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Scholars distinguish between well-defined and ill-defined problems. Briggs and Reinig defined a well-defined solution in terms of space solution space. Pretz, Naples, and Sternberg defined a well-defined problem as one for which the parts of the solution are closely related or clearly based on the information given. Problem finding applies to ...
In particular, the term well-defined is used with respect to (binary) operations on cosets. In this case, one can view the operation as a function of two variables, and the property of being well-defined is the same as that for a function. For example, addition on the integers modulo some n can be defined naturally in terms of integer addition.
The term problem solving has a slightly different meaning depending on the discipline. For instance, it is a mental process in psychology and a computerized process in computer science. There are two different types of problems: ill-defined and well-defined; different approaches are used for each.
An example is a skillful way in which his terrier Tony opened the garden gate, easily misunderstood as an insightful act by someone seeing the final behavior. Lloyd Morgan, however, had watched and recorded the series of approximations by which the dog had gradually learned the response, and could demonstrate that no insight was required to ...
Problem-based learning (PBL) is a teaching method in which students learn about a subject through the experience of solving an open-ended problem found in trigger material. The PBL process does not focus on problem solving with a defined solution, but it allows for the development of other desirable skills and attributes. This includes ...
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Coastline paradox: the perimeter of a landmass is in general ill-defined. Coin rotation paradox: a coin rotating along the edge of an identical coin will make a full revolution after traversing only half of the stationary coin's circumference. Gabriel's Horn: or Torricelli's trumpet: A simple object with finite volume but infinite surface area.
Designing deals with design problems that can be categorized on a spectrum of types of problems from well-defined problems to ill-defined ones to problems that are wickedly difficult. [14]: 39 In the 2010s, the category of super wicked global problems emerged as well. [15]