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How to solve a problem

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We are going to address a few problem solving strategies and techniques before your Mid-term exam. Why before Mid-term? Because I do not want it to be: “نوش دارو بعد از مرگ سهراب” and too late.

Using the term “technique” sometimes seems to be inappropriate as these days you can find techniques for doing every thing, including those things that should be mostly as an art rather than the technique. However, I should emphasize that using the technique does not mean to be “plastic” or “artificial”, but rather, it means how to express yourself more correctly or how to express yourself more closer to what you really think or feel. Hence, the technique won’t give you more, but, it will help you to increase your efficiency. I mean if you never study, say fluid mechanics II, and you know all the techniques in the world in problem solving, and you are going to solve one of its problems, simply you cannot! Because the technique is like a pipe, but the water is nothing but your own ideas and knowledge. So, do not expect to do well in your exam if you just read this page and not studying enough.

To solve a problem, first of all you should organize your method of thinking. Hence, firstly, you should know what does “thinking” mean? According to early Muslim philosophers [1] thinking is a process which forms by departure from some known information to some desired or new information. Organized method of thinking is nothing but a logical method which is based on comparison. Hence, the result of your thinking is a correct result in a range of your problem if your departure from initial information to secondary information was a logical, organized, movement. Mathematically, if you can come back the same way, which you moved through in your initial movement, from results to initial information, then your method of thinking is an organized method and your result is correct if your initial information was correct.

Now that you know what “thinking” means, we address the meaning of a “problem”. The problem is the gap between the initial information and the desired information [2]. So, to solve the problem, you should fill this gap by your organized method of thinking.

Now is the time for addressing a few strategies for problem solving. These strategies include a few steps in solving problems. The first strategy we mention here is the strategy introduced by Polya [3]. He recommends four steps in problem solving, which are:

1)Defining the problem
2)Planning how to solve the problem
3)Performing the plan
4)Looking back

Fogler and LeBlanc [4] represent five steps in solving a problem:

1)Defining the problem
2)Producing different alternatives and plans
3)Deciding which plan should be carried out
4)Action
5)Evaluating the results

Woods [5] recommends the same strategy called McMaster strategy as follows:

1)Define
2)Explore
3)Plan
4)Act
5)Reflect

The Kepner-Tregoe [6] or KT strategy is formed by three steps:

1)Analysis of the problem
2)Decision procedure
3)Detecting potential future defects with the solution

What we mostly do in solving our problems is in the range of the first two steps of the KT strategy.

I remember once I have read that before doing any thing, think for 10 seconds. It is called “10-second” rule [7]. This is the idea behind of the “analysis of the problem”. Do not start executing your solution before reading carefully your problem. Start asking questions about the problem (who, what, where, when & why) and try to find the answers of those questions in the problem. Detect the initial information as “given information” and desired information as “results”. In fact see what the problem is giving you and what does it want? Then, write initial and desired information in mathematical order by getting help from abbreviations and mathematical symbols. Find the constraints of the problem, the condition which the problem is in it and consequently the rules, laws or principles which are able to describe the problem. Then, find the equations which can get you from “given information” to the desired “results”.

Till here, you know what the problem is and you have few plans to solve your problem. For the second step, you should decide which plan should get used to solve the problem. Consider the priorities and start acting by using the best plan. Is it possible that by your first try you get to no-where? Yes! So, in this stage you need to keep your confidence. The problem solver should have the positive attitude towards the problem. Simply, do not give up. Hence, if your try did not work, go for another plan and execute it. For the final step evaluate the results of your solution.

In solving engineering problems the following five steps should be taken:

1)Understand the problem and the goals
2)Formulate the options for solution
3)Consider the constraints
4)Perform the selected plan for solving the problem
5)Evaluate the procedure and results

References:

1)مرتضی مطهری، “آشنایی با علوم اسلامی، منطق، فلسفه”، انتشارات صدرا، 1358 هجری شمسی.
2)Frensch, P. A., and Funke, J., “Complex Problem Solving“, Hillsdale, Lawrence Erlbaum, 1995.
3)Polya, G., “How to Solve It“, 2nd edition, Doubleday, 1957.
4)Fogler, H. S., and LeBlanc, S. E., “Strategies for Creative Problem Solving“, Englewood, Prentice-Hall, 1994.
5)Woods, D. R., “Problem Based Learning: How to Get the Most from PBL. D. R. Woods“, McMaster University, Hamilton, 1994.
6)Kepner, C. H., and Tregoe, B. B., “The New Rational Manager“, Princeton, Princeton Research Press, 1981.
7)Pande, P. S., “The Six Sigma Leader“, McGraw-Hill, 2007.

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