Don't worry -- a month isn't long in the grand scheme of things. How long did your mom take to potty train you? It certainly wasn't over night! Have patience, and be consistent and you're pup will be potty trained.

Puppies go potty within a certain amount of time from eating and drinking. Some puppies its only half and hour, others as long as an hour. One thing is that if he takes half an hour then he'll always take half an hour. They are very consistent that way. They need to go potty after each nap, after exercise, and after they eat & drink. Don't free feed - give food at scheduled intervals throughout the day. Let him eat as much as he needs and then take the remainder of the food away after 15 minutes or so. Like I said, he'll have ot go within a predicatable amount of time. Keep him VERY close to you during that time in case he has to go a few minutes early. If you can't keep him with you, then crate him until you can take him out.

Take him out the same door every time.

Correction after the fact does not work. Never ever EVER rub his nose in it. Don't even bother showing his mess to him. Just clean it up and promise yourself to be there next time. Why is rubbing his nose in it and showing him his mess bad? Because you are trying to tell him WHERE he went was bad. He hears that GOING at all is bad. He'll become ashmaed of potty and hide from you when he has to go. Yes, some dogs managed to become potty trained despite this tactic, but more dogs develop lifelong potty issues as a result of rubbing their nose in their poo/pee.