*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.

Rote instructional methods promote retention (the ability to solve problems that are identical or highly similar to those presented in instruction), but not problem solving transfer (the ability to apply what was learned to novel problems).

For example, in 1929, Alfred Whitehead used the term inert knowledge to refer to learning that cannot be used to solve novel problems.

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?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 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.It takes sixty days for the lake to be completely covered with water lilies. " In this problem, the problem solver must invent a solution method based on working backwards from the last day.Based on this method, the problem solver can ask what the lake would look like on the day before the last day, and conclude that the lake is half covered on the fifty-ninth day. It is also customary to distinguish between well-defined and ill-defined problems.The definition of problem solving covers a broad range of human cognitive activities, including educationally relevant cognition–figuring out how to manage one's time, writing an essay on a selected topic, summarizing the main point of a textbook section, solving an arithmetic word problem, or determining whether a scientific theory is valid by conducting experiments.A problem occurs when a problem solver has a goal but initially does not know how to achieve the goal.Thus, the hallmark of problem solving is the invention of a new method for addressing a problem.This definition has three parts: (1) problem solving is cognitive–that is, it occurs internally in the mind (or cognitive system) and must be inferred indirectly from behavior; (2) problem solving is a process–it involves the manipulation of knowledge representations (or carrying out mental computations); and (3) problem solving is directed–it is guided by the goals of the problem solver.

## Comments Non Routine Problem Solving

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