Is it really important to enroll your child into extra-curricular classes after school? I have seen many parents send their kids to drawing and dance classes after school.

No, I don't think its important. Till last year when I was living in Mumbai, I saw that there is this culture of sending kids to extra-curricular classes and keep the kid engaged throughout the day with one thing or the other. I, too, used to send my kid to dance class but only with a notion for him to have fun with other kids, not with the primary motive to learn dance. Also, the classes were just two days a week so it didn't put pressure on him. Instead of sending him to a class everyday, I would rather make him have a nap or let him play with his own toys and spend time with him.