"Positive" in dog training does not mean rainbows and unicorns. It refers to adding something, a reinforcement or a punishment.
A correction is a two step process. It starts with getting the dog's attention, diverting him from whatever he is thinking or doing that you disagree with. After you have his attention, you communicate the behavior that you desire instead so the communication goes from A to Z, and finishes with the dog learning the rule or boundary you are communicating.
Positive Reinforcement Only dog trainers will tell you to ignore behaviors you disagree with, reward those you desire, and never give a dog a marker of "no" or any other correction. This is a movement which has developed in the past 15 years. They will recommend euthanasia but never correct a dog's undesired behaviors.
Among the problems with this approach is that dogs have personalities. There comes a time when the enjoyment of doing something wrong or paying attention to an exciting distraction becomes much greater than any cookie or praise which can be offered by the handler. This leaves the handler with no recourse for blocking the behavior, just instead waiting it out. When the dog calmly returns his attention to the handler, that is when he/she gives the dog the biscuit or praise. So what the dog learns is that, if he does what he wants first but then later pays attention to the handler, he gets a reward. This reinforces the dog's undesired behavior.
We suggest you seek Balanced dog trainers who use positive reinforcement as their foundation, but be able to read canine body language and communicate rules, boundaries and limitations when needed. A Balanced approach adapts to the individual temperament and situation of each dog vs. using a one-size-fits-all approach which may be effective for many but not all. A Balanced trainer is firm but not harsh, using the lowest level of energy to adapt to even the most sensitive dog.
“Purely Positive Training - The Worst Thing to Happen to Dogs?,” Charwin Curly Coated Retrievers
“The Problem with All Positive Reinforcement Training - In Defense of Corrections,” Ali Meza, Doggie Joggie - giving dog its day
“Dog Training - What Works and What Doesn’t,” Michelle Welton, Your Purebred Puppy - Honest Advice About Dogs
“Are Dogs or Dog Trainers Getting Dumber? All Positive vs Discipline,” John Wade Ask the Dog Guy