The sound position in the Shafi‘i school is that he is not required to perform wudu, nor is his guardian required to compel him to do so, because he is not legally accountable.
Moreover, requiring his guardian to compel him to do so would entail hardship, while it is not obligatory upon him. When there is hardship in a matter that is not obligatory for a child, his guardian is not to compel him to observe it.
The well-known position in the Hanbali school is that a child may not touch the Quran without wudu, and that his guardian must require him to perform it, just as he requires him to perform wudu for prayer (2), because it is an act whose permissibility is contingent upon ritual purity; thus, his guardian must require him to observe it.
They made an exception for a writing tablet: a child may touch it, so long as his hand does not fall upon the letters (3). Some of them explained this on the grounds of hardship (4), while others explained that this writing is not like that in the mushaf (585), for what is written in the mushaf is intended to remain fixed and permanent, whereas this is not ...
If you were to write Quranic text in reverse and place it before a mirror, it would appear in the mirror as Quranic text that is not reversed. Yet it is not forbidden to touch the mirror, because the Quran was not written upon it.
The apparent meaning of the jurists’ words is that it is not permissible to touch a fixed blackboard (5) without wudu if a verse has been written on it. However, one may write the Quran upon it without wudu, so long as one does not touch it. It may be said that this apparent meaning is not intended.