Do you have a heat lamp, or just a UVB lamp? What are the exact temps?
You need to be supplementing. Go buy two supplements, 1. a multivitimin supplement such as Jurrasi-vite, and 2. a pure calcium carbonate supplement such as jurrasi-cal or Rep-cal. Supplement with the pure calcium supplement at every other feeding, and with the multivitamin supplement once a week. This is very important and probably plays a big part in his slow growth.
Also, you need a bigger tank. I personally think a 10gallon is too small for any size beardie, not just because there is no room to run, but because there is no room for a thermogradient. Beardies need a basking spot of 100-110degrees, and a cool end in the low 80s. In a 10gallon tank it is close to impossible to get the temps right because if one end of the tank is 100degrees then the whole tank will be 100degrees and you will cook the little guy. Buy at least a 20gallon long tank for now, get a good acurate thermometer (an indoor/outdoor digital thermometer from wal-mart is good...those stick on ones from the pet store are junk) and make sure the basking temps and the cool temps are good.
He is not THAT undersized, considering he is only 4 months old, but it does sound as if you need to do a lot more research about beardie care. Check out some good websites such as beardiedragon.com and beautifuldragons.com and get some good books such as The Bearded Dragon Manual by Phillipe De Vosjoli. I would bring a fecal sample to a vet as well just to rule out parasites, fecals should be done 1-2x yearly on all reptiles even if they look to be in great health.
How often are you feeding him?
For starters:
-get him into a bigger tank (20-30gallon long is a good size for a 6inch) and be prepared to go even bigger as he grows
-get a basking light if you do not already have one
-get a good thermometer and check the temps, do not attempt to get your tank to the 100s in the ten gallon, please, move him to a bigger tank first
-get a fecal done at the vet
-make sure he is fed daily, or at the very least every other day, feed him as many insects (supplemented) as he will eat in 10-20minutes. You can leave veggies in his tank all day so he always has something to pick at if you want. You can also leave the bearded dragon food in his tank all the time as well.
If you make a few changes to your husbandry then your beardie should grow like a weed and be just fine 
Good luck! and keep us posted
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