Aspect of Adaptability increases Basic Skill damage by 80% when above 50% Mana.
Through testing on the dummies i confirm this is working as expected for Sorcerer and all 4 Basic Skills.
However, when using Flameweaver unique, placing a firewall, and firing the fire bolt through the firewall, the resulting damage is no longer affected by Aspect of Adaptability.
The damage per bolt, or for all 3 bolts combined, is exactly the same with or without Aspect of Adaptability equipped.
Funny, I was messing around with fire bolt and I noticed this aspect could come handy, when I tested it on dummy I noticed that something was taking its functionality away, trail and error and yeah, the gloves do disable it. This is 100% oversight, because game probably thinks fire bolt is neither basic or core skill xD When it goes thru the fwall. It becomes something else lol. The aspect works as long as you attack fbolt on the dummy, but the moment fwall is placed and projectile gets /altered - it’s gone.
Any fix blizz devs? 
BUMP 
Patch 1.4.4 notes:
Fixed an issue where Firebolts going near but not through Firewall would still split into 3 when using Flameweaver.
Happy you tinker around firebolt interactions, really.
Fixed an issue where the following Aspects were not dealing as much damage as intended:
Dust Devil's Aspect Aspect of Surprise Trickster's Aspect Aspect of Artful Initiative Vengeful Aspect Aspect of the Arrow Storms
Unhappy adaptivity aspect is not on the list. TL:DR it doesn’t do what it’s supposed to do, whenever a projectile is altered by some effect. Flameweaver + Firewall alters fire bolt. Druid’s staff Greatstaff of the Crone can cast storm strike, also doesn’t work. There’s prob more bugged out interactions, one comes in mind with Staff of Lam Esen, but doubtful anyone is playing that, so there hasn’t been reports about it.
Greatstaff of the Crone works OK for me.
Edit.: Using Claw as basic skill (obviously). You don’t see the visual effect as when casting manually, but the dmg is there.