Appropriate difficulty expansion can enhance children's interest in learning and improve thinking ability, but the premise should be appropriate, if the difficulty is too much, the child's existing knowledge system and thinking ability can not be connected.
Most children don't have the strength to take the lead, and the so-called Peiyou is more just a pseudo-Peiyou. It can create the illusion of winning at the starting point, but it does not have enough motivation to support it to reach the end.
For example, the learning of the Olympiad, the most intelligent part of the children, the difficulty of the Olympiad is slightly beyond their ability, and they can broaden their thinking through training, but for most children, the difficulty is beyond the thinking ability, although they are also learning and can do the right questions, but they do not rely on thinking, but the ability to do the questions with a set of models, they are just reflexively substituted into the numbers, and there is no thinking process during the period.
A large number of children practice Olympiad thinking, but reflected in how to do without thinking, the ability to do the right thing, they will be in junior high school geometry and function learning, the results are very good, relying on their primary school practice of Olympiad thinking, do not think about the ability to do problems with a set of models.
However, after high school, the types of questions change and are complicated, and thinking ability is needed as the foundation, rather than skills and routines.
In our time, there were also many math competitions, but there were few special competition training, and everyone really competed to see who was smarter, unlike the current Olympiad math is also a variety of conceptual routines, more just to satisfy the vanity of parents.