* How to Solve It * (1945) is a small volume by mathematician George Pólya describing methods of problem solving. [1]

If this technique fails, Pólya advises: [6] "If you can''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''t solve a problem, then there is an easier problem you can solve: find it." Or: "If you cannot solve the proposed problem, try to solve first some related problem. Could you imagine a more accessible related problem?"

Problem solving consists of using generic or * ad hoc* methods, in an orderly manner, for finding solutions to problems. Some of the problem-solving techniques developed and used in artificial intelligence , computer science , engineering , mathematics , or medicine are related to mental problem-solving techniques studied in psychology.

Considered the most complex of all intellectual functions, problem solving has been defined as a higher-order cognitive process that requires the modulation and control of more routine or fundamental skills. [4] Problem solving has two major domains: mathematical problem solving and personal problem solving where, in the second, some difficulty or barrier is encountered. [5]

Your problem may be modest; but if it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery. Such experiences at a susceptible age may create a taste for mental work and leave their imprint on mind and character for a lifetime. (26, p. v.)

A ladder 5 meters long leans against a wall, reaching over the top of a box that is 1 meter on each side. The box is against the wall. What is the maximum height on the wall that the ladder can reach? The side view is:

Assume the wall is perpendicular to the floor. Use your calculator to find the maximum height to the nearest.01 meter.

The recent transition to the information age has focused attention on the processes of problem solving and decision making and their improvement (e.g., Nickerson, Perkins, & Smith, 1985; Stice, 1987; Whimbey & Lochhead, 1982). In fact, Gagne (1974, 1984) considers the strategies used in these processes to be a primary outcome of modern education. Although there is increasing agreement regarding the prescriptive steps to be used in problem solving, there is less consensus on specific techniques to be employed at each step in the problem-solving/decision-making process.

One conclusion that may be drawn from these investigations is that individual differences in problem solving and decision making must be considered to adequately understand the dynamics of these processes (Stice, 1987). Attention must be paid to both the problem-solving process and the specific techniques associated with important personal characteristics. That is, individuals and organizations must have a problem-solving process as well as specific techniques congruent with individual styles if they are to capitalize on these areas of current research.