good strong hug, can do wonders. Often when a child is overwhelmed emotionally -- for whatever reason -- if you time out with them and cuddle and not talk at all, this will be reassuring. Time out is time off. You aren't mad and if you are -- don't try this until you are calm and happy.
• Choices -- allow her to make choices and to live with the consequences. If you ask if she wants a sweater and she says no but decides she is cold -- let her solve the problem. Then you can praise her for solving her own problem.
• Make sure she is not being bullied at school or daycare. This can make children emotional even when everything seems fine.

I'll answer this by asking "How long is a piece of string?".

And it really comes down to individual approaches and techniques that work for some and not for others.

I am going to answer this as a parent, because I too have a 7yo boy that shouts when he can't do something, yet I tell him "YOU CAN"! That makes it worse by the way. He turns my offer of "encouragement" into an argument and it's not about the task anymore, it's about who wins the argument.

Anyway, that was in the old days (a few months back actually). I don't let us argue. I simply don't go beyond my own personal frustration.

I used to shout and demand he try again and again until he got it right. Oh boy was that stupid on so many levels!

Ok here is what I do. Give it a try...

[1] Child sitting at the table trying to write some words or doing some homework

[2] You're busy doing the cooking

[3] Child starts making grunting sounds and murmering some swear words now and then

[4] Your ears prick up but you don't react - yet

[5] Child yells - STUFF THIS I CAN"T DO IT!

[6] You look at him, smile and listen. Let him get his frustration and anger out. Let the steam dissipitate

[7] Now it's your turn. Approach and offer to help. If rejected, then go back to what you're doing. DO NOT INSIST ON HELPING. Even if you know he's making mistakes - let him!

[8] If child accepts help, sit down next to them. DO NOT STAND NEXT TO THEM. That adds to possible anxieties.

[9] Offer - ok, how can I help. DO NOT ATTEMPT TO DO ANYTHING. DO NOT REACH OVER THEIR WORK OR IN FRONT OF THEIR EYES.

[10] Child starts another tantrum because you're not doing it all! or something like that. If so Repeat step 6

[11] Again ask - may I look? may I try? MAY I... very important the word MAY

[12] Offer him a drink, treat, something to distract them and bring them down to calmness.

[13] Now take their problem seriously and suggest in snippetts a way to go forward, like ".. hey I have an idea... stuff these small letters, lets draw one in any colour you want and make it big ... like the whole sheet even...".

MAKE IT FUN!

and so on.

Just... let her be. Let her figure it out on her own how to deal with it. The last you wish to do is to reinforce/reward the negative behavior.
You giving her attention at a negative spike will turn this into behavior that is rewarded by attention from a loved one. This will trigger more negative behavior to get more attention.

I had a 4 year old that discovered donkey kong on the N64 a few years back. He loved it but found it very hard. Regularly there would be screams of frustration, a controller being thrown on the ground, or sobbing on the floor.

Just, let it play out. Once the frustration is vented they'll pick off on their own where they stopped to vent, determined to get it.
At that point, where the venting is done and they are 'normal' again you can say you can do it. I believe in you. You'll learn it. At no point you wish to do this when they are frustrated because it will only amplify the frustration and reward the negative behavior.

You want to reward the picking up again, getting back on the horse. Not in anyway acknowledging the venting of frustration.

He now plays donkey kong better than I did, and he taught it himself, with minimal help from me(okay, I beat a few bosses, but the actual game play he did himself, solving all the puzzles(even though he can't read english))

A kid that young needs to learn how to deal with his own emotions. How to recognize them, how to deal with them, how to continue afterwards.
If you stop them too soon, they will never come to learn their "limits" and fail to recognize situations later because they are unfamiliar with the full extent of the emotions. Better they "rage" when young, and be mindful of themselves when older, than that they rage when teenager/adult without self taught limits.

Do in short: do not defuse. Offer her a punching bag instead. let her scream a bit. it's healthy. it will teach other lessons than what she was doing.

Then, when calm again, do the steps you listed.

It is better to let her get the cognition herself, so she will not be frustrated but have a feeling of success. You could give her some clues by asking something concerning the issue, e.g.

"Could it be better to write this word with two... ?"

If inevitable, explain the errors with positive formulations, e.g. "It would have been better if...". This sounds much better than "You've done wrong at..."

This may (or may not) add perspective without necessarily adding more knowledge to what has been mentioned already above:

I think of children as empty canvases with a clear purpose in their formative years of life to go around gathering ink. It is not until they mature and grow that they start using the ink they gathered throughout their journey, painting their canvases with warm colors of success, cold ones of failure and many other hues of various experiences.

Inadvertently as a parent, you'll be guilty of having not only given them ink, but also painted on their canvas. This is not a bad thing, but it's probably best to be careful about what you paint. Be it religion, education, career choices, hobbies and any other easily impressionable subject - in conclusion your responsibility towards your child is to give them the tools to survive independently when you'll no longer be around. The earlier they become independent the better, even if you're still there for them.

Remember we are not taught by others - we teach ourselves. Education aims to give us tools and motivation to further explore a subject. This is why we're given homework at the end of a class rather than ending with facts filling up our heads in class till they burst and then assume we soaked in everything.

If you want your children to succeed at whatever subject they're failing at, find ways to make them truly love the subject. They'll teach themselves in a matter of weeks or months and astonish you at their sudden progress. Before you know it you'll find yourself buying books for them on the subject which you no longer understand and your child skims through it as though all the stated facts are obvious.

If they never find passion in that subject, it isn't for them. No point torturing them and wasting their time on a subject they'll struggle all through their early years to achieve a low passing grade, and never again use it for the rest of their lives.

Help guide her, keep her ink clean, stop her canvas from getting smudged and show her the different techniques of going on about painting herself a bright and vivid painting!

Alternatively you could tie her up to a chair and do her homework as you repeatedly call her a li'l sh*t, nailing full marks after full marks. That'll show 'em! :D (just joking of course)

Try putting them in a nappy. Kids want to be grown up, like their friends and family. If you put them in a nappy every time they get frustrated and tell them they are behaving like a baby so you are going to treat them like a baby, very quickly they associate frustration with being babyish and in order to get away from babyishness they will make every effort to avoid becoming frustrated.

This is not a method of discipline, but moreover it is a method of behavior-modification using negative reinforcement. If you give the child a candy or chocolate while they are calm they will also associate being calm with pleasure as they enjoy the taste of the candy. This will encourage calm behaviour as well.