Carrots turning dark at heads, and on skin after chopping?
I ran a school tuckshop and also a college cafeteria for some years and I have seen this many times with new staff members. 

The problem with discolouration is any damage to the skin. If preparing carrots in advance or in larger quantities ( sliced, grated, etc ) the skin needs to be thoroughly removed before storage. If any trace of skin is left they will get a brown discolouration.

The heads are a different matter. Carrots are root vegetables and, like potatoes, if any moisture is around the plant will make signs of growth. It's not harmful, they can be cut off a bit further down and any new fine roots which begin to grow can come off with peeling. When cutting down to tops you might see the green colouring further down in the centre. This isn't harmful, in fact nutritionally adds some chlorophyll and folate among others to the diet, but can taste bitter. 

Hope this is helpful, good luck