The non-routine problem is a kind of unique problem solving which requires the application of skills, concept or principle which have been learned and mastered. It is also meant that whenever we are facing an unusual problem or situation which we don’t know the procedures to solve it, we are facing the non-routine problem.
Non-routine problem solving serves a different purpose than routine problem solving. While routine problem solving concerns solving problems that are useful for daily life (in the present or in the future), non-routine problem solving concerns that only indirectly. Non-routine problem solving is mostly concerned with developing students’ mathematical reasoning power and fostering the understanding that mathematics is a creative endeavor.
Non-routine problem solving can be seen as evoking an ‘I tried this and I tried that, and eureka, I finally figured it out.’ reaction. That involves a search for heuristics (strategies seeking to discover). There is no convenient model or solution path that is readily available to apply to solving a problem. That is in sharp contrast to routine problem solving where there are readily identifiable models (the meanings of the arithmetic operations and the associated templates) to apply to problem situations.