Encourage them to be more independent. Apply the 5 Whys framework. By encouraging the person to question the problem repeatedly, they will be able to get to the root cause of the problem &, find the best solution, and find ways to visualize the problems. The key to empowering employees to better solve problems is to transform managers into coaches.
Transformation is difficult, but it will revolutionize your organization. To allow the student to develop their problem-solving skills, we must stop giving the answers. The person you're training is the closest to the problem, so be sure to ask for their perspective and really listen to them. At its best, coaching can build very strong and productive relationships between managers and their people.
The collaborative coach is a partner who supports the person you are training and works with them to achieve success. They tend to focus very closely on the process and flow of a given coaching conversation and to stick to their rules of participation. To be a better leader, not only do you need to teach the thinking and methodology behind problem solving, but you must also develop your own experience as a problem solving coach. Organizations that focus on coaching often have a smaller margin of control for each manager, but because they get more benefits from those employees as a result of training, the benefits remain positive.
I can't think of many investments with greater and more sustainable long-term returns than creating an organization in which every manager is a coach. You should think about how many team members a manager can train without diluting or sacrificing quality. Managers must make decisions on a situation by situation basis about when they are managers first and when they are coaches first. I know an executive who strives to keep his schedule very clear and open to be available to his team for training or other needs.
Otherwise, there will be more managers committed to old expectations and who will increasingly resist becoming coaches.