Problem Solving
We all solve problems on a daily basis, in academic situations, at work, and in our day-to-day lives. Any job will bring problems that must be faced. In order for you to make your boss’s job easy, it is important to have the right skills to resolve these problems, and the personal resilience to handle the challenges and pressure they may cause. To solve problems, you need to be able to1
• Evaluate information or situations
• Break them down into their key components
• Consider various ways of approaching and resolving them
• Decide on the most appropriate of these ways
Analytical and critical thinking skills help you to evaluate the problem and to make decisions.2 A logical and methodical approach is best in some circumstances: for example, you will need to be able to draw on your academic or subject knowledge to identify solutions of practical or technical nature. In other situations, using creativity or lateral thinking will be necessary to come up with ideas for resolving the problem and finding fresh approaches. To make your boss’s job easier, you will need skills such as communication, persuasion, and negotiation.
Here are some different ways to solve problems.
Whatever issues you are faced with, some steps are fundamental:3
• Identify the problem
• Define the problem
• Examine the options
• Act on a plan
• Look at the consequences
In order to learn to solve problems, there are many different roadmaps and guides to help you, but most of them have the following steps in common:4
1. Evaluate the problem by
• Clarifying the nature of a problem
• Formulating questions
• Gathering information systematically
• Collating and organizing data
• Condensing and summarizing information
• Defining the desired objective
2. Manage the problem by
• Using the information gathered effectively;
• Breaking down a problem into smaller, more manageable, parts;
• Using techniques such as brainstorming and lateral thinking to consider options;
• Analyzing these options in greater depth;
• Identifying steps that can be taken to achieve the objective.
3. Decision making
• Deciding between the possible options for what action to take.
• Deciding on further information to be gathered before taking action.
• Deciding on resources (time, funding, staff, etc.) to be allocated to this problem.
4. Resolve the problem by
• Implementing action;
• Providing information to other stakeholders;
• Delegating tasks;
• Reviewing progress.
• Monitoring the outcome of the action taken;
• Reviewing the problem and problem-solving process to avoid similar situations in the future.
At any stage of this process, it may be necessary to return to an earlier stage—for example, if additional problems arise or if the solution does not appear to be working as desired.
Here are some other ways to solve problems that may or may not be familiar to you:5
• Algorithm:6 An algorithm is a step-by-step procedure that will always produce a correct solution. A mathematical formula is a good example of a problem-solving algorithm. While an algorithm guarantees an accurate answer, it is not always the best approach to problem solving. This strategy is not practical for many situations because it can be so time-consuming. For example, if you were trying to figure out all of the possible number combinations to a lock using an algorithm, it would take a very long time.
• Heuristics:7 A heuristic is a mental rule-of-thumb strategy that may or may not work in certain situations. Unlike algorithms, heuristics does not always guarantee a correct solution. However, using this problem-solving strategy does allow people to simplify complex problems and reduce the total number of possible solutions to a more manageable set.
• Trial-and-error:8 A trial-and-error approach to problem solving involves trying a number of different solutions and ruling out those that do not work. This approach can be a good option if you have a very limited number of options available. If there are many different choices, you are better off narrowing down the possible options using another problem-solving technique before attempting trial-and- error.
• Insight:9 In some cases, the solution to a problem can appear as a sudden insight. According to researchers, insight can occur because you realize that the problem is similar to something that you have dealt with in the past, but in most cases, the underlying mental processes that lead to insight happen outside of awareness.
There are a number of different obstacles that can interfere with our ability to solve a problem quickly and efficiently. Researchers have described a number of these mental obstacles, which include functional fixedness, irrelevant information, and assumptions.10 Functional fixedness refers to the tendency to view problems only in their customary manner. Functional fixedness prevents people from fully seeing all of the different options that might be available to find a solution. When you are trying to solve a problem, it is important to distinguish between information that is relevant to the issue and irrelevant data that can lead to faulty solutions. When a problem is very complex, the easier it becomes to focus on misleading or irrelevant information. When dealing with a problem, people often make assumptions about the constraints and barriers that prevent certain solutions.
Another useful analogy for problem solving is to think of the problem as a maze.
To solve the problem, you need to travel from the starting point, called the initial state, to the endpoint, called the goal state. The initial state includes all of the knowledge and resources you currently have available. The goal state refers to the solution that you want to reach. To get from the initial state to the goal state, you have a number of tools you can use, called operators.
In a maze, these operators might be left turn and right turn. The set of possible ways to travel from the initial state to the goal state is called the problem space.
Generate and Test
The most obvious way to attempt to solve a problem is simply to mentally test every possible path leading from the initial state to the goal state. This imaginary process of trial and error, called the generate-and-test strategy, considers all possibilities available at every step. However, generate and test is not a realistic problem-solving method for most complex problems as there will be far more potential solutions than time will allow to test. Instead, we must rely on strategies that consider only a subset of the possibilities.
Hill-climbing Strategy
One strategy that can be used is the “hill-climbing strategy.” The hill-climbing strategy always moves you toward a solution. Imagine that you want to solve a maze using this strategy. At every fork, you would take the direction that leads toward the exit. However, there are problems with this strategy; the correct path sometimes does not follow this specific direction you think you are headed, and you miss the exit. This is also true of more complex problems, like the river-crossing type. For example:
Three missionaries and three cannibals want to get to the other side of the river. There is a small boat, which can fit only two. To prevent a tragedy, there can never be more cannibals than missionaries together.
One cannibal and one missionary there, missionary back.
Two cannibals there, one cannibal back.
Two missionaries there, one missionary and one cannibal back.
Two missionaries there, one cannibal back.
This one cannibal takes the remaining cannibals to the other side.
Subproblems Strategy
Another, more effective strategy is to break each problem down into a few subproblems. Evidence suggests that people work problems through this way. When working through complex problems, people often tend to work quickly at some points and pause at others. Analysis of their progress suggests that they work quickly when solving a subproblem, and work slowly when deciding what subproblem to tackle next. Smaller problems are easier to solve because there are fewer possible paths to consider.
Working Backwards
Some problems, especially unfamiliar ones, are best-solved by starting at the goal state and working backward toward the initial state. Many people solve mazes in this way, because there are fewer choices to consider in the end than in the beginning. This strategy, while not always helpful, can reduce the overwhelming number of paths available from the initial state.
Reasoning by Analogy
One method that works for many different types of problems is reasoning by analogy. In reasoning by analogy, the problem-solver uses his or her knowledge about previous, similar problems to find out the best way to solve the current one. The use of analogies hinges on familiarity since analogies are not helpful without some previous experience with similar problems. Analogies are simply patterns in the structures of problems. Because experts are more likely to see patterns in the structures of problems, as we saw in the section on expertise, they are best at reasoning by analogy. Novices tend to examine the superficial aspects of the problem, such as comparing two problems that are both about flowers, rather than the structural aspects of how the problem is set up, such as comparing two problems that both require subtraction.
Mental Imagery in Problem Solving
Mental imagery is often useful in problem solving. Verbal descriptions of problems can become confusing, and a mental image can clear away excessive detail to bring out important aspects of the problem. Imagery is most useful with problems that hinge on some spatial relationship. However, if the problem requires an unusual solution, mental imagery alone can be misleading, since it is difficult to change one’s understanding of a mental image. In many cases, it helps to draw a concrete picture since a picture can be turned around, played with, and reinterpreted, yielding new solutions in a way that a mental image cannot. There are many models for problem solving and many of them will require teamwork.