ProblemSolving

=**Problem Solving**=

​ Problem solving is “using existing knowledge and skills to address an unanswered question or troubling situation” (Ormrod). There are two types of problems: well-defined problems that have a clearly stated goal, information needed, and a correct solution and ill-defined problems that may not have a clear goal, all the information needed or one single solution (many possibilities may exist). Although, students are most often presented with well-defined problems in school, building skills to solve ill-defined problems is extremely important, as the real world will present these more often than a well-defined problem.

Problems are solved in one of two ways: through //algorithms// (a set of steps that will guarantee a correct solution) or //heuristics// (general strategies that may or may not lead to a successful solution). Algorithms are usually more helpful in solving well-defined problems provided that students understand how the algorithm works and when it should be used. Heuristics are especially important for ill-defined problems. Heuristics involves strategies such as breaking the problem up into smaller goals, changing complex numbers to simpler numbers, creating an analogy, and putting the problem aside for a few hours to a couple days.

Problem solving is affected by cognitive factors.
 * Working memory puts a limit on how much information can be thought about at one time while working through a problem.
 * Encoding the information into working memory in certain ways may cause a problem to be more easily or more difficultly solved. A mental set is created by repetitive practice of a certain type of problem, leading to automaticity in encoding, which can cause students to misinterpret a problem or overlook certain important aspects of the problem leading to an incorrect solution.
 * Metacognitive processes are also an important factor in problem solving, helping students to determine when a particular strategy should be used and allowing for flexibility in the use of problem solving strategies.

 image: http://sss.usf.edu/504tutorial/Module2/CollabProbSolving.html

Kelsey Rogers