The answer is actually not quite so simple. I constantly improved on my teaching method over the years, based on personal experience of nearly 45 years as player and coach.
For lower levels such as beginners and novices, I teach in a very methodical and systematic way. I find that too many coaches are all over the place, which really confuse many kids. This slows down their progress, or even cause them to be frustrated and quit. I prefer that my students equally master every piece and every theme, systematically. This will prevent holes in thinking logic later on. This is why I came out with the best-selling 5 volume “Learn Chess The Right Way”. Many schools and clubs are now successfully using this system.
For intermediate and advanced levels, I prefer to teach students to understand positions, ideas, and develop the strong skill to be problem solvers instead of memorizing things in books or endless computer analysis. Not only that it will help the students on the chess board now, it will also help them for the rest of their lives in any profession they choose to pursue. Critical thinking, logical thinking and problem solving skills are so crucial in life. Employers from all across the United States, and around the world, are looking for potential high level employees who possess these skills.
For top level players, in my opinion, there is no one size fits all training method. I have to spend a lot of time to dissect each student’s strengths and weaknesses. Then I have to help them work on improving and strengthen those areas.
This is a very time consuming process and hard work. But if an IM wants to be a GM, a 2500 GM wants to be 2600, a 2600 GM wants to be 2700, or a 2700 GM wants to be 2800, they have to make significant changes. Every player is uncomfortable or not as good in some areas of the game. Unless they are willing to make sacrifices, sometimes even with their ratings, to become sound in every part of their games, they will hit a plateau.
For example, some players need to learn to play more positionally while other may need to play more aggressively. Some need to work on other specific parts of their games. Some need to work on their fitness and endurance. Some need to eat healthier and quit smoking / drinking. Some need to work on their sleeping habits. Some need to work on their mental and emotional fitness, etc.
There are many factors that can hinder the growth of chess players. Changes are never easy. Getting out of your “failing” comfort zone is always difficult. But students have to ask themselves this question: If things are not working, and my rating is not going up the way I planned, what do I have to lose?
So, to sum it up. Are the coaches / players objective enough to dissect the problems? And, do students want badly enough to improve to reach their maximum potentials, or are they just happy to be where they are. This is where the process begins. Talk is cheap. Only decisive and correct course of action will fix the problems.
No matter how good any system is, unless the students are willing, ready, and able to work hard, be disciplined, and follow the process every day, the maximum progress will not happen. I can show any student how to improve, but I cannot make the improvement for them.