How can I teach my daughter to see her errors?
An 11-years daughter of mine, when checking a piece of her writing or math exercise, where she has one or more errors, simply misses them, whispering contentedly something as 5*6=36.
Normally, if I ask her to count that multiplication, she does it correctly. She is GOOD in math, for example, and participates in math olympiads, not winning, but with good results. But if she already did a mistake, she starts to count the known example not as it should be, but as it is written already. The already written text becomes a new dogma. And the fact that I have checked the piece of text and gave her the number of errors in it, does not help. After the first pseudo-check, if she hasn't noticed an error, she becomes even more sure in correctness of the text and the second check goes even more formally. She repeats the check 1-2 times and after that refuses to do it and says she has it correct. If I prove it is not so, she agrees, but she still does not obtain any training in error finding.
What is interesting, if the erroneous exercise is complex, she recount it correctly. But if it is a simple, one- or two-step task, she can't.
I know, it is very difficult for absolute majority of people to see their errors. In writing, in mathematics - does not matter. As for me, I can find my own errors only by repeating checks, for I can easily do and later miss an error. But with effectiveness of my daughter she almost cannot find them at all.
Any exercises, methods, rituals, or god knows what else are welcomed.
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She may be "reviewing" her work without really thinking it through again. It is easy to just read "2+2=5" and nod your head. Only when you actually engage with the numbers and think "2+2=4, 4=/=5" do you realize something is wrong.
Try to encourage her to essentially "do it again" in her head to see if what she has written is consistent with what she is thinking.
I know you say that she knows her multiplication. To be honest if I'm looking at something like the 8-times table.. I have no idea (for the most part) if it is written wrong unless I start at 1x8 and go through the whole table (2x8, 3x8, etc). I think its a byproduct of having learned it by rote memorization. I personally cannot just pull the solution to 9x8 out of thin air unless I go through the process: "9x8 is 8 less than 10x8 which is 80 so 9x8 is 72". I have similar "tricks" for other multiples, but to just SEE that a multiplication is wrong is actually quite hard for me. (and I'm an engineer!)
Something that I remember from university: Sometimes you just try your best and honestly have no idea if you did something right or not. For more complex things even if it is marked as wrong, its hard/impossible sometimes to see where the error is.
Another tactic you can try is for YOU to do some work (and do some of it wrong on purpose), say.. a page of math problems and then get HER to mark it and correct it for you. Start with "This worksheet contains 4 incorrect answers, can you correct them?" and move to "This worksheet may or may not contain an unknown number of errors, try and find and correct them."
This has been focused on math, but I think some exercises I remember from WAY-back-when is things like "what does not belong... to the pattern of numbers/list of words, etc". Later it was "circle the incorrect punctuation/spelling and correct it", "find the run-on-sentence" and things like that.
I'm going to start with something of a tautological statement here but, in order to know you've made an error, you have to know you've made an error. You can't know you've messed up until someone has told you at least once that you have screwed up and what the right answer is. You can look at 5 * 6 = 36 and instantly know that that is wrong. Why? You've done it a lot. And, at some point in your life, you probably got it wrong at least a couple times too. This is old hat for you, but it's new to her. So don't be too upset or disappointed when your child makes an error. It happens.
As far as trying to help your child catch her own errors, help her get in the habit of giving her work a quick once over when she's done. For example, for anything I write (be it an email or an answer like this one) I will give it a quick read through when I'm done to make sure things look ok, that it flows fine, that I haven't left out words or sentences, etc. Have her do a quick check to see if anything jumps out at her that she thinks might be wrong. Give those things a closer look. And then let it go. No one is perfect. She'll make mistakes and learn from them. I still make mistakes and learn from them, they are just different ones now than the ones from 5 years ago. Don't expect perfection and don't harp on it.
If I prove it is not so, she agrees, but she still does not obtain any training in error finding.
To me it sounds like a pretty natural reaction. When I'm proven wrong about something trivial, I will readily acknowledge it and then forget it. That's because it is of no importance to me and forgetting it has no consequences.
Math assignments are important, but are they to her? What I'm aiming at is, is there any incentive for her to internalize the importance of checking for and finding her own mistakes? For example, my motivation to do well in tests was to obtain a university degree. What I had to learn or develop was an intrinsic motivation to search for and find my own mistakes, so I don't have to face the consequences. She performs well at math olympiads, where she probably does have the intrinsic motivation. But it may lack at home.
It is a bit difficult to make practical suggestions on extrinsic motivation like punishment and rewards (I'm not a parent, so I have not much practical experience). Both have their pitfalls. Punishments can make her resent it / you, kill her joy etc. Rewards can turn into bribery. The lines can blur (she can do X if she's successful, is it a reward or punishment (if she doesn't, she is not allowed to do X)?). It also depends on your parenting style.
Oftentimes, you have a combination of punishment and reward, i. e. if you fail it has negative and if you succeed it has positive consequences. An idea perhaps worth sharing (number just to illustrate the idea): Imagine she gets 15$ pocket money. So she only gets 10$ but, if she is successful, she gets an additional 10$. So now she gets either 10$ or 20$, depending on her performance.
There are other possible reasons she underperforms:
Are the assignments
too hard? Maybe unlikely, but for the sake of completeness.
too easy? Compare them to the tests from the math olympiad. If she knows her way around higher levels of mathematical abstraction, the more "pedestrian" problems may not matter too much to her.
uninteresting? Again, what is so different about what she does in the math olympiad?
real world problems? They become clearer this way and illustrate the applicability in the real world.
problems she may face? If she spends 36$ of her own money for a 30$ item, she will have a stronger incentive to check for errors next time. Learning it "the hard way" is certainly quite effective, but not easy to implement (it needn't be so mean).
You could try multistage tasks, wherein such problems play a minor part, but the correct result depends on them. This way, she can solve more intersting problems and can't negate smaller ones.
It's sort of human nature to be blind to one's own mistakes, so people like engineers or accountants who need their work to be error free use a number of techniques that essentially make you do something different to "break" your error blindness. Some of these techniques include:
Peer review. My children are very accustomed to checking each other's work.
Use a calculator.
Do the inverse calculation. For example, to check 5*6=36, do 36/6 and expect it to be equal to 5, which it obviously won't, so you know it's wrong.
Change the problem slightly and see if the answers make sense in relation to each other. For example, do 6*6 and 4*6 and see if your answer is halfway between.
Solve it in a different way, like counting up by 5's or 6's.
Automation. There are computer programs that can quiz your children and provide instant feedback, so the wrong answer doesn't have time to "sink in."
On the opposite end of not giving time to sink in, the alternate is to give enough time to forget. Set your work aside for a day or two, then review it.
You don't have the same constraints as a school. Take advantage of that.
Teach her to give herself permission to be wrong every day. She may be "trying" to be right.
Knowing that you will be wrong, regularly, is important.
In fact, if you begin to look at an assignment of say, 30 questions, as that it is highly unlikely you will finish it without at least 1 error, you can start to formulate in your head that it may be necessary to give it that look over. Or, in the process of completing said assignment, keep your mind open to those little inconsistencies when you obtain your solution, which might have been an error.
Those long division problems with ridiculous remainders or decimals in the answer are an example. A healthy thought to have when encountering a conundrum like this is:
"What is more likely, that the teacher assigned me a problem with a ridiculous answer, or that I made a mistake in my math solving it?"
When you loop back in to double check because something seems off, I think that is what the OP is looking for his subject to do on her own.
So my answer simply is be very open to the possibility that you are not right. Understand that this will have a higher probability to a degree that is inversely proportional to the amount of knowledge you have on the subject matter and the amount of time and effort you put in to your answer(s).
Be ready to be wrong in life, because you will oh so often be exactly that.
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