Answer
As-salamu `alaykum,
May Allah bless you and your wife, and your proactive roles as parents that extend beyond the physical issues (though important) to the moral issues which should always come first.
The way you and your wife have chosen to train your son seems fine, but it seems that you are getting board: “is going on for rather longer than I had hoped”. I want to assure you that every child grows and learns at his own pace, it is only when we start comparing our children to others that we become restless and begin suspecting whether they are ‘average ‘ or not. Please don’t put yourself into this vicious circle, it will only make things more difficult, not only in potty training, but pertaining to every milestone of his growth.
Pertaining to your covering his private parts, the area of the private parts is a very sensitive one, an extensive network of nerves, arteries and veins lie there nurturing the sensitive genitalia. To keep it slightly warm Allah (SWT) surrounded it by numbers of glands, as it shouldn’t be too cold. When we keep it uncovered for a long time we are counteracting the effect of these glands and we are subjecting the genitals to “ascending infection” i.e. infection by germs from the surrounding environment , which in turn may cause irritation to the urethra and urgency, thus prolonging the time of potty training.
Islamically speaking, we all know that the child is not held accountable until he reaches the age of maturity, meaning that the concept of “awrah” and the sin for uncovering the private parts is not perused yet. But nevertheless he should be trained for keeping his dignity very early in life, simply because Allah has created every one in a pure and descent state not only in belief, but in manners and behavior as well.It is his parents and the surrounding environment that stains this purity either by not nurturing the seed of goodness he owns or by adding wrongs from every direction.
The child is born having the seeds of haya` (Shyness) within, we know from the holy Qur`an, that when Adam and Eve ate from the tree they were aware of their nakedness for the first time in their lives and in that awareness, they covered themselves with the leaves of the garden. Why then they were keen to cover themselves knowing that there are no other people living with them !! it is the fitrah (Primitiveness)then.
Allah praised people who had haya` and so did prophet Mohammad (PBUH). He once saw a man washing in a public place without a lower garment.
“Allah is characterized by modesty and concealment. So when any of you washes, he should conceal himself. (Abu Dawud 31 #4001)
“Every deen has an innate character. The character of Islam is modesty “ (Muwatta: 47, # 2.9)
It is also preferred that parents start teaching high moralities while their children are so young, and not wait until they become older, if we wait until they are seven or ten it would be too late . For example we teach our children to stand beside us as toddlers while we pray to get used to the act of prayers, yet we begin teaching them the actual prayers when they are seven. Prophet Muhammad used to teach his grand sons Al Hassan and Al Hussein morals while they were still learning how to walk, and Allah praised prophet Yahya for being knowledgeable in deen and in morals while still a child.
“O Yahya! take hold of the Book with strength, and We granted him wisdom while yet a child, And tenderness from Us and purity, and he was one who guarded (against evil), And dutiful to his parents, and he was not insolent, disobedient ” (Quran 19:12-14)
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