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## What is Problem Solving?

We come across a number of problems every day. Some of these problems are minor whereas others are major ones. Some problems are easy to solve and while others require great effort and time to solve and still some are unsolvable. A problem may be defined as any conflict or difference between one situation to other situations that is, our goal. Problem-solving refers to transforming one situation into another to meet a goal.

The main aim of problem-solving thinking is to move from the current unsatisfactory state to a state in which the problem is solved. A thinker in a problematic situation is goal-directed and motivated by the need to reduce the discrepancy between one state of affairs to another. The problem which we must solve differs along several dimensions, some are well defined and have much information while others have minimum knowledge.

Long-term memory and observation of the situation can aid in problem-solving. When we recognize a similar problem was solved in the past, the information from the memory system can be retrieved and applied to the solution of the current problem. If the problem is new and there no solution in the long-term memory we can use several strategies to deal with the problem.

## Methods of Problem Solving

When problems are difficult to solve different strategies are used by the problem-solving thinkers such as algorithm, heuristic, trial and error, and insight.

### Algorithm

The algorithm is a step-by-step procedure that guarantees a solution if followed correctly. In an algorithm, if particular rules are followed it is solved in time if a solution exists. If you are given numbers to multiply, the correct application of the multiplication table from the past learning help in solving the problem. For example, length multiplied by width gives the area enclosed by the rectangle.

### Heuristic

When algorithms are inapplicable to solve complex problems we follow a much more effective problem-solving technique known as heuristics. Heuristics often provide useful shortcuts. They are rules of thumb. Heuristics breaks the problem down into smaller sub-problems and increase the probability of the solution but do not guarantee the solution of the problem. Heuristic makes more efficient use of time, provides a quick solution, or may not provide any solution.

Heuristics guide our cognition involving strategies that our past experience suggests but that may or may not be applicable at the present, so the solution is not guaranteed. Human beings try to solve problems more by using heuristic than algorithms. Because algorithms require much more cognitive capacity, knowledge of the subject, and effort which most of us do not possess.

Problems like the nine-dot problem require the thinker to connect them by drawing four continuous straight lines without lifting pen and palm from the paper. Similarly, the match stick problem needs the thinker to assemble all six matches to form four equilateral triangles, each side should be equal to the length of one match.

For there solution, continue to read.

### Trail and Error

Trial and error involve trying different possible solutions one after another until one works. Trial and error is not a cognitive strategy. It is the simplest problem-solving approach commonly used by people. It is like a hit-miss or gains approach, which may be instantly solved the problem or take much time. It does guarantee that solution will be discovered. Trial and error are used by people who do not have much information about the problem to adopt a more systematic, standard step to solve the problem.

### Insight

Sometimes we are unaware of using any problem-solving strategy. We feel puzzled over a problem for some time and stay away from it. Then, suddenly the sudden flashes of inspiration hit us and the problem seems organized and solved. This is called insight. Human beings gain a sense of satisfaction when solved problems through insight.

We feel happy after solving a difficult problem or discovering how to resolve a conflict. Take an example of insight, a thirsty crow seeing the water level beyond reach, drops small pebbles into the jar to raise the water level, and quenched its thirst.

Solutions of the earlier mentioned problems.

The **nine-dot problem** is solved by going outside of the square frame into which dots are perceptually groped. The lines have to be extended beyond the dots as shown. Most participants fail to hit on this solution because of the preoccupied mental set.

In **six matchstick problems**, need to arrange six matches into four equilateral triangles, the matches have to be assembled into the three-dimensional pyramid.

## Steps in Problem Solving

Life is a series of problems. Solving a problem needs clear steps to follow. Certain definite steps help in smooth solutions to the problems. Psychologists have developed certain steps to solve problems. However, they are not totally in agreement on this basic issue but they believe and compromise on the major aspects. Different six major steps are found to be relevant to resolve a problem.

### Identification of the Problem

The first step of problem-solving explains issues, obstacles, and goals related to the problem. It should be clearly specified. The tools and techniques and the needed operation to be finalized.

### Formulation of Potential Solution

This step describes different alternatives to be drawn for possible solutions. The alternatives need to be critically examined. The information stored in long-term memory and other sources may help to generate possible alternatives solutions.

### Evaluating the Alternatives

It describes each alternative to be judged with its outcomes, eliminating poor choices, reducing error, saving time and effort, enhancing closer to the goal.

### Examining the Consequences of each of the Alternatives

Explains every alternative is analyzed on the basis of outcomes it draws. The one that has more positive valences are chosen while choices which have more negative results are neglected or eliminated.

### Implement the Potential Solution

Illustrates after evaluating the pros and cons effect of the solutions, it is time for making strategies or plans to put them into action. If it does not guarantee a solution a careful assessment of the effects of various other solutions is to be done.

### Implement the Solution

This the last step in problem-solving. It involves selecting the best solution, examining it with implementing perspective, and applying it to action.

Also, consider the problem-solving steps suggested by the Lahey 1995, p321,

## Steps in Solving Problem

### 1. What is the problem?

- Define the problem in clear, specific terms.
- Avoid mental sets and try to think about the problem in flexible ways.

### 2. Generate all possible solutions

- At first, do not judge any solution.
- Wild ideas are welcome.
- See if some of your possible solutions can be combined to make a better possible solution.

### 3. Now, eliminate any possible solutions that are clearly poor choices

- An alternative with no chance of success should be dropped.
- Intuitive (without conscious thought or judgment) solutions based on heuristic reasoning should be eliminated in situations where logical reasoning is possible.

### 4. Examine the likely consequences of the remaining possible solutions one at a time

- List all possible negative consequences of this option.
- List all possible positive consequences of this option.
- Eliminate the option if it is more likely to produce negative than positive consequences.
- Compare all remaining options in terms of likely consequences.
- Select the solution with the greatest likelihood of more positive consequences than negative consequences.

### 5. Generate all possible ways to implement the solution you have chosen

- Use steps 2-4 to select the best way to implement the solution.

### 6. Implement the solution

- Implement the best option.