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Problem Solving

Purpose

Problem solving is a critical skill that you will need in all aspects of your life. By building on your existing skills and creating a solid foundation in problem solving techniques, you will be on your way to successfully solving problems.

The phrase "problem solving" consists of very general concepts covering a wide range of different activities and ways to approach solving problems. Problem solving can be fun and intriguing! This tutorial will help you learn how to approach problem solving so you can maximize your college experience.

Goals and Objectives

The main goal of this tutorial is to introduce learners to the most important concept in any problem solving situation - identification of the true problem. Upon completing this tutorial, you will be able to:

• Define the concept of problem solving

• Describe the differences between puzzle problems, well-structured problems, and ill-structured problems

• Summarize the reasons why problem solving skills are valuable

• Explain the differences between the scientific method and problem solving

• Demonstrate how to determine the true problem in any problem solving situation

Activities

• Read the information about problem solving

• Complete Activity 1 - What is an Ill-structured Problem? to see if you understand what an ill-structured problem is

• Read the information about approaching and solving ill-structured problems

• Read the information about dealing with the real problem

• Complete Activity 2 - Determining the Real Problems to see if you can determine the real problem in different situations

• Read about Jose's father's problem and practice what you have learned about problem solving

Note: All external links in this tutorial will open in a new window or tab.

References

Summary

Instructor's Guide

Information about Problem Solving

Why is problem solving important to you?

Research methodology is used quite a bit to discover new things and test new ideas. Most research techniques use some kind of problem solving methodology. If you learn how to solve problems now, you will be able to approach many academic situations with the tools you need to handle them.

Today's businesses want employees who can adapt to new situations rapidly and effectively.

• The ideal employee is a master of basic skills such as reading, writing, and numeracy.

• The ideal employee is also a master of learning, communication, critical thinking, creative thinking, and problem solving.

• The ideal employee can respond to a problem quickly, correctly, and with little or no supervision.

If you can solve problems, you can write your own ticket to whatever job you want.

Defining Problem Solving

Problems can be classified into puzzle problems, well-structured problems, and ill-structured problems.

Puzzle Problems

Many games contain puzzle problems and are not "serious" in nature, nor is there any real-life consequence for failing to solve them.

Well-structured Problems

Some problems which are simple and well-defined are called well-structured problems and include a set number of possible solutions - solutions are either 100% right or 100% wrong. An example of a well-structured problem is a typical mathematical (2 + 2 = 4) question. This question has a definitive correct answer.

Ill-structured Problems

In contrast to well-structured problems are ill-structured problems. In these cases, problems may have many possible answers because they are complex and poorly defined. The "best" solutions to ill-defined problems depend on the priorities underlying the situation. What is "best" today may not be "best" tomorrow. Ill-structured problems, because they are more difficult to "solve," require the development of higher order thinking skills and the ability to construct a convincing argument for a particular solution as opposed to all other possible solutions.

To summarize ill-structured problems:

• They are complex and poorly defined.

• They have many possible answers.

• They do not have one best answer.

Here is an example of an ill-structured problem:

The population of your community is growing. Your water supply will not support many new people. What do you do?

This is a complex problem. It affects the people, the environment, and the quality of life itself. To arrive at a good solution, you need to use math, science, political science, psychology, and probably more!

This problem actually occurs frequently in areas with a growing population. In one community facing this problem, more than 20 possible solutions were presented to the public. A solution was then chosen upon which the majority of the public agreed. It wasn't the "right" solution because all of the 20 possible possible solutions had strengths and weaknesses.

The lesson here is that ill-structured problems usually have several workable solutions. Each solution has advantages and disadvantages that depend on who is affected by the solution. The solution chosen is often the one that has the best argument for it.

Activity 1: What Is an Ill-Structured Problem?

Check to see if you understand what an ill-structured problem is by completing the quiz below.

Approaching and Solving Ill-Structured Problems

Approaching Ill-Structured Problems

So, how do you go about solving an ill-structured problem? The best way to approach an ill-structured problem is to begin by gathering information. Here are some ideas of what to look for.

Define the Problem

• Whose problem is it (individual, group, or situation) and why?

• How do key people, those most involved, define the problem and how do they feel about it? Try to separate fact from opinion by distinguishing what people say from what they actually do.

List Why the Issue is a Problem

• Is there a gap between the actual situation and what is desirable?

• Are any standards violated?

• What would happen if the problem remained unsolved?

• Are there unintended consequences that could result from taking action to solve the problem?

List What Will Happen When the Problem is Solved

• What are the ideal outcomes?

• What are the actual outcomes? For example, has productivity improved; are people more satisfied?

• Does the statement of the problem define the actual cause of the problem, or is it just one of the symptoms?

Solving Ill-Structured Problems

To start figuring out how to solve an ill-structured problem, here are some steps you may want to follow. Consider the information you have gathered through your investigation as you determine what the real problem is and how best to solve it.

1. Gather information.
2. Determine the real problem.
3. State the real problem.
4. Identify alternative perspectives.
5. Determine constraints.
6. Generate possible solutions.
7. Choose the best solution.
8. Plan the steps for implementing the solution.
9. Adapt the solution.
10. Monitor the solution and make adjustments as needed.

Dealing with the Real Problem 

Identifying the real problem is the most important step because:

• a full understanding of the problem is crucial.

• symptoms must be differentiated from causes.

Why It's Important to Determine the Real Problem

First, in order to have a full understanding of the problem, you need to gather complete and accurate information. After defining the problem, more information is needed to confirm the cause of the problem. Sometimes what seems to be a problem is not really a problem at all.

For example, you tell your friend that you are always late for class because your alarm never goes off. Your friend may think the problem is that the alarm is broken or not working properly, when the truth is that you always forget to turn the alarm on before you go to bed. 

It is important to have a full understanding of the problem before you begin solving it.

Separating Symptoms from Causes

The most common problem in real-life problem solving is that we fail to identify the real problem and instead solve the wrong problem or a different problem. What we think is the real problem often isn't, it's just a symptom of the real problem.

Here is another example: guests on the upper floors of a hotel complain that the elevators are slow. It might seem logical to assume that the real problem is that the elevators are slow. But maybe it isn't. Can you guess what the hotel did to solve it?

Hotel management concluded that the real problem was that guests were concentrating on how long they had to wait for the elevators. They decided to install mirrors beside the elevator to take people's minds off the wait. Customer complaints ended after the mirrors were installed.

It is important to examine all possible causes of a problem before moving on to the next major step - solving the problem.

Activity 2: Determining the Real Problems

Complete the quiz below to see if you can determine the true problems in the given situations.

Juan's Problem

Jose's father, Juan, is a manager of a small department store. Juan has a problem. Recently, sales have dropped off. What are the first things Juan should do? Select as many answers as apply, and then compare what you have selected with the list below.

Compare your list to this one:

After Juan talked to other employees, other store owners, and reviewed the economic status of his customers, he made a list of reasons on possible effects. What should Juan include in his list? Choose all that apply, and then read the next section to see if your list agrees with Juan's:

Here's what Juan could include in his list:

Next, Juan decided to list what would happen when the problem was solved. Here is what Juan wrote. Which of these are appropriate explanations?

1. Sales are down this month.
2. Everyone is scared.
3. If this problem is solved, the store's projected sales for this month will meet or exceed the expected sales.
4. My boss will be so happy, I might get a raise for solving the problem!
5. Store employees will not have to worry about a layoff.
6. The store's projected sales will meet the expected sales, which were set by the store's owner.

Here are the explanations why Juan should include some phrases in his writing.

• Statement 1 is a statement of the problem, not what will happen if the problem is solved.
• Statement 2 is a general comment that really doesn't say what will happen when the problem is solved.
• Statement 3 is an ideal outcomes, and should included.
• Statement 4 is an outcome related to satisfaction and should be included.
• Statement 5 is an actual outcome of solving the problem, and should also be included.
• Statement 6 is an actual outcome of solving the problem, and should be included.

One thing Juan never thought to question was the expected sales figures for this month. What if they were unrealistic? Then the problem is not that sales were to low, but that the expectations were set too high. If that is true, then everything that Juan does to solve the problem will only address a symptom of the problem, not the problem itself.

Keep in mind that identification of the true problem is the most important step in problem solving.

After careful consideration, Juan decided to look at sales figures for the same month over the past five years. He found that sales were consistently lower for the same time period in the previous years. From this information, he determined that the figures for expected sales were incorrect and needed to be adjusted downward. After meeting with the store owner and presenting all of the relevant information, the owner agreed to adjust the figures.

References

Content

For additional information on problem solving, please consult the following references:

• Central Queensland University. (2002). Problem based learning for students. March 24, 2004. Retrieved from http://pbl.cqu.edu.au/content/studs.htm. *

• Education Office, Fermilab, IL. (1999). Tutorial on Problem-Based Learning. Retrieved November 09, 2012 from http://www-ed.fnal.gov/trc/tutorial/pbl.html.

• Health Sciences, Queen's University at Canada. (1991). Problem based learning home page, School of Medicine. Retrieved March 24, 2004 from http://meds.queensu.ca/medicine/pbl/pblhome.htm#contents. *

• Jonassen, D. H.(n.d.) Research problem solving. Retrieved March 24, 2004 from http://tiger.coe.missouri.edu/~jonassen/PB.htm. *

• Jonassen, D. H. (1997). Instructional Design Models for Well-Structured and Ill-Structured Problem-Solving Learning Outcomes. Educational Technology, Research & Development, 45(1).

• The Center for Problem-Based Learning (PBL), The Samford University. (1998). Problem based learning at Samford University. Retrieved March 24, 2004 from http://www.samford.edu/ctls/problem_based_learning.html.*

• U-Study, University of Saskatchewan. (2000). Traditional problem solving. Retrieved March 24, 2004 from http://internet.ggu.edu/university_library/critical/probsolv.html. *

• University of Delaware. (1999). Problem-Based Learning Clearinghouse. Retrieved June 6, 2017 from http://www1.udel.edu/inst/ .

* Indicates that the original Website is no longer available.

Image Credits

Process of Problem Solving

• Source: http://commons.wikimedia.org/wiki/

• File: Process_of_problem_solving.jpg

• This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.

Running Water

• Source: http://commons.wikimedia.org/wiki/

• File: Water_supply.jpg

• This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.

Summary

Three Types of Problems

• Puzzle
• Well-structured
• Ill-structured

Solving problems is an important survival skill in today's information society where we must deal with a complex, technologically advanced world. There are many different kinds of problems to be identified and solved. They exist in a variety of forms within your major or your chosen future profession including, of course, mathematics, psychology, and the physical sciences, as well as the arts and humanities.

Advantages of Having Good Problem-solving Skills

Therefore, potential advantages of having good problem solving skills include:

• Your problem solving skills will be valuable throughout your life.

• Effective problem solving skills will help you find jobs you want.

• Effective problem solving skills will help you approach many academic situations with the tools you need to handle them.

Instructor's Guide

Quizzes, Reflective Questions, and Activities

The following are the assignments embedded in the Problem Solving tutorial:

• Activity 1: What Is an Ill-Structured Problem?

• Activity 2: Determining the Real Problem

Relationship to Other iStudy Tutorials

This activity is the first step in most research methodologies. A typical research methodology can be described as:

• Identification of the Problem

• Data Collection

• Data Analysis

• Report Writing

• Review, Revision, and Publication of Findings

Therefore, it is recommended that instructors introduce this tutorial to students prior to any tutorials that deal with data collection and analysis, report writing, or the review, revision, and publication process.

Suggested In-Class Methods of Presentation

Lecture

• Explain the purpose of the session. Refer to the Purpose section for more detail.

• Explain general information about problem solving, including well-defined problems, ill-defined problems, and why problem solving is an important skill.

Discussion

• Provide examples of ill-structured problems. Instructors should provide several examples and invite students to cite some examples as well.

• Explain that determining the true problem is the most important step in problem solving.

• Break the students up into small (four-five person) groups. Provide each group with a problem, such as a current social issue. Each group should work with the provided problem to create a probable problem statement, listing why it is the problem and what will happen when the problem is solved as showed in Key Points listed below.

• Each group should present its findings to the class and be prepared to discuss them. Instructors can assess students' understanding of identification of the true problem at this point by observing how each group presents its findings and responds to questioning.

• OPTIONAL - Have students look in your local or college newspaper for examples of problems faced by students, the community, the state, the nation, or the world. Have them identify the true problem or problems.

Note : This is an excellent opportunity to utilize and reinforce the cooperative learning techniques from the Cooperative Learning tutorial.

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Key Points

These points are covered in the iStudy module, but should be emphasized in any discussions.

• Steps in a problem solving process.

• Identifying the real problem.

• Separating symptoms from causes.

• Defining and analyzing the problem.

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Assessment Criteria

Through observing both the group's and the individual's activities, the instructor may assess student performance. Assessment criteria are as follows (instructors supply the percentage weights):

Instructor's Guide

Quizzes, Reflective Questions, and Activities

The following are the assignments embedded in the Problem Solving tutorial:

• Activity 1: What is an ill-structured problem?

• Activity 2: Determining the true problems

Relationship to Other iStudy Tutorials

This activity is the first step in most research methodologies. A typical research methodology can be described as:

• Identification of the Problem

• Data Collection

• Data Analysis

• Report Writing

• Review, Revision, and Publication of Findings

Therefore, it is recommended that instructors introduce this tutorial to students prior to any tutorials that deal with data collection and analysis, report writing, or the review, revision, and publication process.

Suggested In-class Methods of Presentation

Lecture

• Explain the purpose of the session. Refer to the Purpose section for more detail.

• Explain general information about the problem solving, including well-defined problem, ill-defined problems, and why problem solving is an important skill.

Discussion

• Provide examples of ill-structured problems. Instructors should provide several examples, and invite students to cite some examples as well.

• Explain that determining the true problem is the most important step in problem solving.

• Break the students up into small (four-five people) groups. Provide each group with a problem, perhaps a current social issue. Each group should work with the provided problem to create a probable problem statement, listing why it is a problem and what will happen when the problem is solved as showed in Key Points listed below.

• Each group should present its findings to the class and be prepared to discuss them. Instructors can assess students' understanding of identification of the true problem at this point by observing how each group presents its findings and responds to questioning.

• OPTIONAL - Have students look in your local or college newspaper for examples of problems faced by students, the community, the state, the nation, or the world. Have them identify the true problem or problems.

Note : This is an excellent opportunity to utilize and reinforce the cooperative learning techniques from the Cooperative Learning tutorial.

[top of page]

Key Points

These points are covered in the iStudy module, but should be emphasized in any discussions.

• Steps in a problem-solving process.

• Identifying the true problem.

• Separate symptoms from causes.

• Define and analyze the problem.

[top of page]

Assessment Criteria

Through observing both the group's and the individual's activities, the instructor may assess student performance. Assessment criteria are as follows (instructors supply the percentage weights):