Concerning means that which affects one's happiness or welfare. It is an expression of solicitude, anxiety and compassion towards a thing or person.
"I've been wanting to speak to you concerning the results of the children, they were bad."
Disconcerning is a ridiculous attempt at negating the tenets of the original word, concerning. It attempts to introduce negativity by adding the prefix "dis" which is not acceptable in this instance.
Discerning means an act of perceiving differences and distinguishing something as different by detecting by senses or intuition.
"Discerning the truth between both your words is going to be tedious."