Based on my own experience, I’ve come to believe that none of no material incentive s can be compared compares with the simple moral support. Paying attention to the child, encouraging and teaching him them to find a pleasure of in studying, parents can achieve results great results, because when the child is interested in studying, none of these promotions incentives are needed go to the wayside. (the idiom is 'fall by the wayside' and is more colloquial).

However, it is the right of (/'up to' =the responsibility of) all the parents to decide which promotion method to use. They can try to think come up with of their own system or use any of the methods mentioned above. It seems that the most optimal variant (this sounds very scientific!) best option would be is to combine all of them.

Very well written, well done!

Parents offering extra pocket money as a promotion method (this sounds to formal/impersonal - vocabulary you'd use when discussing advertising ) to their children to encourage hard work. in studies.

There are several methods used to incentivise/motivate of promotion and motivation (English is a verb-heavy language - the verb is usually preferable to the noun) are used to make children to study well. Some parents use a system of moral encouragements, some parents give presents, and while others the third type(this doesn't sound natural - I'm not sure you'd use 'type' with people.) uses money as a universal motivator. Child psychologist’s opinions on which method is the most effective are differ as all of them have disadvantages and pitfalls. 

The most ambiguous method is promotion (Promotion - as a noun, it usually refers to a job promotion or a sales promotion) incentivising children with money. Lots of childcare professionals consider it asto be one of the most effective methods; they and offer suggest trying out the following approach: to try next model of its application- during the period of a week or a month, parents should put a small stones in a box for each good mark and then, in at the end of the week, should give their child an honestly earned salary after counting depending on the number of stones collected.
A definite plus (a bit colloquial) advantage of this method is that it encourages in development of motivation (too many nouns!) children to “earn” as much as possible. Thus, child expert’s advice is not to overlook the way in which their children spend their “salaries” (Salary is too formal ) "earnings"- by analyzing (/analysing) the spending with the child, parents can help to teach him them (= him or her) to properly and profitably manage their earnings.

In spite of these advantages, it seems that this method has lot of minuses drawbacks. First of all, (comma always needed after introductory clause) children get used to studying only for some encouragements a reward. The process of studying andto  getting increase knowledge become unimportant and depreciate( depreciate is usually used when referring to value) for children. The second, equally important aspect is the growing appetites and needs of today’s children. At some point, parents may find that their budget is does not stand up for to their children's queriesdemands.