These connections also create flexibility in her thinking, enabling her to extend her knowledge to new mathematical situations and beyond. Good problem solvers, says Robert McIntosh, Mathematics Associate for the Northwest Regional Educational Laboratory, can see past the surface features of problems to common underlying structures. They can monitor their own thinking strategies, recognizing when an approach or tactic is not being productive and modifying it as necessary. Furthermore, good problem solvers are resourceful, confident, and willing to explore. They re persistent and tolerate a measure of frustration.
Japanese students are some of the most tenacious problem solvers.
And in this increasingly complex world, the ability to transfer knowledge and skills to meet changing conditions and challenges is essential. From our best judgment, we create education standards based on past experiences, research, advice from practitioners, and societal expectations. When the National Council of Teachers of Mathematics began issuing its standards for math teaching and learning in the 1980s, problem solving rose to the fore of standards reform. Across the country, states are writing mathematics standards and assessments to include problem solving, acknowledging the importance of assessing students ability to reason, communicate, make connections, and apply their knowledge to problem situations. Thus, problem solving is an area teachers are increasingly expected to teach and assess.