Everyone has already replied that social awareness is important. I guess the question is more directed towards children. Since our children will be our future citizens, we should inculcate the habit of social awareness so that when they grew up, they lead social projects and help the poor and needy. Teaching children about social awareness will also develop their overall personality – compassion, humility, adjustment which is very important.
In my view, rather than concentrating on adults who are adamant and stubborn, it is best to mould children.
Very important and pertinent question Swapna Ji ! 
Yes, awareness towards social responsibility is very important especially in the areas of social ethics, collective social responsibility, civic sense and environment!
But how do we inculcate them is more important. We need to brain storm and identify the areas where awareness is required. Also we need to device methods to address the respective issues in those specific areas.
My take on this is that we can achieve this by including Spiritual education as part of the curriculum. Spiritual education (Yoga, Meditation etc) will empower them with the basic knowledge on how to handle their physical health, emotions and social well-being, thus paving way for a better society! 🙂
100 % important as giving them academic education . . without which they are directionless money makers . .