Some psychologists seem to believe that "more crying = better", but that is an oversimplification. Suppressing feelings is inauthentic, sure. But if you just keep poking at someone until you make them start crying, that is not the original authentic emotion either. Make sure your (or rather your brother's) desire to see your daughter cry "properly" will not go as far as to make her cry over the fact that her father refuses to stop tormenting her emotionally until she makes a "proper" show of crying. Make sure it's about her, not about your brother's idea of what is a "proper" form of sorrow.

Just to be sure, check if he does not have some problem with hearing. That could explain both the lack of musical skills and the loudness.

+1 for cartoons. It shows that knowing another language can be a source of FUN, not just a duty.

I think the problem with Piaget is mostly with people interpreting his findings without understanding statistics. One thing is saying that an average child does X at age of N years. A completely different thing is insisting that every child must do X at age of exactly N years -- not a year sooner and not a year later, otherwise something horrible happens. No, people are different. (Just like finding an average height of a person does not mean that everyone taller or shorter is sick.) On the other hand, if more recent science is available, use that. That's how science works.

Definitions of Left and Right are mostly rationalizations. Reality is: Some people want something. Politicians realize they could gain votes by promising it; unless it alienates their existing voters. So if the idea seems compatible with the other ideas of the party, it is added to the party line. Thus clusters of compatible ideas are created, partly by similarity, partly by historical accident. Then ideologues try ex post facto to explain why these ideas should belong together. Sometimes there is a reason, but sometimes it's an accident. Let's not try to explain what really does not exist.

@Hannibal: A good reason for a downvote are the simplictic assumptions in this answer. (All schools are the same, evil. All bored children are bored because they are geniuses.) Well, sometimes it is true, and sometimes it is not. I am a fan of homeschooling in general, but if you try it, you may find out the hard way that the teachers were not as stupid as you thought, and that it is really difficult to make your child interested in something else than e.g. video games. You may find that talking about things is fun, but at the end your child remembers nothing. Etc. Children are different.

Not enough information here. Dozen different parents could write the same question, yet the problem could be different for each of their children, and would require a different solution. Some children are bored because they are bright. Some children are bored because they are dumb. Some children have medical problems. Some children need more physical activities in their free time. Some children are computer-game addicts and become aggressive when they have to turn off the computers. Some children are so concerned with a problem outside of school (e.g. in family) that they can't focus. Etc.

A discussion of a specific subject could also be very useful, because it could bring a lot of specific ideas. The rule "align the subject with your child's interests" is useful in general, but to be implemented, we need specific ways to do it.

Not all rewards work in the same way. For example, it is generally true that external motivation supresses internal motivation. (People do X voluntarily. You start rewarding them for doing X. They learn that X brings rewards. Then you stop rewarding them. People stop doing X, because now they believe it's only worth doing X for a reward.) But there is an exception: a sincere praise does not reduce internal motivation, although it technically is an external reward. The key is that the rewarded person must believe that the praise was deserved. (Undeserved praise is harmful too.)

The normal behavior becomes normal only after we learn it. Until then, it is just a new behavior we learn. Otherwise, we wouldn't have to learn it, right? (In a different country or in a different century, the concept of normality would be different in some aspects.)

The whole concept of "don't get involved" seems outright evil to me. As a former teacher I know the limitations of the school system. Even if one tries their best (which is not always the case), there is lack of time and resources, students disrupting others or taking disproportionate amount of attention, etc. so always something remains unexplained or explained insufficiently. From people I know, usually teachers pay a lot of attention to teach their own kids at home; I guess because they know what the school cannot give them. School should be a service, not a monopoly on education.

There is an amazing computer game for learning algebra, which includes the concept of fractions. dragonboxapp.com It is just a game; if you try it, the worst case is your daughter will say it's boring. The best case: she will learn everything she needs and more, while having fun.

The children copy what you do, so if you want to improve your children, start by improving yourself. The fact that your children copy you should just provide you additional motivation.

You did not mention how much time per day does your son spent playing games. Do you have some limit? Are you actually measuring it? Or does it all depend only on whether the computer or mobile is available at the given moment.