# Thinking Problem Solving Cognition " 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.

" 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.

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Although the four processes of problem solving are listed sequentially, they may occur in many different orderings and with many iterations in the course of solving a problem.

For example, consider the butter problem described by Mary Hegarty, Richard Mayer, and Christopher Monk: "At Lucky, butter costs 65 cents per stick.

For example, for most adults the problem "589 × 45 = ___" is a routine problem if they know the procedure for multicolumn multiplication.

Routine problems are sometimes called exercises, and technically do not fit the definition of problem stated above.

For example, "3 5 = ___" might be a problem for a six-year-old child who reasons, "Let's see. That makes 4 plus 4, and I know that 4 plus 4 is 8." However, this equation is not a problem for an adult who knows the correct answer. It is customary to distinguish between routine and nonroutine problems.

In a routine problem, the problem solver knows a solution method and only needs to carry it out.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.This is two cents less per stick than butter at Vons.If you need to buy 4 sticks of butter, how much will you pay at Vons?Cognitive processing aimed at figuring out how to achieve a goal is called problem solving.In problem solving, the problem solver seeks to devise a method for transforming a problem from its current state into a desired state when a solution is not immediately obvious to the problem solver.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.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.

## Comments Thinking Problem Solving Cognition

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