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Suppose students must find the difference of 567 and 153.
Successful mathematical problem solving depends upon many factors and skills with different characteristics.
In fact one of the main difficulties in learning problem solving is the fact that many skills are needed for a learner to be an effective problem solver.
The main goal in teaching mathematical problem solving is that students develop a generic ability to solve real life problems and apply mathematics in real life situations.
Problem solving can also be used, as a teaching method, for a deeper understanding of concepts.
It is used to solve problems and with the advent of the computer technology, it has helped in making social, economical and technological advances that few decades ago would have been unthinkable.
Learning mathematical facts and contents is important but is not enough.
Problem-solving is a process—an ongoing activity in which we take what we know to discover what we don't know.
It involves overcoming obstacles by generating hypo-theses, testing those predictions, and arriving at satisfactory solutions.
Problem-solving involves three basic functions: Problem-solving is, and should be, a very real part of the curriculum.
It presupposes that students can take on some of the responsibility for their own learning and can take personal action to solve problems, resolve conflicts, discuss alternatives, and focus on thinking as a vital element of the curriculum.