Should a minimum ASVAB score be required to be an NCO?
I think it is very necessary.
As a young 19 year old PFC, I had a real tough time listening to an NCO who could not spell simple words, do simple math, or understand simple logic. I always had to second guess myself following this NCO's orders, wondering if this leader even thought the scenario through he/she was sending us to? Would we be reprimanded by another NCO? Just be wasting our time? End up looking stupid ourselves? Taking this NCO's training seriously was even tougher, because in the various minds of the lower enlisted soldiers, this NCO was an idiot. In addition to just losing confidence in our NCO, we also lost our confidence in the promotion system.
Now I am not saying we need to be geniuses, or anything ... but I think being proficient at high school level English and math would be beneficial. Keep current ASVAB scores for MOS's as they are, but make a pre-req for a certain score before going to a promotion board (Which will be the same across all MOS's, but naturally in certain MOS's, the fact you qualified for the MOS in general would mean you already meet that pre-req). Those who do not meet the score, take FAST class until they make it, or they never get to lead soldiers.
What do you think?
To the point about the NCO not being qualified to be your superior. I've had to teach an officer how to start a jeep and others how to rapel. In no way did I ever think they were unfit to be officers I just thought of them being uninformed. That part is fixable the ability to lead not so much in my opinion.
Is communication necessary? Yes it is. But communication is a two way street. Someone has to speak, but someone also has to listen. Everyone has weaknesses or quirks. Members of a team need to learn to identify, both in themselves and others, what all of those weaknesses and quirks are so they can work together effectively and cover down on eachother to close any gaps left by everyones respective weaknesses.
I have seen this many times as well. However, I think basing a promotion off of a ASVAB score would be wrong. The test score only shows the book knowledge of the person. If it was based off the score, it would also limit a person to 4 years of service unless they were able to take it again and score higher. The promotions process has been messed up for a while. I feel once you are eligible for Cpl, it should be strictly based on your mos performance, leadership ability, record of over all performance and esprit de corps. Any man or woman can be molded into good leaders if they are willing to learn and make mistakes.
What it comes down to is, I don't care if they can spell or write an essay. Can they lead Marines into battle and perform their job proficiently.

NCOs
