Problem Soving Strategy

What is Problem Solving?


Problem-solving is a tool, a skill, and a process. As a tool is helps you solve a problem or achieve a goal. As a skill you can use it repeatedly throughout your life. And, as a process it involves a number of steps.


Purpose of Problem Solving Strategy


The purpose of Problem Solving Strategy are as follows:
  1. to help students think about a problem without applying their own pre-conceived ideas.
  2. defining what the problem looks like is separated from looking at the cause of the problem to prevent premature judgment.
  3. clarifying what makes an acceptable solution is defined before solutions are generated, preventing preconceptions from driving solutions.
  4. to help student understand complex ethical dilemmas, think about the future or do some strategic planning in classroom.

Principles of Problem Solving Strategy

George Polya (1887 – 1985) was one of the most famous mathematics educators of the 20th century (so famous that you probably never even heard of him).  Dr. Polya strongly believed that the skill of problem solving could and should be taught – it is not something that you are born with.  He identifies four principles that form the basis for any serious attempt at problem solving:

  1. Understand the problem
  2. Devise a plan
  3. Carry out the plan
  4. Look back (reflect)

1. Understand the problem
  • What are you asked to find out or show?
  • Can you draw a picture or diagram to help you understand the problem?
  • Can you restate the problem in your own words?
  • Can you work out some numerical examples that would help make the problem more clear?
2.  Devise a plan
A partial list of Problem Solving Strategies include:
  • Guess and check 
  • Solve a simpler problem                     
  • Make an organized list                 
  • Experiment
  • Draw a picture or diagram           
  • Act it out
  • Look for a pattern                        
  • Work backwards
  • Make a table                                
  • Use deduction
  • Use a variable                             
  • Change your point of view
3.  Carry out the plan
  • Carrying out the plan is usually easier than devising the plan
  • Be patient – most problems are not solved quickly nor on the first attempt
  • If a plan does not work immediately, be persistent
  • Do not let yourself get discouraged
  • If one strategy isn’t working, try a different one
4.  Look back (reflect)
  • Does your answer make sense?  Did you answer all of the questions?
  • What did you learn by doing this?
  • Could you have done this problem another way – maybe even an easier way?

Elements of a Problem

1. Understanding the problem
2. Describe any barriess
3. Identify various solutions
  •  Create visual images
  • Guesstimate
  • Create a table
  • Use manipulatives
  • Work backward
  • Look for a pattern
  • Create a systematic list
4. Try out a solution
  • Keep accurate and up-to-date records of their thoughts, proceedings, and procedures.
  • Try to work through a selected strategy or combination of strategies until it becomes evident thta it's not working, it needs to be modified, or it is yielding inappriate data.
  • Monitor with great care the steps undertaken as part of a solution.
  • Feel comfortable putting a problem aside for a period of time and tackling it at a later time.
5. Evaluate the results




Procedural Steps of Problem Solving Strategy


Step 1 - Problem Definition

Before you are ready to take any steps to solve the problem, you first have to be sure that you are clear about what the problem really is. It can be easy to get distracted by solving a different problem than what is actually causing distress if it is easier than dealing with the real problem. This step involves thinking about the following questions:
  • How is the current situation different from what I actually want it to be?
  • What do I actually want, or how do I actually want things to be?
  • What is preventing me from achieving my goals, or from things being the way I want them to be?
It can be very helpful to write down the answers to these questions so that you are forced to clarify that the problem you are defining is the actual one you want to solve. Just thinking about things in your head can cause confusion and end up distracting you from the actual problem at hand.

If you are dealing with more than one problem at a time, it may be helpful to prioritize them. That way you can focus on each one individually, and give them all the attention they require.


Step 2 – Problem Analysis

Once you have defined the problem, you need to think about it from different perspectives to insure that you understand all the dimensions of the problem.

The following questions can be useful to help you analyze the problem.
  • How is this problem affecting me?
  • How is this problem affecting other people?
  • Who else is experiencing this problem?
  • How do other people deal with this problem?
After you have completed this step, check to make sure that your definition of the problem still fits. It is not unusual at this point to find that the problem you really want to solve is different than the one you initially identified.
Step 3 –  Establish your Goals

Once you have looked at the problem from different perspectives, you can decide what you want to achieve and establish your goals.


You need to answer the very specific question:
  • What is my immediate goal?
Examples:
  • Improve my time management skills
  • Complete assignments on time
  • Enhance my thinking

Step 4 – Generate possible Solutions


During this stage the goal is to generate as many possible solutions as you can. Do not worry about whether or not they are realistic, practical, or effective. Frequently a solution you might eliminate initially, with work can be developed into a very effective solution.

It can be very helpful to ask yourself what you have done in the past when faced with similar problems, and how other people you know have dealt with similar situations. In addition, you can also approach friends, family, a counselor, teachers, books, or the internet, etc. to obtain ideas for solutions. Be sure to write down all the possibilities you generate so that you can approach this task systematically.


Step 5 – Analyze the Solution

During this stage, you will examine each alternative and write down both the advantages and disadvantages to each. Some considerations to keep in mind include:
  • Is it relevant to my situation?
  • Is it realistic?
  • Is it manageable?
  • What are the consequences – both good and bad?
  • What is the likelihood that it is going to help me reach my goal?


Step 6 - Implementation


The last step is to implement the solution you have chosen. This step involves identification of all the steps necessary to implement it, and also on-going monitoring of the effectiveness of the solution to make sure that it actually solved the problem. During this stage of the process, ask yourself the following questions:
  • How effective is the solution?
  • Did it achieve what I wanted?
  • What consequences (good and bad) did it have in my situation?
If the solution was successful in helping you solve your problem, then you can feel satisfied with your efforts and what you learned. If you feel dissatisfied in some way, you can either modify the solution to work better, or you can scrap it and turn to other alternative solutions, or begin the process again.


Remember that problem-solving is a cycle – it involves searching for a solution to a problem that will lead to various possible solutions which then need to be evaluated. If the problem is solved, then you have found an effective solution. If the problem has not been solved, then you start the process again.


Group Member:
    1. Amit Rai
    2. Bikram Limboo
    3. Deki Choden
    4. Kinzang Choden
    5. Prem B. Limboo
Reference:

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