The matters that should be taught to the Muslimoon are the Quraan and the Sunnah. These matters should be taught with good while in the masjid. Learning the Quraan should be done in circles (halaqaat).
Shaykh ‘Abdullaah al Bukhaari stressed how memorization of the Qur’aan should be taught with correct understanding. Learn the aspects of Tawheed. This is how men, women and children should all be taught. This is what the Pious Predecessors did constantly in the reminder of benefit (i.e., learning the Quraan and learning Tawheed). Learning the Qur’aan should be very important for all Muslimoon.
In regards to learning Quraan through the family, they should establish learning it by way of a schedule. Also, the family should go over the suwar that have been memorized, and give out homework assignments (i.e., memorization).
In learning the Quran, the male teachers should teach the boys and the women teachers should teach the girls.
Also, we should learn more than just memorization. We should know the meaning of the Book. The one who is teaching should be sound in ‘Aqeedah (belief) and sound in Manhaj. This is of the methodology of the Pious Predecessors. How can we be upon the (correct) methodology if we’re not memorizing the Book of Allaah? ‘Abdullaah bin Mas’ood (radhiyallaahu ‘anhu) learned from the Messenger (sallallaahu alaihi wa sallam) by way of his memory up to 70 suwar.
The Muslimoon should be constant in memorizing Quraan. Without practice, the Muslim can forget. The Shaykh (hafithahullaah) stressed the virtues of reading the Quraan and (warned) not to boycott it. By the aspects of boycotting it, one forgets how to recite it properly.
How can the man (husband) teach the women and children properly when he isn’t learning the Quraan himself? This is not being intact with memorization. It’s a must to learn the Quraan.