I don't have an academic answer unfortunately, but experientially, for the most part the biggest issue seems to be that the mindset of the child is different in a conversation with their parents than with a teacher.
My children were entirely differently behaved in daycare versus at home, when they were younger. My oldest refused to nap under any circumstances at home from about 18 months on - unless we had done something incredibly tiring such that he fell asleep in the car or the stroller, anyway; if we tried to put him down for a nap at home it was two hours' wasted time on our part. But at daycare, he was the best napper in the class - napped 2.5 hours a day, went right down. Being in a different environment led him to have a different set of habits.
My younger son (6) goes to a Montessori school, and he still exhibits this to a remarkable degree. At home he is silly and hard to keep focused, even for six; if you saw him you’d think he had ADHD.
But at school he’s a totally different person. He is the most focused kid in his age group. He complains constantly about the other kids not paying attention when he tries to teach them things. His teacher raves about his focus and ability to complete tasks.
We have been able to leverage this at home- by getting him into ‘school mode’. This started when I had some trouble at bedtime and would ask him questions about school - he’d quiet right down and immediately become serious and talk about it. We learned that we could use this to teach him tasks, and are able to get through to him a lot more easily than we could before.
As an example, I taught him to clean the bathroom last month, one section per week. Montessori lessons work by focusing on showing - doing - teaching (show, then they do it, then they teach it), and by being very tactile and explicit. They follow concrete recipes, and usually have discrete sets of tools they set up before doing the task.
So I got a bucket with cleaning supplies in it, and put him in the school mindset by telling him we were going to give him a lesson (using the same words they use at school). I gave him a lesson modeled after one I saw during a parent meeting. He paid attention and then went to bathroom two and followed the instructions well. He’s now cleaned the toilet three times, and the third he did completely independently.
Comparing this to teaching him to fold laundry, which we’ve struggled with for months. I suspect here we have an issue - our oldest we get to fold by letting him watch a show while he folds. He works best with external incentives, so this works very well for him. But it breaks the school environment - so our youngest has a lot of trouble with what’s really an easier job, because he’s in fun at home mode not school mode.
Second, no matter what you try you’re going to have conflicting emotional baggage that makes it harder.
If your teacher tells you something, you’re used to taking that as constructive criticism (if you have decent teachers anyway). A parent saying something, though, seems more personal - just like if the gym instructor tells you to lose ten pounds versus if your spouse tells you the same thing, right?
That I’ve not really found a good way to work around, any more than I have a suggestion for how to talk to spouses about weight. Being cognizant of it is the most useful thing in my opinion - if you are aware your child is likely to take more personally your teaching, then you can adapt to be more sensitive.
I think there’s space here too to get out of parent mode - if you find yourself getting into a normal pattern where it will end in arguments, stop and get out of it. Identify what starts the pattern and break it. When i teach my seven year old something, I often get the ‘I know that dad’ or ‘duh’ - and I know I need to change the pattern. So I try to get him to show me the answers instead of showing him, and if it’s something in his wheelhouse he usually can. (But I haven’t figured this out totally yet sadly; if he can’t figure it out we tend to get stuck. Sigh. )
