Problem
solving can be thought of in at least two ways. First, problem solving
represents a method of instruction where teachers ask process-type questions
that encourage students to explore. These questions may include these:
Can you solve the problem another way? Is there another solution? How can
you justify your solution process? and How does this problem relate to
others that you've solved? Process or problem-solving questions require
extended answers and motivate students to look at the mathematics in a
deeper fashion.
Problem solving also suggests the type of problem that students solve. The standards advocate problems that require an extended time period to solve, that are solved with problem-solving strategies (working backwards, make a table, guess-and-test, and so on), and that can be extended to probe a concept or idea even further. These problems do not lend themselves to solutions by applying computational methods. They promote higher-level thinking and creative solution techniques.
In grades K4, the study of mathematics should emphasize problem solving so that students can