Theories of Problem Solving

What is Problem?

According to Killen (1996), problem can be defined as any situation where some information is known and other information is needed. It might be something that can gives any doubt situation or something that hard to understand, or difficult task or question, or it might be any given condition to investigate.

What is Problem Solving?

From the definition of problem above, it can be said that problem solving is considered as the process of applying existing knowledge to a new or unfamiliar situation in order to gain new knowledge Killen (1996). It is important for students to realize the knowledge that they have can be applied to the new situation and this will lead them to gain new knowledge.

Meanwhile, according to Mayer and Wittrock (2009), problem solving is achieving goals that involves cognitive processing when no solution method is obvious. Mayer and Wittrock (2009) also add some information to their definition that consist of four parts; (1) problem solving is cognitive, it means that, problem solving occurs within the students cognitive system, and their behavior, (2) problem solving is a process, it means that, problem solving involve applying students’ cognitive to the new situation to enrich their cognitive, (3) Problem solving is directed, it means that, problem solving is guided to reach some goals, (4) problem solving is personal, it means that problem solving depends on the knowledge and the skill of the students.

Types of Problem Solving

According to Mayer and Wittrock (2009) problems are categorized as ill-defined or well defined, based on how problem and goal are represented. A problem that having a clear single solution and can be solved by an algorithm are termed well defined, for example in arithmetic problems 3x = 2 (solve for x) or in crossword puzzle. A problem usually having multiple possible solutions; cannot be solved by an algorithm are termed ill-defined, for example writing a story.

Cognitive Processes in Problem Solving

According to Mayer and Wittrock (2006) there are four major cognitive processes in problem solving:

1) Representing - in which the problem solver constructs a cognitive representation of the problem.

2) Planning - in which the problem solver devises a plan for solving the problem.

3) Executing - in which the problem solver carries out the plan.

4) Self-regulating - in which the problem solver evaluates the effectiveness of cognitive processing during problem solving and adjusts accordingly.

Gastalt Theory of Problem Solving

This theory described by Duncer (1945) and Wetheimer (1959) in Mayer and Wittrock (2009), where problem solving occurs with a flash of insight. Insight means that when the students moves from state not knowing how to solve a problem to knowing how to solve problem. From this point the students will find out the way to solve the problem. In this situation, the students probably will build a schema, or visualize the information to solve the problem. The Insight also involve the students to create a new way that makes the problem easier to solve or quickly solve the problem that already knows how to solve.

Information Processing Theory of Problem Solving

This theory described by Newl and Simon (1972) in Mayer and Wittrock (2009), in which problem solving is carrying out a series of mental computations. It means that the problem that represented to the students should carrying a new idea for them to learn.

The Problem should be a Means

Problem solving as a teaching strategy should be viewed as the strategy that can enter every aspect of the curriculum, rather than seeing it as just a topic in the curriculum. Problem-based learning should give the students immediate effects on what students learn and also give long-term effects on the type of problems that the students can solve. When problem solving is used as a teaching strategy, the emphasis should be on the students learning about the subject, rather than simply learning to solve problem. This point is important to be considered because some students may just finding the answer rather than develop an understanding of the principle and concepts inside the problem. Therefore, students must learn how to solve problems in order to learn about the subject as well as when they work in small group. The choice of the problems also will have a very significant impact on what students can learn about your subject (Killen, 1996).

Advantages of Problem Solving as a Teaching Strategy

According to Killen (1996), when used effectively, problem solving has a number of advantages over direct instruction. The advantages as follows;

1) Problem solving provides a challenge for students, and they can derive great satisfaction from discovering new knowledge for themselves.

2) Problem solving engages students actively in learning.

3) Problem solving helps students to develop new knowledge for themselves and feel responsible for their own learning.

4) Problem solving teaches students that their solutions should be explainable and justifiable.

5) Problem solving can develop students'· critical thinking skills and their ability to adapt to new learning situations

Limitation of Using Problem Solving as a Teaching Strategy

1) Unless the problems are motivating, Students may see them simply as busywork.2) Unless students are interested and believe that they can solve the problem, they may

be reluctant to try.3) Appropriate problems take time to develop since each problem needs to be carefully

structured to produce specific students learning outcomes.4) Unless the students understand why they are attempting to solve a particular problem,

they may not learn what the teacher want them to learn.