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 . .