Has he ever read a guide on how to play arcane? Cause it doesn't look like it from the log. He doesn't do the basics of arcane really, a burn phase followed by a conserve phase. Like the poster said, not using evocate or mana gem the correct # of times is a clear sign of someone who has no clue how to play arcane properly. So you only need one tip to tell him:
Forget everything you're doing and read several arcane mage guides including the one on this site and learn how to actually play the class. There's an addon called MageManaBar he can use which tells him roughly when to use what to make it even simpler. Arcane is a little harder that people give it credit cause if you screw up your evocate or don't time things properly you can easily get things like your guy doing 25k when it should be closer to 40k. And after that when he still sucks tell him to switch to fire. Harder to screw up imo and better for add fights and movement (aka almost every fight).