*In addition, the problem solver must monitor the problem-solving process and make adjustments as needed.A challenge for educators is to teach in ways that foster meaningful learning rather than rote learning.For example, for most adults the problem "589 × 45 = ___" is a routine problem if they know the procedure for multicolumn multiplication.*

When the goal of an educational activity is to promote all the aspects of problem solving (including devising a solution plan), then nonroutine problems (or exercises) are appropriate.

In a nonroutine problem, the problem solver does not initially know a method for solving the problem.

Well-defined problems may be either routine or nonroutine; if you do not have previous experience with water jar problems, then finding the solution (i.e., fill the 127, pour out 21 once, and pour out 3 twice) is a nonroutine problem.

In an ill-defined problem, the given state, goal state, and/or operations are not clearly specified.

" In the problem translation phase, the problem solver may mentally represent the first sentence as "Lucky = 0.65," the second sentence as "Lucky = Vons - 0.02," and the third sentence as "4 × Vons = ___." In problem integration, the problem solver may construct a mental number line with Lucky at 0.65 and Vons to the right of Lucky (at 0.67); or the problem solver may mentally integrate the equations as "4 × (Lucky 0.02) = ____." A key insight in problem integration is to recognize the proper relation between the cost of butter at Lucky and the cost of butter at Vons, namely that butter costs more at Vons (even though the keyword in the problem is "less").

In solution planning, the problem solver may break the problem into parts, such as: "First add 0.02 to 0.65, then multiply the result by 4." In solution executing, the problem solver carries out the plan: 0.02 0.65 =0.67, 0.67 × 4 = 2.68.

For example, in the problem, "Write a persuasive essay in favor of year-round schools," the goal state is not clear because the criteria for what constitutes a "persuasive essay" are vague and the allowable operators, such as how to access sources of information, are not clear.

Only the given state is clear–a blank piece of paper.

Ill-defined problems can be routine or nonroutine; if one has extensive experience in writing then writing a short essay like this one is a routine problem.

The process of problem solving can be broken down into two major phases: problem representation, in which the problem solver builds a coherent mental representation of the problem, and problem solution, in which the problem solver devises and carries out a solution plan.

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