We have covered the different barriers that a person might face when trying to solve a problem. This Chapter covers the different strategies that can be used to solve problems. However, it is not limited just to these. There are many others methods. These methods are a few of the most common strategies that have been used in the process.
Problem solving strategies are those steps that are used to identify the problems that one faces while trying to achieve a goal. This is usually referred to as the ‘problem solving cycle’. The cycle usually begins with identifying the problem,followed by defining the problem – the goals; try to identify a strategy that could be used to decide on the problem, separate the relevant and irrelevant information and land on an accurate solution. This is called a problem solving cycle since problems keep arising. The minute you finish solving one problem, you have the next problem right before you. This problem solving cycle is explained in detail in Chapter 3.
The techniques given below are the strategies that are most commonly used while solving problems.
Abstraction
Abstraction is a technique where the actual problem is broken down into smaller problems. Each of these problems is first solved in order to find a solution to the bigger problem. These solutions are first tested on a system. If the solution works, it is applied to the real system. Another name for this technique is to divide and conquer. This technique was used by most armies while invading any country during the medieval period.
For instance, consider a mathematics problem on differentiation. The problem here is to identify whether the function provided is a maximum or a minimum function. For this, we have to find the first and second derivatives. Once we find the first and second derivatives, we can deduce whether or not the function is maximum or minimum. Here you have used abstraction to solve the problem. You have identified your set goal and divided the problem into smaller problems and used the solution obtained in those problems to solve the bigger problem.
BrainstormingBrainstorming is a perfect strategy to use when there is a group of people involved in solving the problem. This is a great technique since multiple methods to solving a problem come up during discussions. Each member of the group can see how the problem at hand can be solved. Based on their perspectives, they can provide solutions to the problem. These solutions can be combined and developed to form an accurate or optimum solution.
Hypothesis Testing
Hypothesis testing is a common statistical method where assumptions are made to explain the problem at hand. The method works towards proving the assumptions that have been made.
For example, we have to identify if there is a relation between smoking and lung cancer. The problem here is to identify the relationship. The assumption (hypothesis) made could be that there is no relationship between smoking and lung cancer. The alternative to this assumption (hypothesis) is that there is a relation. Since our main assumption is that there is no relation, we have to find certain techniques to prove whether this hypothesis is true or not. That way we will be able to identify a solution to the problem.
If there is no connection then we do not have to come up with further solutions. However, if the hypothesis is proved false, we have to identify certain solutions to reduce the effect of smoking on the lungs.
Lateral Thinking
Lateral thinking is thinking out of the box. The major barrier to this strategy is the mindset. One cannot think out of the box since he is used to a certain method of solving problems. Lateral thinking often obtains solutions which make the problem seem very obvious.
For example, the production of soap was supposed to be 2000 per hour. Over the last few days, the production dropped to 80 soaps an hour. Through the other strategies you try to identify ways to overcome this problem and increase the production rate. However, it is different in lateral thinking. The solution to the problem might state that there is no harm in a drop in production since this would mean that the quality of the soap has increased. This increase in quality would mean a greater number of sales implying a higher profit. This would in turn motivate the workers and the employees to do better!
Means End Analysis
In means end analysis you create sub goals in order to reach the final goal. You try to bridge the gap between the initial state and the final goal state. There are many examples to this method of problem solving that are very popular. One of the best examples is the ‘Towers of Hanoi’.
While using this strategy you have to identify the initial state and also your final goal. The initial state to this problem is represented by the first three disks of the tower being stacked in the order of the size of the disk on the first peg, also called the start peg. The goal is to represent these disks being stacked on the last peg, or the end peg, which is the third peg. This must be done in exactly the same order!
The rules to this problem are:
- You can only do this by moving one disk at a time.
- You can only move a disk that is on top of the stack
- You cannot put a bigger disk on top of a smaller disk.
Since we are using the technique of means end analysis, we will have to first create our sub goals. Below is one possible way of creating sub goals.
- Move the disks that are on the largest peg onto the second peg
- Move the biggest disk to the third peg
- Move the other disks onto the third peg as well.
This can be applied continuously in order to reduce the magnitude of the problem. You will finally come to a stage where you will only have to move one disk to reach your final goal. You can use this strategy to solve problems that you might face in your daily life as well – identify the correct train connection, correct road map to follow to go on a road trip. You will have to identify every aspect of your journey in order to reach your final goal. These small aspects of your journey are your sub goals.
Analogy
Analogies are another common strategy to solve problems. Here similar problems are viewed and solved. Using these solutions the problems that are being faced now can be solved. A recent study was conducted where a song that is stuck in your head was compared to an itch. You can only let go of the song or forget the song by singing it repeatedly. That solution is something similar to relieving yourself off an itch by repeatedly scratching yourself. This is also called restructuring.
The perfect example for this is the radiation problem that was stated by K. Duncker in the year 1945. When you have a patient with a tumor, you might have to use radiation in order to get rid of the tumor. This ray is harmless. But when the intensity of the ray increases, it kills the tumor inside the body but also harms the other healthy tissue that comes in its way. The problem here was to identify how to prevent the latter.
When the experiment was conducted on a certain number of subjects, they were asked to identify a solution to the same problem. They were stumped and could not identify a solution. The problem was then restructured. The subjects were told a story that went along these lines:
‘A General was looking at capturing his enemy’s fortress. He decided to launch an attack at the enemy. He had a large army and was confident of winning. Thenhe learned that every road that led to the fortress was rigged with mines. Only small groups of men could pass through those roads without setting the mines off. He then divided his men into smaller groups and then led the attack on the enemy’s fortress.’
Here the General was compared to as the source of the problem, the enemy’s fortress was compared to radiation, the fortress was compared to the tumor and the big army was compared to the ray. The solution that was obtained through this method was that the ray had to be subdivided into smaller rays which could then be sent in without harming the healthy tissue in its way. That way only the tumor would be harmed.
It was then stated that this strategy was a three step strategy:
Notice
You will have to try to identify or notice an analogical connection that might exist between the source of the problem and the target problem.
Map
Once you identify the problems, you will have to map the attributes in the analogous problem to the problem at hand.
Apply
You will have to then use the solution that was used in the source problem to solve the target problem.
Proof
In this strategy you have to be pessimistic in the beginning and state that the problem cannot be solved. You will then have to prove why this problem cannot be solved. The minute you reach the stage where you find that it is difficult to prove your assumption, you will have to begin solving the problem.
Reduction
Reduction is a combination of both Abstraction and Analogy. You will have to break the problem down through abstraction and by using analogy you will have to identify solutions to those smaller problems. Using these solutions, a consolidated solution is found for the bigger problem.
Trial and Error
Trial and error is one of the most common strategies that are used to solve problems. However, this is very tedious and might take a lot of time. Here you will have to try and use all the different solutions that you might find to solve a problem. You will have to see which solution worked best to solve the problem. You might not find the accurate solution in the first go. The barrier, mindset, might actually prove helpful in this situation. You can use all the solutions that you are used to in order to solve the problem at hand.
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