@binip - I would love suggestions on helping DD learn to cope with school! Right now her coping mechanism is avoidance, which is unhealthy. So, assuming that you've got a 6yo who believes learning should be fun (because so far it has been), but who is not even experiencing "learning is not fun" because she's not learning in school, what would you do?
So, assuming that you have gone through all of the other suggestions here and you feel that you've got a good idea that what is really bothering your daughter is the fact that she's sitting for about seven hours and not really learning anything--then here's my advice.
I do think it's important to determine that, given some of the follow up information you've given. A lot of kids are bored in school, but don't act out like your daughter is acting.
In the case that it's really boredom, I would say a couple of things:
--Make a distinction between learning and school. Let her know what school is about and don't ask her to enjoy it. In her case, school is about proving that she knows the material, NOT about learning. This may be something she doesn't want to do. Fine. That's okay. Let her know that you, too, do things you don't want to do.
--Help her think of diversions. Teach her multiplication at home, and beside the addition problems, have her do multiplication. 1 + 7 = 8, but 1 * 7 = 7. Do what they ask then do what you want as a reward.
--She doesn't want to play with the other kids, that's fine. But see if she'd like to meet other kids outside of school who share her interests.
In other words, try to meet her needs outside of school so that she can accept the truth about school, which is that she may not get what she needs from it.
You mentioned that homeschooling is hard for you. Could you take another job that would help you pay for private school for your kids? Or private tutors?
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Below, I talk about some of the reasons that I'm just not into the idea of making school "work" for the child. I'd love for that to happen, but there are 300 million people in this country, expectations of education are across the board, and we have a LOT of people who are not incentivized to learn anything at all because of structural inequality. So you have to think... what can I expect from the school?
First of all, you say learning has been fun thus far. Fair enough. But she didn't enjoy kindergarten. You believed first grade would be better and said so. So, her expectation is not coming from previous experience. It's coming from social expectations that in school, you learn something. And that is an expectation that she could afford to drop.
School is about demonstrating existing knowledge for a lot of kids. That's the success. Not everyone likes demonstrating knowledge, but that's what it's about.
Second of all, I don't believe it's ever useful to give someone hope when there is none. Quite frankly, for the vast majority of children whose parents don't have exceptional resources in terms of time, and who are in-between an IQ of 145+ in a district with a good gifted program, and "right at the 50th% in terms of intelligence, is extroverted, naturally people-pleasing, and REALLY LOVES sitting at a desk for several hours a day", school is not going to be much fun most of the time. There is no reason to tell most kids that school will be fun.
I have no idea why so many people insist it is, will be, or should be fun. It's clearly not "fun" for many, many children, though some teachers really try.
You don't have to be a genius to know the seasons at age six. They are teaching to the bottom 10%. That's incredibly low (particularly as it's towards the end of the year). In my child's general education first grade class, they are growing plants and plotting graphs. This is gen-ed.
Homeschooling with tutors might be your only solution long term.