In the real world problems are the fuel of inventions. We do not invent items we have no need of. The most successful individuals in life are the ones who can solve problems in the most efficient way. It is only natural that education would move to a more problem based learning.
Problem based learning was said to be originated in the 1970's at a medical university in Canada. However, some great philosophers including Socrates have been known to use this form of education throughout history. As with many great things, we have just recently rediscovered this form of education.
Problem based learning is learning based around given problems. However, these are not your typical text book problems or questions. These problems are not defined by the teachers and words, but are defined by the students who are provoked into thought by the given situation.
The education is not only related to the subject but related to life. These problems may be based on math, but you are going to be increasing the student's life skills as well. Students will learn who to work as a team, how to define the problem, and how to solve the problem. This form of education truly invokes a student's critical thinking skills.
As a result of the problem based learning form of education, the roles of student are transformed. They are now involved in self-teaching. The role of the teacher is also transformed as they are no longer teaching the student, but become more of a resource for the student to teach themselves.
For this form of education to proceed, both teachers and students will need to learn how to assume their roles. This can present a challenge for teachers as they have to learn a new way of teaching. As life presents problems in this manner for students in their personal lives, they may already be exposed to this form of problem solving, but there are resources out there for teachers who need help presenting these problem sets to their students.