B.Ed. Teaching Notes- Definition, Types of Problem
M.Sc., M.Ed., JRF & NET
Lecturer in Physical Science, Arafa Institute for Teacher Education
A felt difficulty to reach our goals is generally called as a problem. Problem solving involves mentally working to overcome obstacle that stand in the way of reaching a goal.
Definitions of problem and problem solving.
A problem is a situation which is experienced by an agent as different from the situation which the agent ideally would like to be in. – Polya
A problem arises when one has a goal but does not know how this goal is to be reached - Karl Duncker
Polya defined problem solving as finding “a way where no way is known, off-hand… out of a difficulty…around an obstacle”.
According to Mayer Problem solving is “thinking that is directed toward the solving of a specific problem that involves both the formation of responses and the selection among possible responses.”
According to Mayer and Wittrock, problem solving is “cognitive processing directed at achieving a goal when no solution method is obvious to the problem solver”.
TYPES OF PROBLEMS
Well structured and ill structured problems
Problems can be well-defined or ill-defined. Well defined problems are called well structured problems and ill defined problems are called ill-structured problems.
A well-structured problem has a clearly specified statement, a clearly specified goal, and a clearly specified set of allowable operations.
For example, “Solve for x: 2x + 11 = 33” is a well-structured problem because there is clear given statement (i.e., 2x + 11 = 33), a clear goal state (i.e., x = __?_) and a clear set of operations (i.e., the rules of algebra and arithmetic).
An ill-structured problem does not have a clearly specified statement, goal, and/or set of allowable operators.
For example, “develop a research plan for a thesis” is an ill-structured problem for most students because the goal state is not clear (e.g., the requirements for the plan) and the allowable operators are not clear (e.g., the places where students may find information).
What makes a problem well-structured or ill-structured depends on the characteristics of the problem. Although most important and challenging problems in life are ill-defined, most problems solving in schools involves well-defined problems.
Routine and non-routine problems. (Not in B.Ed. syllabus)
When a problem solver knows how to go about solving a problem, the problem is routine. For example, two-column multiplication problems, such as 25 x 12 = ___, are routine for most high school students because they know the procedure.
When a problem solver does not initially know how to go about solving a problem, the problem is non-routine.
For example, the following problem is nonroutine for most high-school students: “If the area covered by water lilies in a lake doubles every 24 hours, and the entire lake is covered in 60 days, how long does it take to cover half the lake?”
What makes problems either routine or non-routine depends on the knowledge of the problem solver because the same problem can be routine for one person and non-routine for another.
The goal of education is to prepare students for solving all types of problems.