National Council of Teachers of Mathematics. Principles and Standards for School Mathematics . The epic quest to solve the world s greatest mathematical problem. Improving the quality of teaching in mathematics and science. If problem solving is at the heart of mathematics, then nonroutine problems are at the heart of problem solving.
True problem solving involves nonroutine, or open-ended, problems.
Moving into the territory of nonroutine problems is full of unknowns. Solution methods and answers are not made explicit. Decisionmaking is shared between teachers and students. Teachers must predict what tactics and questions might come up in class, preparing for them as best they can. Teachers need mathematical expertise to anticipate students approaches to a problem and how promising those approaches might be.