Math inspired problem solving techniques:
In secondary schools, students are often taught methods to solving standard problems. They repeatedly use the same methods on the same types of questions to gain familiarity. While this approach may work in secondary school where questions are pretty standard, it can fail in advance level maths where every problem looks unique albeit the underlying concepts is the same.
This requires the student to switch FROM remembering a series of steps TO arriving at a solution to breaking down a complex solution into parts where concepts can be applied to solve and then after solving each part, piece the information together to solve the main and larger problem.
A challenge with students when facing such problems is that they are stuck when they are unable to recall any method for solving the entire problem and they do not know techniques that can help them clarify the problem and break it into parts to solve; some get lost in solving the parts and forget to piece the parts back to solve the main problem.
We see this problems with adults too, many adults do not have a vision for their lives, they do not break it into goals and methods for achieving a vision, they do not seek to learn effective methods for their daily tasks, they do not know how to access or organize the information and resources available to them to come up with effective solutions for their life, much of their life is carried out in a thoughtless manner, urged on by whatever happen to capture their attention. They get lost in the busyness of they daily errands and forgot the larger purpose of what they are trying to do or what they hope to achieve at first they begin a project.
Or they may choose to keep their lives very simple, forgoing opportunities for unleashing their full potential and bringing the maximum benefits they can deliver to themselves and society, just like students who only keep to the easy questions, avoiding the learning and overcoming of complicated questions.
Therefore it is critical that we train our students not to remember solutions to problems but rather the ability to 1) clarify a question in terms of its goals, 2) to clarify the information they are provided and organized them so that the mind can access and analyze those information with minimal effort, 3) to select the relevant methods from a whole hosts of methods they are taught 4) to apply the relevant methods in resolving different parts of the problems and 5) finally, not to forget the to piece up the different solutions to the fractions of the main problem to solve the main problem.
And also the courage to attempt the solution for difficult challenges in life.
And if the students can have these skills, then whichever field of knowledge that he desires to acquire expertise in, he will not be inhibited from acquiring them. The only limitation that remain would be the time he has in his lifespan and so he should then be left with the important question which should be clarified as early as possible, what would i want to experience coming to this world, and what experience would i want to leave for those with me and coming after me?